Table of contents

This is the second time that the Modern Practice in Stress and Vibration Analysis conference has come to the University of Glasgow and it is with great pleasure that I write this preface for the event in 2012. The remit of the Modern Practice in Stress and Vibration Analysis conferences is relatively broad and encompasses scientific and technological research in stress analysis, the mechanics of materials, applied dynamics, metrology and instrumentation, system identification, structural health monitoring, nondestructive evaluation, and vibration theory and analysis. Within these relatively traditional subject areas we also see burgeoning new themes emerging, in which new manufacturing technologies, energy harvesting, micro and nano-mechanic applications, biomechanics, and advanced modelling feature very strongly. The conference converges around six keynote addresses over the three days, each one being linked to a central theme for the conference. The first day opens on the morning of Wednesday 29 August 2012 with an address by Professor Walter Lacarbonara of the University of Rome on 'Nonlinear dynamics enabled design and control', in which ideas taken from nonlinear dynamics and once considered to be highly specialised are now informing the design and control of mechanical systems. This is followed by an afternoon address by Professor James R Barber of the University of Michigan on the topic of 'Frictional systems under periodic load – History-dependence, non-uniqueness, and energy dissipation', where fundamental mechanical issues are considered in the performance of loaded mechanical systems in which complicated friction mechanisms play an important role. The second day begins with a morning lecture by Professor Fabrice Pierron of Paris Tech entitled 'A novel photomechanical approach to dynamic testing of materials', and covering the testing of materials, an important theme which has long been central to this conference series. This is followed by the British Society of Strain Measurement's sponsored Measurements Lecture, which also features as the fourth keynote address of the conference, and is given in 2012 by Dr Cathy Holt of the University of Cardiff. The third and final day of the conference opens with a keynote lecture by Professor Wieslaw M Ostachowicz of the Polish Academy of Sciences in Gdansk on another long-standing conference theme, and entitled 'Structural health monitoring by means of elastic wave propagation'. The final keynote lecture takes place in the afternoon of the last day and is given by Professor Jerzy Warminski of the Technical University of Lublin, Poland. The title of the lecture is 'Nonlinear phenomena in mechanical systems dynamics', and is in deliberate juxtaposition to the opening keynote address, emphasising the pervasive nature of modern nonlinear dynamics.

I am delighted to welcome authors and delegates to this Modern Practice in Stress and Vibration conference, run under the auspices of the Institute of Physics Applied Mechanics Group and held at the University of Glasgow. I would like to thank Claire Garland and Dawn Stewart of the Institute of Physics for all their work and assistance, the local organising committee, the scientific committee, and lastly the authors of the papers featured in this conference proceedings. I extend my warmest welcome to all our conference delegates.

Matthew Phillip Cartmell Conference Organiser

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

There is a growing interest towards design of high-performance structures and devices by seeking ways to exploit advantageously different nonlinearities at different scales rather than constraining operations to avoid nonlinear phenomena. Tools of robust nonlinear modeling and analysis are shown to be turned into design tools for achieving high levels of vibration control authority and synthesis of engineered systems and materials. A brief overview of methods and results on active resonance cancellation and passive nonlinear hysteretic vibration absorbers is illustrated. Recent results on the diffused hysteresis exhibited at the nano-microscale in nanocomposites due to the powerful nonlinear stick-slip mechanism exhibited by carbon nanotubes dispersed in a hosting matrix are discussed. The optimization of the main microstructural parameters is shown to lead to unprecedented levels of damping capacity in next-generation nanostructured materials tailored for wide-band vibrational energy dissipation.

Nominally static contacts such as bolted or shrink-fit joints typically experience regions of microslip when subjected to oscillatory loading. This results in energy dissipation, reflected as apparent hysteretic damping of the system, and also may cause the initiation of fretting fatigue cracks. Early theoretical studies of the Hertzian contact problem by Cattaneo and Mindlin were confirmed experimentally by Johnson, who identified signs of fretting damage in the slip annulus predicted by the theory.

For many years, tribologists assumed that Melan's theorem in plasticity could be extended to frictional systems — i.e. that if there exists a state of residual stress associated with frictional slip that is sufficient to prevent periodic slip in the steady state, then the system will shake down, regardless of the initial condition. However, we now know that this is true only if there is no coupling between the normal and tangential loading problems, as will be the case notably when contact occurs on a symmetry plane.

For all other cases, periodic loading scenarios can be devised such that shakedown occurs for some initial conditions and not for others. The initial condition here might be determined by the assembly protocol — e.g. the order in which a set of bolts is tightened — or by the exact loading path before the steady cycle is attained. This non-uniqueness of the steady state persists at load amplitudes above the shakedown limit, in which case there is always some dissipation, but the dissipation per cycle (and hence both the effective damping and the susceptibility to fretting damage) depends on the initial conditions. This implies that fretting fatigue experiments need to follow a well-defined assembly protocol if reproducible results are to be obtained. We shall also present results showing that when both normal and tangential forces vary in time, the energy dissipation is very sensitive to the relative phase of the oscillatory components, being greatest when they are out of phase.

With sufficient clamping force, 'complete' contacts (i.e. those in which the contact area is independent of the normal load) can theoretically be prevented from slipping, but on the microscale, all contacts are incomplete because of surface roughness and some microslip is inevitable. In this case, the local energy dissipation density can be estimated from relatively coarse-scale roughness models, based on a solution of the corresponding 'full stick' problem.

This paper presents numerical and experimental approach for damage detection in structures. Presented methods are based on the phenomenon of elastic wave propagation. The results are provided for isotropic and anisotropic plates with damage in form of fixed mass or notch cut.

The goal of the paper is to present selected, untypical, and intuitively unexpected phenomena from nonlinear mechanics. Particular attention is paid to the dynamics of self-, parametric and external excited systems. Interactions between these various vibration types lead mainly to quasi-periodic responses. However, in the selected domains of system parameters, the effect of frequency locking is observed. Furthermore, external harmonic force imposed on such a system produces a specific internal loop inside a resonance zone. As an example of nonlinear autoparametric systems, a structure (oscillator) with an attached pendulum is presented. The nonlinear terms introduced by pendulum motion cause instabilities in the resonance region. This instability transits the pendulum to rotation or chaotic motion. An application of nonlinear couplings for the reduction of unwanted vibrations is also studied. In order to reduce vibrations, the main structure is coupled to an electrical oscillator by a quadratic term. It has been shown that such a coupling leads to the amplitude saturation phenomenon which can then be used to design a nonlinear control strategy.

In this article we study a two-degrees-of-freedom model of a rotor system with a bearing clearance. During operation the rotor makes intermittent contact with an outer snubber ring, which results in complex dynamical behaviour. Specifically, the system will be analyzed numerically by a path following method, where we will use the toolbox TC-HAT, which is a module for modeling non-smooth systems by AUTO 97.

