Table of contents

This volume of Journal of Physics: Conference Series contains papers presented at the 4th Symposium on the Mechanics of Slender Structures (MoSS2013) run under the auspices of the Institute of Physics Applied Mechanics Group and hosted by Harbin Institute of Technology (China) from 7–9 January 2013. The conference has been organized in collaboration with the Technical Committee on Vibration and Sound of the American Society of Mechanical Engineers and follows a one day seminar on Ropes, Cables, Belts and Chains: Theory and Applications and the MoSS2006 symposium held at the University of Northampton (UK) in 2004 and 2006, respectively, the MoSS2008 symposium held at the University of Maryland Baltimore County (USA) in 2008 and the MoSS2010 symposium hosted by Mondragon University and held in San Sebastian (Spain) in 2010.

The remit of the Symposium on the Mechanics of Slender Structures series involves a broad range of scientific areas. Applications of slender structures include terrestrial, marine and space systems. Moving elastic elements such as ropes, cables, belts and tethers are pivotal components of many engineering systems. Their lengths often vary when the system is in operation. The applications include vertical transportation installations and, more recently, space tether propulsion systems. Traction drive elevator installations employ ropes and belts of variable length as a means of suspension, and also for the compensation of tensile forces over the traction sheave. In cranes and mine hoists, cables and ropes are subject to length variation in order to carry payloads. Tethers experiencing extension and retraction are important components of offshore and marine installations, as well as being proposed for a variety of different space vehicle propulsion systems based on different applications of momentum exchange and electrodynamic interactions with planetary magnetic fields. Furthermore, cables and slender rods are used extensively in civil engineering; in cable-supported bridges, guyed masts and long-span roofs of buildings and stadia. Suspended cables are also applied as electricity transmission lines. Chains are used in various power transmission systems that include such mechanical systems as chain drives and chain saws. Moving conveyor belts are essential components in various material handling installations. Other structures such as pipelines, plates, beams, mechanical linkages and DNA structures also fall into this category.

The behaviour of these elements plays a significant role in the performance of the host structure and a holistic approach is needed in the analysis and design of the entire system. This meeting brings together experts from various fields: structural mechanics, thermo-mechanics, dynamics, electrodynamics, vibration and control, structural health monitoring, artificial intelligence, materials science and applied mathematics to discuss the current state of research as well as rising trends and direction for future research in the area of mechanics of slender structures. The event is aimed at improving the understanding of structural and thermo-mechanical properties and behaviour of slender structures. The papers presented at the conference cover analytical, numerical and experimental research in various applications of slender structures.

The Organizing Committee gratefully acknowledges support received from the co-sponsoring institutions and would like to thank the authors for their hard work and high quality contributions.

Dengqing Cao Harbin Institute of Technology

Stefan Kaczmarczyk The University of Northampton

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.

Some aspects of research wok on the mechanics of thin elastic rod based on Kirchhoff-Cosserat's model were summarized. The analytical mechanics with arc-coordinate s and time t as double variables was established to formulate the motion of elastic rod. In stability analysis the difference and relationship between Lyapunov's stability and Euler's stability were discussed. The first approximate stability was determined by the characteristic equation with double eigenvalues in different domains, one of which can be determined by geometric conditions in static analysis. The Lyapunov's and Euler's stability conditions of the rod in space domain are the necessary conditions of Lyapunov's stability in time domain. As applications of the Kirchhoff's rod in molecular biology, the explanations of nucleosome structure and the chromosome coiling of DNA were given. Concerning the application in engineering the shape of a hanging rod under gravity and the coiling and stretching process of an extendable space mast were discussed. The motion of an axial moving beam with constant velocity and axial extensive force was discussed as an example of exact Cosserat's rod, the special case of small deformation is the Timoshenko's beam.

The high-order modes and the moving wave characteristics of rotating thin shell are investigated in this paper based on transfer matrix method when the damping effects of the hard-coating layers are applied on the shell. Firstly, the dynamic model of the thin shell is obtained based on the Love theory, with introducing centrifugal force and Coriolis force. Then, the transfer matrix formulas of the shell with partially coated layers at different segments are obtained under the clamped-free boundary condition, in which the mechanical property of the hard-coating material is simplified to be linear and isotropic. The modal characteristics of the shell are calculated numerically. The obtained higher order modal frequencies of the partially coated shells are compared with those of the bare shell. The effects of the material parameters and locations of the hard-coating layers are also illustrated based on the different modal characteristics., great care should be taken in constructing both.

