The Effect of Damages on Modal Frequencies of Flat Glass Fiber Reinforced Polyurethane Foam Sandwich Structures

In this research work, experimental and numerical analyses were conducted to ascertain the impact of damages on modal frequencies of sandwich structure. The structure consists of laminated E/glass epoxy face sheets with [0°/90°]s stacking sequences and polyurethane foam core. The fabrication processes involved are hand layup technique, mold filling process and the use of adhesives to assemble the structure. Damages introduced during fabrication, encompassing core damage, delamination between face sheets and core and impact damage. Experimental modal testing was conducted on four distinct specimens using a Fast Fourier Transform (FFT) analyzer under cantilever boundary conditions. The results reveal significant variations in modal frequencies and mode shapes in the structures. A consistent six-mode frequency bandwidth is observed within the 2000 Hz range across all specimens. The numerical analysis was performed by Finite Element Method (FEM). Experimental and numerical results were in a good agreement. It was observed that modal frequencies decrease due to the presence of damage in the fabricated structures.


Introduction
Polymer composite sandwich structures have high bonding strength, specific strength, and durability; hence, they find a number of applications in various fields such as marine, aeronautical, automotive, etc. [1][2].The sandwich structures absorb considerable impact energy during impact; hence, they are used as damping structures or bumpers in automotive industries [3].Usually, sandwich structures possess a higher damping ratio than polymer structures due to their molecular mobility, viscoelastic nature, and interfacial bonding strength between the core and face sheet [4].The sandwich structures can absorb high-impact energy, which may lead to failure in sandwich structures in the form of delamination and core damage, which in turn leads to interracial crack propagation [5].The failure of either the core or skin leads to total loss of integrity and failure of the sandwich components [6].The degradation of both stiffness and strength in composites is linked to the appearance of micro-cracks or debonding during the fabrication phase.Degradation of stiffness and strength leads to loss of dynamic properties, which play a significant role in construction, automotive, and mechanical component design [7].Damage causes changes in the vibration characteristics as well as a deterioration of stiffness and strength.Therefore, it's critical to comprehend how damages affect how structures vibrate.A constrained mode approach was presented by Tracy et al. to model the delamination in the sandwich beam.This method assumes that the delaminated layers will always come into contact with one another along their entire length, but they cannot slide over one another [8].The influences of delamination on the natural frequencies of composite plates and beams were also studied by several researchers by many methods such as nondestructive testing like ultrasound, die penetration, vibration analysis, etc. [9, 10, and 11].Integration of vibration testing is essential for damage assessment for accurate detection of type and location of damage, but certain challenges still exist in the statistical pattern recognition paradigm process.There are currently many methods, such as acoustic emission [12], electrical impedance [13], vibration-based thermography [14], and wave-guided techniques [15], to detect damage in complex sandwich structures.Damage results in changes to the structure's physical properties, and these changes can be used as a gauge for the overall health of the structure.It is possible to extract the vibration characteristics and identify and analyze the corresponding change from the signal that the sensors affixed to the structure are monitoring.Furthermore, one may determine the changes in the physical parameters of the structure to determine the state of health of the structure by analyzing the vibration characteristics.Recently, test signals have been able to be accurately and swiftly evaluated and processed because to the quick growth of current computer technology, as well as the advancement of sensor and signal processing technologies.As a result, vibration-based structural health monitoring technology has emerged as a focal point for both domestic and international research.A broadband vibration-based technique was used to inspect very large composite structures, which revealed various sites for the severity of the damage [16].Yasin et al. developed a damage identification technique based on changes in modal strain energies before and after damage occurs in sandwich structures [17].The identification of damage for feature selection and extraction requires Engineering judgment [18] to measure the susceptibility to damage, the severity of the damage, etc.
It is evident from the review of the literature that curvature and delamination/debond affect the vibration behavior of composite structures is described.Consideration of other damages like core damages and impact damages of the sandwich structures are poorly known.Thus, in this research, the experimental and numerical analysis was performed to investigate the effect core damaged and impact damaged including delamination of sandwich structures on the modal frequencies reported.The modal frequencies of damaged structures compared with undamaged structures.The polymer sandwich structure is fabricated with a glass fiber/epoxy face sheet and a PU Foam core using the hand layup technique.To evaluate the modal parameters (frequency and mode shapes) of damaged and undamaged specimens and acquire the required data for damage assessment.