Linear modal analysis of L-shaped beam structures indicates that there are two independent motions, these are in-plane bending and out of plane motions including bending and torsion. Natural frequencies of the structure can be determined by finding the roots of two transcendental equations which correspond to in-plane and out-of-plane motions. Due to the complexity of the equations of motion the natural frequencies cannot be determined explicitly. In this article we nondimensionalise the equations of motion in the space and time domains, and then we solve the transcendental equations for selected values of the L-shaped beam parameters in order to determine their natural frequencies. We use a numerical continuation scheme to perform the parametric solutions of the considered transcendental equations. Using plots of the solutions we can determine the natural frequencies for a specific L-shape beam configuration.

This paper proposes a vibration analysis for an isotropic plate containing an arbitrarily orientated surface crack as an enhancement to previous work on cracked plates for which the orientation of the crack angle was not included. The governing equation of motion of the plate with this enhanced crack modelling represents the vibrational response based on classical plate theory into which a developed crack model has been assimilated. The formulation of the angled crack is based on a simplified line-spring model and the cracked plate is subjected to transverse harmonic excitation with arbitrarily chosen boundary conditions. It is found that the vibrational characteristics of the plate structure can be affected significantly by the orientation of the crack in the surface plate. For reasons of comparison and validation a finite element model is used for a further modal analysis in order to corroborate the effect of crack length and crack orientation angle on the modal parameters i.e. the natural frequency and also the vibrational amplitude, as predicted by the analysis. The results show excellent agreement between the two methods.

In this study, finite element analysis of beam on elastic foundation, which received great attention of researchers due to its wide applications in engineering, is performed for estimating dynamic responses of shallow foundation using exact stiffness matrix. First, element stiffness matrix based on the closed solution of beam on elastic foundation is derived. Then, we performed static finite element analysis included exact stiffness matrix numerically, comparing results from the analysis with some exact analysis solutions well known for verification. Finally, dynamic finite element analysis is performed for a shallow foundation structure under rectangular pulse loading using trapezoidal method. The dynamic analysis results exist in the reasonable range comparing solution of single degree of freedom problem under a similar condition. The results show that finite element analysis using exact stiffness matrix is evaluated as a good tool of estimating the dynamic response of structures on elastic foundation.

The work presented is devoted to the investigation of a state-of-the-art technological solution for the design of a crush-can characterized by optimal energy absorbing properties. The work is focused on the theoretical background of the square tubes, circular tubes and inverbucktube performance under impact with the purpose of design of a novel optimized structure. The main system under consideration is based on the patent US 2008/0185851 A1 and includes a base flange with elongated crush boxes and back straps for stabilization of the crush boxes with the purpose of improvement of the energy-absorbing functionality. The modelling of this system is carried out applying both a theoretical approach and finite element analysis concentrating on the energy absorbing abilities of the crumple zones. The optimization process is validated under dynamic and quasi-static loading conditions whilst considering various modes of deformation and stress distribution along the tubular components. Energy absorbing behaviour of the crush-cans is studied concentrating on their geometrical properties and their diamond or concertina modes of deformation. Moreover, structures made of different materials, steel, aluminium and polymer composites are considered for the material effect analysis and optimization through their combination. Optimization of the crush-can behaviour is done within the limits of the frontal impact scenario with the purpose of improvement of the structural performance in the Euro NCAP tests.

This study investigates the vibration characteristics of a proposed candidate structure for smarter car bodies. The material is conceived as a three-layer laminated structure in the form of a trimorph plate. The vibration response of the plate is investigated for large deflections by considering the effects of geometric nonlinearity. First, the governing equation for the mid-point deflection of the plate is developed based on classical laminate plate theory (CLPT). The governing equation is solved, and a simulation is run for different possible layer-stacking sequences. Comparisons are made between the nonlinear vibration response of this trimorph plate both with and without the effects of the von Kármán geometric nonlinearity. The results show that for the same material properties the different layer-stacking sequences produce different vibration responses, and from there it is concluded that layer-stacking sequencing is a basis for the definition of a suitable material configuration for high performance automotive applications.

The finite strain longitudinal free vibration of a rod is studied. Utilizing second Piola-Kirchhoff stress and Green strain tensors, the equation of motion is written in terms of displacement in reference configuration. Three different types of homogenous boundary conditions may be considered for the rod, leading to three nonlinear eigenvalue problems. The series solutions with three terms satisfying the boundary conditions are utilized and the relationships between amplitudes of vibration are obtained by means of the Galerkin method. The backbone curves are drawn and the internal resonance between different modes of vibration is analyzed.

In this paper, a model of the milling process of fibre reinforced composite material is shown. This classical one degree of freedom model of the milling process is adjusted for composite materials by variable specific cutting forces, which describe the fibre resistance. The stability lobe diagrams are determined numerically. Additionally, to eliminate the chatter vibration, small relative oscillations between the workpiece and the tool are introduced. Basing on numerical simulations the range of amplitude and the frequency of excitation is found for chatter reduction.

Several difficulties are faced in joining thinner sheets of similar and dissimilar materials from fusion welding processes such as resistance welding and laser welding. Ultrasonic metal welding overcomes many of these difficulties by using high frequency vibration and applied pressure to create a solid-state weld. Ultrasonic metal welding is an effective technique in joining small components, such as in wire bonding, but is also capable of joining thicker sheet, depending on the control of welding conditions. This study presents the design, characterisation and test of a lateral-drive ultrasonic metal welding device. The ultrasonic welding horn is modelled using finite element analysis and its vibration behaviour is characterised experimentally to ensure ultrasonic energy is delivered to the weld coupon. The welding stack and fixtures are then designed and mounted on a test machine to allow a series of experiments to be conducted for various welding and ultrasonic parameters. Weld strength is subsequently analysed using tensile-shear tests. Control of the vibration amplitude profile through the weld cycle is used to enhance weld strength and quality, providing an opportunity to reduce part marking. Optical microscopic examination and scanning electron microscopy (SEM) were employed to investigate the weld quality. The results show how the weld quality is particularly sensitive to the combination of clamping force and vibration amplitude of the welding tip.

Carbon fiber reinforced polymer composite (CFRP) laminates are attractive for many applications in the aerospace industry especially as aircraft structural components due to their superior properties. Usually drilling is an important final machining process for components made of composite laminates. In drilling of CFRP, it is an imperative task to determine the maximum critical thrust forces that trigger inter-laminar and intra-laminar damage modes owing to highly anisotropic fibrous media; and negotiate integrity of composite structures. In this paper, a 3D finite element (FE) model of drilling in CFRP composite laminate is developed, which accurately takes into account the dynamic characteristics involved in the process along with the accurate geometrical considerations. A user defined material model is developed to account for accurate though thickness response of composite laminates. The average critical thrust forces and torques obtained using FE analysis, for a set of machining parameters are found to be in good agreement with the experimental results from literature.