Clamp band joints are widely used to fasten spacecrafts onto launching systems. Due to the unilateral constraints and the frictional slippage at the joint interface, clamp band joints may bring nonlinearity into launching systems during launching process. In this paper, the dynamics of a slender launching system with clamp band joint is investigated using harmonic balance method. Firstly, the formulas for the joint stiffness of the clamp band joint are proposed. Then, the finite element model for the launch vehicle and the spacecraft connected by the clamp band joint is developed, where the clamp band joint is represented by a massless beam element. Finally, harmonic balance method is applied to calculate the steady state response of the launching system.

The paper presents an experimental research on motion control of a ground-based tethered subsatellite with a controllable rigid arm between the subsatellite and the tether. The forces acting on the tethered subsatellite are first obtained through the dynamic similarity between the subsatellite and a tethered satellite orbiting the Earth. And then, an experimental system for simulating the tethered subsatellite is designed and elaborated in detail, including the airflow embranchment, the measuring and control subsystems, the power and communication subsystems, et al. Furthermore, the operating principle of the ground-based experimental system is illustrated, and the applicability of which is validated by a test of an on-orbit nonlinear optimal control problem.

In molecular biology, the elastic rod is wound on the elliptic cylinder can be used as a simplified model of the DNA and protein molecules, in which the elliptic cylinder is used to simulate the heterogeneity of the protein molecules. The problem can be described as a long thin weightless rod constrained, by suitable distributed forces, to lie on an elliptic cylinder while being held by end tension and twisting moment. The Cosserat director theory is used to formulate this problem. More complicated shaped are possible and special attention is given to localized configurations described by homoclinic and heteroclinic orbits of the oscillator. The analytical results of homoclinic and heteroclinic boundary conditions are obtained from Padé approximation. By using the analytical results of homoclinic and heteroclinic solution, both internal force and 3D configuration are discussed in detail. The results of analytical and numerical integration are compared to verify the effectiveness and feasibility of the analytical method.

Based on the Donnell assumptions and linear visco-elastic theory, the constitutive equations of the cylindrical shell with multilayer Passive Constrained Layer Damping (PCLD) treatments are described. The motion equations and boundary conditions are derived by Hamilton principle. After trigonometric series expansion and Laplace transform, the state vector is introduced and the dynamic equations in state space are established. The transfer function method is used to solve the state equation. The dynamic performance including the natural frequency, the loss factor and the frequency response of clamped-clamped multi-layer PCLD cylindrical shell is obtained. The results show that multi-layer PCLD cylindrical shell is more effective than the traditional three-layer PCLD cylindrical shell in suppressing vibration and noise if the same amount of material is applied. It demonstrates a potential application of multi-layer PCLD treatments in many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles.

Most elevators applied to tall buildings include compensating ropes to satisfy the balanced rope tension between the car and the counter weight. The compensating ropes receive tension by the compensating sheave, which is installed at the bottom space of the elevator shaft. The compensating sheave is only suspended by the compensating ropes, therefore, the sheave can move vertically while the car is traveling. This paper shows the elevator dynamic model to evaluate the vertical motion of the compensating sheave. Especially, behavior in emergency cases, such as brake activation and buffer strike, was investigated to evaluate the maximum upward motion of the sheave. The simulation results were validated by experiments and the most influenced factor for the sheave vertical motion was clarified.

In this paper a new method of pattern recognition based on higher-order cumulant and envelope analysis is presented. The core of this new method is to construct analytical signals from the given signals and obtain the envelope signals firstly, then compute and compare the higher-order cumulants of the envelope signals. The higher-order cumulants could be used as a characteristic quantity to distinguish these given signals. As an example, this method is applied in fault diagnosis for 197726 rolling bearing of freight locomotive. The comparisons of the second-order, third-order and fourth-order cumulants of the envelope signals from different vibration signals of rolling bearing show this new method could discriminate the normal and two fault signals distinctly.

In this study, the critical load and buckling of the single pile foundation subjected to the vertical load are investigated. Considering the second-order moment of the soil-structure interaction, the refined model of the single pile foundation is derived. Then, the critical load and buckling phenomenon of the single pile foundation is examined. Moreover, the effects of the vertical load and the foundation parameters on the critical load and buckling of the single pile foundation are systematically investigated.