Material selection
Among the materials are glass fiber, epoxy (LY 556 grade), and hardener (HY 951) for the fabrication of sandwich face sheet, polyol, and isocyanate for the fabrication of PU foam, and epoxy was used as a binding agent between foam and face sheet.Each used material's characteristics are stated Table 1.

Sandwich fabrications
The process involved mixing of polyol and isocyanate in a 1:1 ratio using a mechanical stirrer for two minutes.This mixture was then poured into an airtight mould measuring 150 x 150 x 14 mm and allowed to set for 30 minutes.The resulting foam core was subsequently cut from an 8 mm thick foam block measuring 150 x 150 x 8 mm using a foam cutting machine.For the face sheets of the sandwich structure, epoxy (LY-556) and Triethyl tetramine (HY-951) were mixed in a 90:10 ratio using a mechanical stirrer for two minutes.The glass fibre mat was layered with mixed epoxy resin using the hand layup technique, which was cured for 24 hours.The prepared PU foam is placed between the glass fibre face sheets bonded using epoxy resin and loaded in to the hot press machine for a 24-hours curing process.Using a sandwich-cutting machine extra materials from the sandwich structure is removed to obtain the dimensions of 150 x 150 x 12 mm for the analysis.

Introduction damages
The procedure to prepare undamaged composite specimens was explained in the previous section.The core damage was introduced during core fabrication by using glass beads at the centre was set as the 10% volume of the core.The delamination was made by introducing teflon tape placed between top face sheet and core during the adhesion of sandwich structure.Subsequently, the impact damage was inflicted on the sandwich structure using a drop weight tester.The impact was initiated from a height of fall 1 meter, with a 2 kg mass, resulting in random impact defects at the centre of the sandwich structure.

Vibration and modal testing
For the free vibration and modal testing, a total of four samples such as undamaged, core-damaged, delaminated, and impact-damaged sandwich specimens were employed to investigate the modal frequencies to pertaining to six modes under cantilever boundary condition.Calibration and initialization were carried out on the vibration tester for conducting the experiment.To excite vibrations in the specimen, an electrodynamic shaker was employed, connected to a force sensor.8 channels Fast Fourier Transform (FFT) analyzer which is used to converts time domain signal to frequency domain signal.Each specimen, measuring 150 x 150 mm, was securely fixed in a specially procured test fixture, aligning with the required boundary conditions.Additionally, the accelerometer having the sensitivity of 100 mV/g was connected to the FFT signal analyzer (channel 2), while the force sensor having the sensitivity of 112.41 mV/N should be fixed to the electrodynamic shaker and linked to the FFT channel analyzer (channel 2) shown in Fig. 1.The responses of the specimen was recorded using an accelerometer at 36 distinct sample points.The force sensor was affixed at a suitable point on the specimen to capture all modes through that location.

Finite Element Method (FEM) of Modal Analysis
The finite element model of undamaged and damaged cantilever sandwich specimen was modelled as per the dimensions used in experimentation to predict the modal frequencies by using ANSYS Workbench.It begins with the creation of a 3D model in SOLIDWORKS, where the structure is divided into three separate parts and then assembled into a complete unit.This assembled model is saved as an IGES file for importation into ANSYS Workbench, for modal analysis.Material properties such as density, Young's modulus are assigned (refer Table 1) to the core and skin layers of the sandwich structure.The connections between these parts are set to 'bonded' to ensure they act as a single, integrated structure.Fig. 2 shows the geometric models with finite element meshes for the undamaged sandwich structure.Four-node SHELL 181 elements were simulate the skins and eight-node SOLID 185 elements were simulate the core.In total, 8100 SHELL 181 elements were used, as the upper and lower face sheets were divided into 4050 elements, repectively.At the same time, 16470 SOLID 185 elements were utilized for modelling core.The FE mesh sensitivity study was performed to validate the modal frequencies of all samples.

DewsoftX Modes
The experimental modal frequencies and mode shapes are acquired by conducting modal analysis tests on the undamaged and damaged GFRP specimen at 36 sample points represented in Fig. 3 and Table .2 respectively.This section discusses the outcomes of modal testing on four distinct specimens subjected to cantilever boundary conditions.