Carbon fabric-reinforced polymer (CFRP) composites used in sports products can be exposed to different in-service conditions such as large dynamic bending deformations caused by impact loading. Composite materials subjected to such loads demonstrate various damage modes such as matrix cracking, delamination and, ultimately, fabric fracture. Damage evolution in these materials affects both their in-service properties and performance that can deteriorate with time. These processes need adequate means of analysis and investigation, the major approaches being experimental characterisation and non-destructive examination of internal damage in composite laminates. This research deals with a deformation behaviour and damage in woven composite laminates due to low-velocity dynamic out-of-plane bending. Experimental tests are carried out to characterise the behaviour of such laminates under large-deflection dynamic bending in un-notched specimens in Izod tests using a Resil Impactor. A series of low-velocity impact tests is carried out at various levels of impact energy to assess the energy absorbed and force-time response of CFRP laminates. X-ray micro computed tomography (micro-CT) is used to investigate material damage modes in the impacted specimens. X-ray tomographs revealed that through-thickness matrix cracking, inter-ply delamination and intra-ply delamination, such as tow debonding and fabric fracture, were the prominent damage modes.

Titanium alloys are widely used in the aerospace and offshore industries due to their high strength-to-weight ratio sustained at elevated temperatures, their fracture-resistance features and exceptionally good corrosion-resistance properties. However, poor thermal conductivity and high chemical affinity of these alloys to tool materials severely impair their machinability. As a result the machining processes of titanium alloys are typically characterized by low cutting feeds and speeds making production of components uneconomical.

Recently, a non-conventional hybrid machining technique, namely, ultrasonically assisted turning has been shown to significantly improve the machinability of intractable alloys with a concomitant improvement in material removal rates, thus improving machining economics. In the current work, a 3D finite element model of turning of Ti-6Al-2Sn-4Zr-6Mo is developed in the commercial software, MSC Marc/Mentat. A constitutive behaviour of the workpiece material under large deformations and elevated temperatures is adequately represented by a Johnson-Cook material model. For validation of the developed numerical model, experimental tests were carried out. The numerical and experimental results were found to be in good agreement.

The finite element (FE) method has been extensively used to model complex cutting processes. However, due to large strains in a process zone, leading to increased element distortions, such simulations are confronted with numerical difficulties. Smooth-particle hydrodynamics (SPH) is a mesh-free computational method, which has been used to simulate multi-body problems. In this paper we present a 3D hybrid modelling approach for orthogonal micro-machining of a copper single crystal with the use of SPH and continuum FE. The model is implemented in a commercial FE software ABAQUS/Explicit. The study is used to gain insight into the effects of crystallographic anisotropy on the machining response of f.c.c. cubic metals.

Mechanical properties of nonwovens related to damage such as failure stress and strain at that stress depend on deformation and damage characteristics of their constituent fibres. Damage of polypropylene-fibre commercial low-density thermally bonded nonwovens in tension was analysed with tensile tests on single fibres, extracted from nonwovens bonded at optimal manufacturing parameters and attached to individual bond points at both ends. The same tests were performed on raw polypropylene fibres that were used in manufacturing of the analysed nonwovens to study quantitatively the effect of manufacturing parameters on tenacity of fibres. Those tests were performed with a wide range of strain rates. It was found that the fibres break at their weakest point, i.e. bond edge, in optimally bonded nonwovens. Additionally, failure stress and strain in tension of a fibre extracted from the fabric were significantly lower than those of virgin fibre. Since damage in nonwovens occurs by progressive failure of fibres, those experiments were used to establish criteria for damage initiation and propagation in thermally bonded nonwovens based on polypropylene fibres. Moreover, the results obtained from the experiments are useful to simulate the damage behaviour of nonwoven fabrics.

Ultrasonically assisted drilling (UAD) is a non-traditional hybrid machining process, which combines features of conventional drilling and vibratory machining techniques to obtain remarkable improvements in machinability of advanced materials. The experiments are conducted on commercially available samples of a carbon fibre-reinforced plastic (CFRP) at a feed rate of 16 mm/min. In this study, a thrust force reduction in excess of 60% is observed in UAD when compared to conventional drilling (CD). Lower delamination was observed when compared to CD techniques. Optical microscopy revealed that the material is removed as a continuous chip in UAD whereas in case of CD we observe powdered dust. Light and scanning electron microscopy of CFRP chips obtained in drilling elucidate fundamental differences in the underlying machining processes in UAD of CFRP.

The recently developed Wavelet Finite Element Method (WFEM) involves combining the versatile wavelet analysis with conventional Finite Element Method (FEM) by utilizing the wavelet and scaling functions as interpolating functions, providing an alternative to the conventional polynomial interpolation functions used in FEM. In this paper, the B-Spline Wavelet on bounded Interval (BSWI) wavelets are utilized in the construction of the wavelet based finite elements for the dynamic analysis of a Vierendeel frame structure subjected to a moving load. The numerical results for these WFEM formulations are compared with the classical Euler Bernoulli elements.

In the presented research the dynamics of a thin rotating composite beam with surface bonded MFC actuator are considered. A parametric analysis aimed at finding the most efficient location of the actuator on the beam is presented. Gyroscopic effects resulting in the beam's initial strain and therefore non-zero voltage in PZT are taken into account. Within the frame of the study maximising the system's response observed in vibration modes for uncoupled and coupled motions is examined. The results are compared to the case of a nonrotating beam and also to the maximum response of the beam with the actuator placed at different positions. To perform the analysis an ABAQUS finite element model of an electromechanical system under consideration is developed. The multi-layer composite beam structure is modelled by shell elements according to a layup-ply technique; the MFC actuator is modelled by 3D coupled field piezoelectric elements. Both modal analysis and frequency response spectra are performed to obtain the structural modal parameters and response amplitude, respectively. The analysis is repeated for three different orientations of the beam's cross-section with respect to the plane of rotation (i.e. arbitrary assumed pitch angles); in all cases the condition constant angular speed is preserved. This work is fundamental for continuing the research for control of dynamics of rotating composite beams with active elements.

The aim of the present work is to carry out a simplified mathematical modelling for nonlinear stress analysis of plates under temperature changes and mechanical transverse loads. The material properties of the plate are proposed to be temperature-dependent. The geometrically nonlinear plate theory is employed to understand the stress distribution due to thermo-mechanical loads. A set of coupled nonlinear partial differential equations are solved using harmonic series expansion to find the static responses. Two boundary conditions are considered for simply supported plates, namely, movable edges and immovable edges. The accuracy of the results is checked by comparing with the output of other solution methods.