As a kind of base excitation, shaking table is often used to test the dynamic characteristics of structures. However, the prediction of response to base excitation hasn't been solved effectively, which limits the further research on the test and analysis method with respect to base movement. This article is based on a cantilever beam and focuses on its response prediction under sinusoidal base excitation. By moment and force equilibrium equations, an analytical model is built for this cantilever beam, and then a method to predict dynamic response at base excitation is proposed. Finally, the method is used to solve the vibration response distributions of the cantilever beam at base excitation. Correctness of this method is also proved by comparing the result with experimental data.

The nonlinear dynamic analysis of a hoisting viscous damping string with time-varying length is investigated. The hoisting string is modeled as a taut translating string with a rigid body attached at its low end. A systematic procedure for deriving the system model of hoisting viscoelastic string with time-varying is presented. The governing equations are developed employing the extended Hamilton's principle considering coupling of axial movement and flexural deformation of string. The Galerkin's method and the 4th Runge-Kutta method are employed to numerically analyze the resulting equations. The motions of elevator hoisting system are presented to illustrate the proposed mathematical models. The results of simulation show that the material viscous damping helps stabilize the transverse vibration. The modeling methods can represent the transverse vibration of hoisting viscous damping string with time-varying length.

The elastic wave propagation in periodic beams with the propagating disturbance is investigated. The effects of the disturbance on the wave propagation in periodic beams are studied. A propagating wave (disturbance) is incident upon the discontinuity and gives rise to transmitted and reflected waves. All of the transmitted and reflected waves of given flexural wave incident upon the beam at some location are found and superposed using the multiple reflections approach. The relation between the wave-field of incident wave (disturbance) and the wave-field of resulting waves on any segment is expressed. Much attention is devoted to the response in the frequency ranges with gaps in the band structure for the corresponding periodic beams with the disturbance. The numerical results of the frequency response function of finite periodic beams with propagating disturbance are presented. With the increase disturbance amplitude, the attenuation of the band gaps gradually decreases. The effects of the number of cells and material parameters on the band gap are also considered.

This paper presents an analysis for the nonlinear in-plane motion of wind turbine blade under the combined action of parametric and forced excitations. The Bernoulli-Euler beam theory is adopted to describe blade motion. Effects including gravity, structural damping and geometric nonlinearity are included in the mathematical model. The rotating speed is considered as a nominal speed with a harmonic perturbation. The periodic oscillation of rotating speed brings about parametric excitations in stiffness and damping terms and forced excitations. The harmonic balance method is applied to get the approximate solution of dynamic response. Numerical integral of original system is used to verify the analytical solution. Influences of structural damping, perturbed amplitude and frequency of rotating speed on blade behaviour are discussed.

In this paper we present analysis and numerical simulations for the natural frequency of pipes conveying fluid in the ADINA system. The slender pipe structures are modelled as shells and the fluid flows are supposed to be three-dimensional (3D) and incompressible. The fluid and structural models are mechanically coupled on their interface through slip and displacement conditions. Several numerical examples for pipes shaped as different configurations show that the natural frequencies obtained based on ADINA codes are generally lower than those predicted by analytical or dynamic stiffness methods. In particular, for curved pipes conveying fluid with relatively high flow velocity, it is found that the evolution trend of natural frequencies with increasing flow velocity is similar as that predicted by the inextensible theory for curved pipes conveying fluid.

In this paper, nonlinear dynamic characteristics of a single span rotor system with two discs are investigated under fixed-point and local arc rub-impact conditions. A twenty-degree-of-freedom model considering the gyroscopic effect is developed, the simple Coulomb friction model and piecewise linear spring model to describe the contact between the rotor and the stator. The vibration chracteristics of the rotor system with two types of rub-impact forms are analyzed with respect to the effects of rotating speed by using spectrum cascades, vibration waveforms, orbits and frequency spectra. The simulation results show that different rotor motions appear, such as P1(period-1), P2, P3 and P4 with the increasing rotating speed under two rub-impact conditions. And some combination frequency components and continuous spectra appear under the local arc rub-impact condition, which are different from those under the fixed-point rub-impact condition.