Fig. 3. Frequency Response of a) Undamaged b) Core Damaged c) Delamination and d) Impact
Damaged GFRP Sandwich Specimen under Cantilever Boundary Conditions.
In Fig. 3 shows the dispersion curves of 36 sample points of all four specimens within the 2000 Hz bandwidth drawn from FFT analyzer.Six distinct mode shapes and their corresponding frequencies are discernible.These dispersion curves deviate from classical forms, exhibiting asymmetry due to the nonmirror-symmetric nature of the sandwich structure.The bar chart should be drawn between frequencies and modes for undamaged and damaged specimens (refer Fig. 4).There is a change in frequency in the case of damaged specimen as compared to undamaged one.For the first and second fundamental mode there is a 3% of change in natural frequencies.For the higher modes the change in natural frequencies is more than 20%.This concludes that the changes in natural frequencies indicates the presence of damages.Frequency Response Function (FRF) plots are not sufficient to identify the damage of the structure even mode shapes also useful to identify the locations of the damaged structure.Mode shapes are commonly employed to identify the damage locations as they carry pertinent information about structural integrity.In the case of sandwich composite specimens, however, mode shapes for scenarios involving core damage, delamination, and impact appear nearly indistinguishable from those of undamaged specimens.This similarity may be attributed to potential variations in composite thickness, affecting the coupling between bending and extension for higher modes.Table 3 provides a comparison of mode shapes between undamaged and damaged specimens under cantilever conditions.Table 3 displays the first six mode shapes (modes 1 to 6) for a PU sandwich structure subjected to a cantilever beam condition.These mode shapes elucidate the dynamic behavior of the sandwich structure.Comparing mode shapes between undamaged specimens and those with core damage, delamination, or impact in GFRP specimens reveals discernible differences both visually and in terms of modal frequencies.Experimental results consistently indicate shifts in natural frequencies compared to undamaged conditions, a trend evident in Frequency Response Function (FRF) plots.
The presence of damage becomes apparent through alterations in both natural frequencies and mode shapes, with more pronounced frequency shifts observed in higher modes.Qualitative comparisons between mode shapes of undamaged and damaged specimens are conducted for various configurations.These comparisons reveal changes in the vibrational patterns, where the first vibrational mode shape exhibits single-lobe vibration, while the second vibrational mode shape manifests as two lobes.These vibrational modes collectively influence the dynamic behavior of the sandwich structure's components.During the cantilever's motion between its highest and lowest peaks from the mean position, it's observed that the generated vibration frequency consistently exceeds the corresponding FEM results, as detailed in Table 3.The discrepancies in vibrational frequency percentages range from 3% to 20% when comparing the experimental findings with FEM results.This variance tends to escalate with a higher number of modes analyzed.The rationale behind this trend lies in the fact that higher modes incorporate more stress, which is directly influenced by experimental conditions but overlooked in FEM simulations.Consequently, the observed variation between experimental and FE results becomes more pronounced as the complexity of modes increases.

Conclusion
In this research work, the effect of damages on modal frequencies of flat glass fiber reinforced polyurethane foam sandwich structures are studied.Flat PU-filled glass fiber-reinforced sandwich composite structure of undamaged and damaged structures was fabricated to carry out experimental studies under cantilever boundary conditions.The electrodynamic shaker was employed to excite vibrations on the specimens and the results are analyzed through FFT analyzer.Six modal frequencies were predicted for all four specimens.The results concluded that the natural frequencies decrease for the damaged structure compared to the undamaged one.The mode shapes indicate the location of the damages.Numerical analysis carried out by using ANSYS for comparative results.The discrepancies in vibrational frequency percentages range from 3% to 20% when comparing the experimental findings with FEM results.This method of detecting damage can be applied for intrinsic identification of damage and continuous health surveillance of sandwich composite structures.

Fig. 1 .
Fig. 1.Experimental Setup of FFT Analyzer used for Modal Testing.

Fig. 4 .
Fig. 4. Modal Frequencies of GFRP sandwich obtained using an FFT analyzer as a function of different damage conditions.

Table 3 .
Mode shapes comparison of undamaged and damaged GFRP