The concept of harvesting electrical energy from ambient vibration sources has been a popular topic of research in recent years. Recently, the realisation that the majority of ambient vibration sources are often stochastic in nature has led to a large body of work which has focused on the response of energy harvesters to random excitations – most of which approximate environmental excitations as being Gaussian white noise. Of particular interest here are recent findings which demonstrate the advantages that Duffing-type nonlinearities can introduce into energy harvesters. The aim of this paper is to identify how well these results can be applied to that of a real energy harvesting scenario. More specifically, the response of an energy harvester to excitation via human motion is studied using digital simulations in conjunction with acceleration data obtained from a human participant. As well as assessing whether Duffing-type nonlinearities can have a beneficial impact on device performance this paper aims to investigate whether Gaussian white noise can indeed be used as a good approximation for this particular ambient vibration source.

Potential applications for stochastic resonance have developed strongly in recent years. This paper presents a study of an application of stochastic resonance in a mechanical system. Since a linear system cannot normally exhibit stochastic resonance, a cantilever beam with an end magnet was used to constitute a bistable nonlinear oscillator. Excited by ambient random vibration, the elastic beam undergoes a modulation of the potential well by means of a periodic excitation and flips between bistable states as a result of this. By adjusting the distance between the end magnet and a fixed magnet it is possible to drive the system controllably between bistable states. An electromagnet was used to provide the periodical parametric excitation which can result in stochastic resonance. The conditions for the occurrence of stochastic resonance are also discussed in the paper. Furthermore, simulations and experimental studies have been implemented to illustrate the application. The experimental results prove that stochastic resonance can occur, and that it can be usefully applied in such a mechanical system under specific conditions.

Recent research into damage detection methodologies, embedded sensors, wireless data transmission and energy harvesting in aerospace environments has meant that autonomous structural health monitoring (SHM) systems are becoming a real possibility. The most promising system would utilise wireless sensor nodes that are able to make decisions on damage and communicate this wirelessly to a central base station. Although such a system shows great potential and both passive and active monitoring techniques exist for detecting damage in structures, powering such wireless sensors nodes poses a problem. Two such energy sources that could be harvested in abundance on an aircraft are vibration and thermal gradients. Piezoelectric transducers mounted to the surface of a structure can be utilised to generate power from a dynamic strain whilst thermoelectric generators (TEG) can be used to generate power from thermal gradients. This paper reports on the viability of these two energy sources for powering a wireless SHM system from vibrations ranging from 20 to 400Hz and thermal gradients up to 50°C. Investigations showed that using a single vibrational energy harvester raw power levels of up to 1mW could be generated. Further numerical modelling demonstrated that by optimising the position and orientation of the vibrational harvester greater levels of power could be achieved. However using commercial TEGs average power levels over a flight period between 5 to 30mW could be generated. Both of these energy harvesting techniques show a great potential in powering current wireless SHM systems where depending on the complexity the power requirements range from 1 to 180mW.

The ability of a granular medium to dissipate vibrational energy is studied at different frequencies and amplitudes. The filler comprises relatively large particles with significant viscoelasticity and is placed in a rectangular box-shaped container and vibrated perpendicular to the direction of gravity. The performance of a model based on wave behaviour that is suitable for very low amplitude vibrations is compared with discrete elements and experimental results. Frequency dependent behaviour for the viscoelastic material is taken into account. The effects of vibration amplitude on performance are considered carefully – especially at the point where particles begin to move relative to each other. One interesting finding is that internal and interface loss mechanisms are closely interrelated – reduction in internal loss increases the mobility of individual particles and therefore more energy dissipation via friction. As a result, the overall effectiveness of the granular medium is less sensitive to material and configurationally parameters than might be expected.

Porosity and inclusion of foreign material is known to reduce the strength of materials, and this paper addresses the particular problem of strength knock-down assessment due to porosity in composite materials. Porosity is often measured in terms of percentage of voids per unit volume of a component, because this can be related directly to ultra-sound absorption. Nevertheless, this is a poor indicator of actual strength knock-down, as it provides little information about void size, shape, orientation and whether they are evenly distributed or are clustered. Characterisation of void clustering enables a link between a cluster characteristic and the strength knock-down. Laboratory based testing achieves controlled porosity in specimens by introducing pin-holes into the RTM in-flow pipework, which entrains voids into the body of the preform within mould tooling. Specimens are manufactured to create resin regions bounded by a fibre reinforced picture frame, to allow for easy load application. Strength knock-downs from test are related to the theoretical expectations.

MEMS resonators offer attractive prospects in several application areas, including high-performance, low cost sensors, among several others. The performance of many resonant MEMS depends critically on the Q factor, and an important, poorly quantified contribution to the overall Q is the support loss. Additionally, the parameter space for the geometry can be of moderately high dimension, making FEA based parametric optimisation computationally inefficient. Thus motivated, a numerical method based on the Rayleigh-Ritz substructure synthesis using quasicomparison functions is developed, applicable to a wide and important class of beam resonators. It is shown to be highly efficient by comparison with classical FEA methods, facilitating a detailed examination of the support Q as a function of position in parameter space. Selected results are presented and briefly discussed, with particular attention given to convergence, computational efficiency and design optimisation. General design principles for multiply-supported framelike beam resonators are considered in the light of the results, and extensions to the modelling are briefly covered.

The Orthogonalised Reverse Path (ORP) method is a new algorithm of the 'reverse path' class but developed in the time-domain. Like the Conditioned Reverse Path (CRP) method, the ORP approach is capable of identifying the underlying linear FRF of a system or structure in the presence of nonlinearities and may well also lead to simplifications in the estimation of coefficients of nonlinear terms. The method has shown itself to be numerically robust not only for simple simulated SDOF systems but also for simulated MDOF systems. The aim of this paper is to discuss an application of the ORP method to an experimental test set-up based on a nonlinear beam rig.

This study explores the possibilities for inverse analysis and modelling from data of a nonlinearly vibrating structure. We are suggesting a statistical approach based on singular spectrum analysis (SSA). The method is based on a free decay response, when the structure is given an initial disturbance and is left to vibrate on its own. The measured vibration response is decomposed into new variables, the principal components, which are used to uncover oscillatory patterns in the structural response. In this study an application of the methodology for the purposes of delamination detection in a composite beam is explored.

The breakdown of the principle of reciprocity is a well-known phenomenon of nonlinear systems. A structure or system is said to exhibit reciprocity when the response at some point j to an input at some point i is identical to the response at point i when the same input is applied at point j. This paper seeks to explain this phenomenon by adopting a functional series representation which describes the input-output relationship. The frequency-domain Volterra Series representation utilises Higher-Order Frequency Response Functions (HFRFs) (generalisations of the linear FRF) to explain the behaviour of nonlinear systems. This breakdown in reciprocity may be observed through a breakdown in symmetry of HFRFs.

Measurement of dynamic displacement is one of the most essential aspects of a structural behavior because it portrays history of the global behavior of structure. In general, structural engineers are accepted these response as reliable physical quantities to evaluate the conditions of a structure. The reason is that these physical quantities can easily generate strain as well as stress, velocity and acceleration at the measuring points. However, it is difficult to directly measure the displacement of the bridge due to problems such as test conditions and the limitations of equipment. Therefore, in this study, an artificial neural network (ANN) demonstrates how it could overcome such limitations and utilize the random dynamic load to obtain the reliable estimations. Numerical analysis is conducted to obtain learning data about the axial strain as well as vertical displacement with time frame at multi-points and then applied to the ANN. The scenario centered on a variety of dynamic loads from the analysis of an urban bridge that was selected based on its general volume of traffic. The analysis was performed to estimate its displacement, which corresponds to the strain on the bridge caused by arbitrary loads of leaning results from the ANN. Then, it is confirmed that the estimated displacements of ANN show well agreements with that of an independent set of traffic scenario.

This study suggests a novel non-model-based method for structural vibration-based health monitoring for composite laminated beams which utilises only the first natural frequency of the beam in order to detect and localise delamination. The method is based on the application of a static force in different positions along the beam. It is shown that the application of a static force on a damaged beam induces forces that push the delaminated layers together resulting in an increase of stiffness to a maximum when the static force is applied on the top and the middle of the delamination area. This stiffness increase in turn causes changes in the structural natural frequencies. The method does not require the frequency of the beam in its baseline condition. A very simple procedure for damage detection is suggested which uses a static force applied at only three points along the beam to detect and localise delamination. The method is numerically validated for a simply supported beam, using a finite element model of the beam. Our results show that the frequency variation with the change of the force application point can be used to detect, localize and in the same time quantify very precisely single delamination.

Damage evolution and mechanisms of deformation have been investigated in the 3rd generation AA2050 aluminium alloy.This Al-Li-Cu alloy is characterised by the presence of second-phase particles which are preferred sites for damage nucleation. Digital Image Correlation (DIC) and high resolution microscopy have been used to establish a correlation between strain distribution and particles/voids volume fraction along the gauge length of tensile specimens. Results show that damage nucleates at about 11% applied strain with a strain to fracture of about 35%.

In this work, the non-contact full-field Digital Image Correlation (DIC) technique has been utilized for measuring and analyzing the contact behaviour of soft materials undergoing large deformation. A vulcanized silicone rubber in contact with a wedge-shaped rigid indenter was investigated. In order to provide confidence in the measured results from the DIC system, an in-plane strain calibration procedure was conducted. Further, a procedure of out-of-plane displacement calibration was also deduced basing on the law of propagation of uncertainty.

This paper is concerned with active vibration reduction of a square isotropic plate, mounted rigidly along one edge to form a cantilever. Optimal placement of ten piezoelectric sensor/actuator pairs is investigated using a genetic algorithm to suppress the first six modes of vibration. A new objective function is developed based on modified H_infinity to locate the sensor/actuator pairs. The plate, with piezoelectric sensor/actuator pairs bonded to its surfaces, is modelled using the finite element method and Hamilton's principle based on first order shear deformation theory including bending, membrane, and shear deformation effects. The effects of piezoelectric mass, stiffness and electromechanical coupling are taken into account. The first six natural frequencies are validated by comparison with the finite element ANSYS package using two dimensional SHELL63 and three dimensional SOLID45 elements and also experimentally. Vibration reduction for the cantilever plate with piezoelectric patches bonded in the optimal location was investigated to attenuate the first six modes of vibration using a linear optimal control scheme. The new fitness function has reduced the computational cost and given greater vibration reduction than other previously published results.

This paper presents a nonlinear mathematical model and numerical results concerning the nonstationary lateral dynamic behaviour of long low tension slender continua deployed and moving at speed in high-rise vertical transportation systems installed in tall structures. The analysis presented in this study involves the identification of conditions for internal lateral resonances that can readily arise in the system when the slowly varying frequencies approach the fundamental or higher frequencies of the structure. The passage through the fundamental resonance leads to dangerously large displacements in the plane of the excitation. Due to the nonlinear (cubic) coupling, interactions between the in-plane modes and the out-of-plane modes occur. These interactions are studied numerically in order to predict and to examine the non-planar motions that may arise due to the autoparametric resonances. In order to suppress the internal resonance interactions higher speed levels and /or cable tension levels should be applied. Alternatively, an active tension control algorithm can be considered.

The present study aims at numerically investigating the feasibility of an adaptive TMD control system applied on lightweight, flexible structures characterized by time-varying inertial properties. The case study will consist of a photovoltaic support structure subject to snow drifting and slippage in windy conditions.

The optimal placement of sensors and actuators in active vibration control is limited by the number of candidates in the search space. The search space of a small structure discretized to one hundred elements for optimising the location of ten actuators gives 1.73 × 10¹³ possible solutions, one of which is the global optimum. In this work, a new quarter and half chromosome technique based on symmetry is developed, by which the search space for optimisation of sensor/actuator locations in active vibration control of flexible structures may be greatly reduced. The technique is applied to the optimisation for eight and ten actuators located on a 500×500mm square plate, in which the search space is reduced by up to 99.99%. This technique helps for updating genetic algorithm program by updating natural frequencies and mode shapes in each generation to find the global optimal solution in a greatly reduced number of generations. An isotropic plate with piezoelectric sensor/actuator pairs bonded to its surface was investigated using the finite element method and Hamilton's principle based on first order shear deformation theory. The placement and feedback gain of ten and eight sensor/actuator pairs was optimised for a cantilever and clamped-clamped plate to attenuate the first six modes of vibration, using minimization of linear quadratic index as an objective function.

The purpose of this study is to investigate the effectiveness of structural control using tuned mass damper (TMD) for suppressing excessive traffic induced vibration of high performance steel bridge. The study considered 1-span steel plate girder bridge and bridge-vehicle interaction using HS-24 truck model. A numerical model of steel plate girder, traffic load, and TMD is constructed and time history analysis is performed using commercial structural analysis program ABAQUS 6.10. Results from analyses show that high performance steel bridge has dynamic serviceability problem, compared to relatively low performance steel bridge. Therefore, the structural control using TMD is implemented in order to alleviate dynamic serviceability problems. TMD is applied to the bridge with high performance steel and then vertical vibration due to dynamic behavior is assessed again. In consequent, by using TMD, it is confirmed that the residual amplitude is appreciably reduced by 85% in steady-state vibration. Moreover, vibration serviceability assessment using 'Reiher-Meister Curve' is also remarkably improved. As a result, this paper provides the guideline for economical design of I-girder using high performance steel and evaluates the effectiveness of structural control using TMD, simultaneously.

An application of the Macro Fiber Composite (MFC) actuators for damping of a composite beam is presented in this paper. The effectiveness of vibration reduction by a selected control method is tested for vertical and horizontal position of the beam. The original model has been studied numerically by using Galerkin's discretisation method. The numerical results for the vertical and horizontal beams are compared.

Additive manufacturing (AM) is increasingly becoming a viable manufacturing process due to dramatic advantages that it facilitates in the area of design complexity. This paper investigates the potential of additively manufactured lattice structures for the application of tailored impact absorption specifically for conformal body protection. It explores lattice cell types based on foam microstructures and assesses their suitability for impact absorption. The effect of varying the cell strut edge design is also investigated. The implications of scaling these cells up for AM are discussed as well as the design issues regarding the handling of geometric complexity and the requirement for body conformity. The suitability of AM materials for this application is also discussed.

Advanced polymer materials are finding an increasing range of industrial and defence applications. Ultra-high molecular weight polymers (UHMWPE) are already used in lightweight body armour because of their good impact resistance with light weight. However, a broader use of such materials is limited by the complexity of the manufacturing processes and the lack of experimental data on their behaviour and failure evolution under high-strain rate loading conditions. The current study deals with an investigation of the internal heat generation during tensile of UHMWPE. A 3D finite element (FE) model of the tensile test is developed and validated the with experimental work. An elastic-plastic material model is used with adiabatic heat generation. The temperature and stresses obtained with FE analysis are found to be in a good agreement with the experimental results. The model can be used as a simple and cost effective tool to predict the thermo-mechanical behaviour of UHMWPE part under various loading conditions.

This work is devoted to the investigation of performance of surgical tools used in orthopaedics in terms of the occurrence of signs of necrosis, the accuracy of the cut and cutting tool design. For the comparison of the surgical tool performance different types of cutting devices were studied in a series of experiments. A Victorian surgical saw, its copy, a contemporary surgical saw, a surgical scalpel and an ultrasonic blade designed for a surgical application were chosen for the performance assessment. Such geometrical parameters as cutting edge shape, angle of teeth inclination, and sharpness of the cutting tools were analysed in terms of the quality of the cut and signs of necrosis. As a result of the analysis of experimental data obtained and theoretical insight the authors have come up with a creative solution for a novel design for a surgical ultrasonic blade which benefits from the design advantages of each of the analysed surgical tools and eliminates their drawbacks.

Bones form protective and load-bearing framework of the body. Therefore, their structural integrity is vital for the quality of life. Unfortunately, bones can only sustain a load until a certain limit, beyond which they fail. Therefore, it is essential to study their mechanical and fracture behaviours in order to get an in-depth understanding of the origins of its fracture resistance that, in turn, can assist diagnosis and prevention of bone's trauma. This can be achieved by studying mechanical properties of bone, such as its fracture toughness. Generally, most of bone fractures occur for long bones that consist mostly of cortical bone. Therefore, in this study, only a cortical bone tissue was studied. Since this tissue has an anisotropic behaviour and possesses hierarchical and complex structure, in this paper, an experimental analysis for the fracture toughness of cortical bone tissue is presented in terms of J-integral. The data was obtained using single-edge-notch bending (SENB) cortical specimens of bone tested in a three-point bending setup. Variability of values of fracture toughness was investigated by testing specimens cut from different cortex positions of bovine femur called anterior, posterior, medial, and lateral. In addition, anisotropy ratios of fracture toughness were considered by examining specimens cut from three different orientations: longitudinal, transverse and radial. Moreover, in order to link cortical bone fracture mechanisms with its underlying microstructure, fracture surfaces of specimens from different cortices and along different orientations were studied. Experimental results of this study provide a clear understanding of both variability and anisotropy of cortical bone tissue with regard to its fracture toughness.

One of the most fundamental problems in Structural Health Monitoring (SHM) is that of projecting out operational and environmental variations from measured feature data. The reason for this is that algorithms used for SHM to detect changes in structural condition should not raise alarms if the structure of interest changes because of benign operational or environmental variations. This is sometimes called the data normalisation problem. Many solutions to this problem have been proposed over the years, but a new approach that uses cointegration, a concept from the field of econometrics, appears to provide a very promising solution. The theory of cointegration is mathematically complex and its use is based on the holding of a number of assumptions on the time series to which it is applied. An interesting observation that has emerged from its applications to SHM data is that the approach works very well even though the aforementioned assumptions do not hold in general. The objective of the current paper is to discuss how the cointegration assumptions break down individually in the context of SHM and to explain why this does not invalidate the application of the algorithm.

The remarkable evolution of new generation wind turbines has led to a dramatic increase of wind turbine blade size. In turn, a reliable structural health monitoring (SHM) system will be a key factor for the successful implementation of such systems. Detection of damage at an early stage is a crucial issue as blade failure would be a catastrophic result for the entire wind turbine. In this study the SHM analysis will be based on experimental measurements of Frequency Response Functions (FRFs) extracted by using an input/output acquisition technique under a fatigue loading of a 9m CX-100 blade at the National Renewable Energy Laboratory (NREL) and National Wind Technology Center (NWTC) performed in the Los Alamos National Laboratory. The blade was harmonically excited at its first natural frequency using a Universal Resonant Excitation (UREX) system. For analysis, the Auto-Associative Neural Network (AANN) is a non-parametric method where a set of damage sensitive features gathered from the measured structure are used to train a network that acts as a novelty detector. This traditionally has a highly complex "bottleneck" structure with five layers in the AANN. In the current paper, a new attempt is also exploited based on an AANN with one hidden layer in order to reduce the theoretical and computational difficulties. Damage detection of composite bodies of blades is a "grand challenge" due to varying aerodynamic and gravitational loads and environmental conditions. A study of the noise tolerant capability of the AANN which is associated to its generalisation capacity is addressed. It will be shown that vibration response data combined with AANNs is a robust and powerful tool, offering novelty detection even when operational and environmental variations are present. The AANN is a method which has not yet been widely used in the structural health monitoring of composite blades.

An evaluation method for estimating the damping of loosely supported single U-bend tube used in a steam generator colliding with a support plate is proposed. First, we performed experimental modal analysis and obtained natural frequencies, modes and damping without collision by Impulse Modal Test and then analysed natural frequencies, modes and damping with collision employing FEM analysis taking account of the collision force. In modelling the characteristics of the collision force, we applied Bijlaard's model for the spring constant and assumed hysteresis. After that, we performed experiments for measuring the damping ratio by changing the gap size and the support plate position. Comparison between calculated and experimental results is made which shows good agreement. Experimentally observed fact showing damping coefficient increases with the initial amplitude is well explained by theoretical model.

Macro-fibre composite (MFC) sensors, originally developed as actuators by NASA, have been investigated for three components of a damage detection system for composite structures; actuation, sensing and energy harvesting. MFC sensors are constructed from piezoelectric fibres embedded in an epoxy matrix and offer greater flexibility than traditional sensors for embedding due to their low profile and low weight. It is proposed that embedded MFCs could be used to act as damage detectors, whilst energy either transmitted ultrasonically or harvested ambiently could be used to power the system. To assess the applicability of the MFCs a scale A320 composite wing was manufactured. Ten MFC sensors were embedded within the wing structure. Through a series of investigations on the wing the use of MFCs as part of an acousto-ultrasonic (AU) and Acoustic Emission (AE) damage detection system were investigated. Utilising AE source location and an AU cross-correlation techniques damage induced by impact was identified. In a further experiment the capability of transmitting and harvesting energy with the same embedded MFC actuators was completed. By impedance matching it was possible to improve the transmitted power. Furthermore an analysis of the MFCs ability to capture ambient vibrations, associated with aircraft structures, was completed. The completed experimental work demonstrated that it would be possible to embed sensors, energise them through active or passive vibration, and detect damage.

The development of diagnostic methods for gear tooth faults in aerospace power transmission systems is an active research area being driven largely by the interests of military organisations or large aerospace organisations. In aerospace applications, the potential results of gear failure are serious, ranging from increased asset downtime to, at worst, catastrophic failure with life-threatening consequences. New monitoring techniques which can identify the onset of failure at earlier stages are in demand. Acoustic Emission (AE) is the most sensitive condition monitoring tool and is a passive technique that detects the stress wave emitted by a structure as cracks propagate. In this study a gear test rig that allows the fatigue loading of an individual gear tooth was utilised. The rig allows a full AE analysis of damage signatures in gear teeth without the presence of constant background noise due to rotational and frictional sources. Furthermore this approach allows validation of AE results using crack gauges or strain gauges. Utilising a new approach to AE monitoring a sensor was mounted on the gear and used to continuously capture AE data for a complete fatigue load cycle of data, rather than the traditional approach where discrete signals are captured on a threshold basis. Data was captured every 10th load cycle for the duration of the test. A developed fast fourier transform analysis technique was compared with traditional analytical methods. In this investigation the developed techniques were validated against visual inspection and were shown to be far superior to the traditional approach.

This paper presents the non-linear investigations carried out on a scaled model of a two-span masonry arch bridge. The model has been built in order to study the effect of the central pile settlement due to riverbank erosion. Progressive damage was induced in several steps by applying increasing settlements at the central pier. For each settlement step, harmonic shaker tests were conducted under different excitation levels, this allowing for the non-linear identification of the progressively damaged system. The shaker tests have been performed at resonance with the modal frequency of the structure, which were determined from a previous linear identification. Estimated non-linearity parameters, which result from the systematic application of restoring force based identification algorithms, can corroborate models to be used in the reassessment of existing structures. The method used for non-linear identification allows monitoring the evolution of non-linear parameters or indicators which can be used in damage and safety assessment.

Nonlinear normal modes (NNMs) are a generalization of the linear normal vibrations. By the Kauderer-Rosenberg concept in the regime of the NNM all position coordinates are single-values functions of some selected position coordinate. By the Shaw-Pierre concept, the NNM is such a regime when all generalized coordinates and velocities are univalent functions of a couple of dominant (active) phase variables. The NNMs approach is used in some applied problems. In particular, the Kauderer-Rosenberg NNMs are analyzed in the dynamics of some pendulum systems. The NNMs of forced vibrations are investigated in a rotor system with an isotropic-elastic shaft. A combination of the Shaw-Pierre NNMs and the Rauscher method is used to construct the forced NNMs and the frequency responses in the rotor dynamics.

This paper describes an analytical method for the wave field induced by a moving load on a periodically supported beam. The Green's function for an Euler beam without support is evaluated by using the direct integration. Afterwards, it introduces the supports into the model established by using the superposition principle which states that the response from all the sleeper points and from the external point force add up linearly to give a total response. The periodicity of the supports is described by Bloch's theorem. The homogeneous system thus obtained represents a linear differential equation which governs rail response. It is initially solved in the homogeneous case, and it admits a no null solution if its determinant is null, this permits the establishment the dispersion equation to Bloch waves and wave bands. The Bloch waves and dispersion curves contain all the physics of the dynamic problem and the wave field induced by a dynamic load applied to the system is finally obtained by decomposition into Bloch waves, similarly to the usual decomposition into dynamic modes on a finite structure. The method is applied to obtain the field induced by a load moving at constant velocity on a thin beam supported by periodic elastic supports.

The paper deals with certain problems related to static and modal analysis of isotropic shell structures by the use of the approach known in the literature as the time-domain spectral finite element method. Although recently this spectral approach has been widely reported as a very powerful numerical tool used to solve various wave propagation problems, its properties make it very well suited to solve static and modal problems. The robustness and effectiveness of the spectral approach has been successfully demonstrated by the authors in the case of a thin-walled spherical shell structure representing a pressure vessel. Static and modal responses of the structure have been investigated by the use of transversally deformable shell-type spectral finite elements and the results of this investigation have been compared to known analytical solutions as well as those obtained by the use of commercially available software for the finite element method.

This study is concerned with autoparametric interaction in a four degree of freedom damped mechanical system consisting of two identical pendula fitted onto a horizontal massive rod which can oscillate vertically and rotationally. One pendulum is harmonically excited. The equations of motion indicate that autoparametric interaction is possible by means of typical external and internal resonance conditions involving the system natural frequencies and excitation frequency. An intriguing phenomenon is demonstrated when the unforced pendulum is decoupled and no energy goes into it, as a result of which it stops oscillating. Numerical simulations are carried out to determine when and why this phenomenon occurs for a different excitation magnitude as well as for zero and non-zero initial conditions of the unforced pendulum.

This paper deals with a system involving a flexible rod subjected to magnetic forces that can bend it while simultaneously subjected to external excitations produces complex and nonlinear dynamic behavior, which may present different types of solutions for its different movement-related responses. This fact motivated us to analyze such a mechanical system based on modeling and numerical simulation involving both, integer order calculus (IOC) and fractional order calculus (FOC) approaches. The time responses, pseudo phase portraits and Fourier spectra have been presented. The results obtained can be used as a source for conduct experiments in order to obtain more realistic and more accurate results about fractional-order models when compared to the integer-order models.

This paper describes a three dimensional wing model, which has been developed for the purpose of studying flutter, both computationally and through wind tunnel testing. A three dimensional, laminar flow aerofoil wing, based on the NACA aerofoil has been designed. The natural frequencies for this aerofoil were obtained through modal analysis. A scale model wing, without taper was manufactured in the laboratory and tested in a wind tunnel. The pressure data was obtained from fluid flow analysis and the deformation results obtained through structural analysis. The analysis was performed in the ANSYS Workbench Environment, accessing FLUENT CFX for the computational fluid dynamics analysis and the ANSYS FEA package for the mechanical analysis. The computational results obtained are compared with the experimental data obtained in the wind tunnel. Comparison of the analysis and test results provides further understanding of the flutter characteristics.

Non-destructive evaluation (NDE) techniques that can be applied in-situ are particularly relevant to the testing of large scale structures that cannot easily be taken into a laboratory for inspection. The application of established laboratory based techniques to the inspection of such structures therefore brings with it a new set of challenges associated with the change in operating environment between the laboratory and 'the field'. The current work investigates the use of thermoelastic stress analysis (TSA) to inspect carbon fibre composite aerospace components for manufacturing defects and in-service damage. An initial study using single transient loads to obtain a measureable change in temperature that can be related to the change in the sum of the principal stresses showed a good agreement with the traditional methodology. However, for large structures, the energy required to obtain a sufficiently large stress change to obtain a resolvable measurement may require an actuator that is not easily portable. Hence a number of ideas have been proposed to reduce the power requirement and deal with small signal to noise ratios. This paper describes the use of natural frequency vibration modes to enable large stress changes to be generated with minimal power input. Established signal processing in the form of a lock-in amplifier and Fourier signal analysis is applied. Tests on a laboratory scale flat plate and full-scale representative wing skin and stringer specimen are presented.

This paper aims at describing the tests campaign carried out on five precast bonded post-tensioned concrete bridge beams, recently dismounted after a service life of 50 years. The girders were part of the deck of a recently dismounted viaduct of an Italian motorway. The beams showed different deterioration levels, mainly due to the different exposure to corrosive agents. The test campaign were designed for evaluating the residual load bearing capacity of the members. Dynamic measurements were acquired before and after the static tests by using different excitation sources. This experimental research highlights that the natural frequencies of the beams can be used as a predictor of the ultimate bending moment of an existing structure.

Long range ultrasonic testing (LRUT) is a relatively new development within the non-destructive testing sector. Traditionally, conventional ultrasonic testing (UT) is performed at high frequencies, in the MHz range, and is capable of detecting small flaws within a range of millimetres; whereas long range ultrasonic inspection is carried out at lower frequencies, typically between 20 and 100kHz, and is capable of highlighting structural detail and discontinuities tens of metres from a test position. Conventional ultrasonic testing relies on the transmission of bulk waves, the velocities of which are independent of frequency and can usually be predicted easily if the elastic properties of the material under test are known. The dynamics of guided waves, however, are dependent upon frequency making the analysis of received data from a specimen complex. This paper will serve as an introduction to time-frequency representation and may allow a clearer understanding of the non-stationary raw signals produced by this inspection process. Currently, LRUT data are assessed in the time or distance domain using the amplitude vs. time 'A-Scan', therefore structural features and potential flaws are highlighted on a time-of-flight basis. However, as the data obtained are dynamic in time and frequency (non-stationary), time-frequency distributions could provide a mode identification or de-noising process to deal with the problem of coherent noise.

The combination of longitudinal and torsional (LT) vibrations at high frequencies finds many applications such as ultrasonic drilling, ultrasonic welding, and ultrasonic motors. The LT mode can be obtained by modifications to the design of a standard bolted Langevin ultrasonic transducer driven by an axially poled piezoceramic stack, by a technique that degenerates the longitudinal mode to an LT motion by a geometrical alteration of the wave path. The transducer design is developed and optimised through numerical modelling which can represent the geometry and mechanical properties of the transducer and its vibration response to an electrical input applied across the piezoceramic stack. However, although these models can allow accurate descriptions of the mechanical behaviour, they do not generally provide adequate insights into the electrical characteristics of the transducer. In this work, an analytical model is developed to present the LT transducer based on the equivalent circuit method. This model can represent both the mechanical and electrical aspects and is used to extract many of the design parameters, such as resonance and anti-resonance frequencies, the impedance spectra and the coupling coefficient of the transducer. The validity of the analytical model is demonstrated by close agreement with experimental results.

The characteristics of a Langevin transducer are studied using a combination of numerical and experimental techniques, which reveal the effect of minor design changes on its performance. The experiments were performed using a microphone and voice-recording software capable of measuring frequencies up to 41 kHz; the obtained signal was analysed in MATLAB. A three-dimensional finite element model of the analysed transducer was also developed in a commercial finite element software ABAQUS/Standard and used for numerical simulations of its response to different excitation conditions. The transducer system was optimised using the results of noise detection and FEA.

A Class V cymbal flextensional transducer is composed of a piezoceramic disc or ring sandwiched between two cymbal-shaped shell end-caps. These end-caps act as mechanical transformers to convert high impedance, low radial displacement of the piezoceramic into low impedance, large axial motion of the end-cap. The cymbal transducer was developed in the early 1990's at Penn State University, and is an improvement of the moonie transducer which has been in use since the 1980's. Despite the fact that cymbal transducers have been used in many fields, both as sensors and actuators, due to its physical limitations its use has been mainly at low power intensities. It is only very recently that its suitability for high amplitude and high power applications has been studied, and consequently implementation in this area of research remains undeveloped. This paper employs experimental modal analysis (EMA), vibration response measurements and electrical impedance measurements to characterise two variations of the cymbal transducer design, both aimed at incorporation in ultrasonic cutting devices. The transducers are fabricated using the commercial Eccobond 45LV epoxy adhesive as the bonding agent. The first cymbal transducer is of the classic design where the piezoceramic disc is bonded directly to the end-caps. The second cymbal transducer includes a metal ring bonded to the outer edge of the piezoceramic disc. The reason for the inclusion of this metal ring is to improve the mechanical coupling with the end-caps. This would therefore make this design particularly suitable for power ultrasonic applications, reducing the possibility of debonding at the higher ultrasonic amplitudes. The experimental results demonstrate that the second cymbal design is a significant improvement on the more classic design, allowing the transducer to operate at higher voltages and higher amplitudes, exhibiting a linear response over a practical power ultrasonic device driving voltage range. The results also show that the device can be accurately tuned using finite element modelling and that the cymbal exhibits a modal response as predicted by the finite element models.