Mode Shapes Research Articles

Novel rod-sprung-mass model to investigate characteristics of building structural vibration induced by railways

Railway-induced vibrations in building structures require predictions to assess the serviceability. Fundamental properties such as the predominant modes of railway-induced vibrations are critical in structural design and mitigation approaches. However, the existing numerical models are customised to specific buildings. This renders these models unsuitable for broader mechanistic investigations. To address this, this study proposes a rod-sprung-mass (RSM) model to investigate the dynamic behaviour of structures under vertical ground excitations induced by railways. The columns were modelled as axial vibration rods, with each floor suspended on the rod as a sprung mass. The model was validated using a three-story steel frame structure and a five-story concrete structure. Subsequently, the dynamic characteristics of the structures and railway-induced responses were discussed. The structural vertical modes are attributed to the interaction between the columns and slabs, and the structural natural frequencies are outside the frequency range of the individual components. Parametric studies revealed that lower-order structural modes are generally predominant. Under such circumstances, the floor response tends to first decrease and subsequently increase with the floor height. As a result, low-rise buildings exhibit the maximum amplitude on the top floor, whereas the maximum amplitude is on the ground floor for high-rise buildings. Meanwhile, when structural high-order modes become predominant owing to a high-frequency input, the responses of the middle floors intensify, and the peak responses can be altered to the middle floors. This study emphasises the necessity of considering vertical global modes, whereas existing studies have focused mainly on mode shapes on particular floors. The RSM model is an efficient tool for structural design and vibration control.

Scattering of vortices with excited normal modes

We consider head-on collisions at critical coupling of vortices modeled by the Abelian-Higgs model. We investigate the two-vortex scattering, whereby the vortices are excited by the shape mode causing fluctuations in the gauge-invariant quantities. When the vortices are excited with a sufficiently large amplitude the moduli space approximation fails, and we observe an interesting behavior in which the vortices can become trapped in a quasibound state with multiple bounces. We perform a detailed investigation on the behavior of these excited vortices and sample a phase space of solutions. Interestingly, we find a fractal structure dependent on the initial phase of the mode and velocity of the vortices. Published by the American Physical Society 2024

Dynamic characteristics of bridges with short pylons and outwardly inclined cable planes

This study developed a cable-stayed bridge characterised by short pylons and outwardly inclined cable planes. The dynamic characteristics of this bridge were investigated using the Lanczos eigenvalue and finite element methods. The first ten mode shapes and frequencies were analysed to this end. The influences of key parameters, such as the inclination angle of the pylons and the height and stiffness of the cable–pylon anchorage, on the dynamic characteristics of the bridge were examined. The results showed that the transverse bending modes of the main girder occurred first, while modes related to pylons appeared later. The torsional vibrational modes appeared in the 10th order, indicating the bridge had suitable wind resistance. Further, the outwardly inclined cable planes enhanced the lateral seismic resistance of the bridge. Increasing the rigidities of the cable–pylon anchorage and main girder can improve the dynamic characteristics of the bridge. This is accomplished by reducing the height of the cable–pylon anchorage and adding auxiliary piers.

Analysis and measurement of vibration characteristics of a hollowing defect based on a laser self-mixing interferometer

Abstract To solve the problems with the existing methods for detecting hollowing defects, such as inconvenient operation, low efficiency and intense subjectivity, and to improve the efficiency of the acoustic-optic fusion method for detecting hollowing defects, in this paper the vibration characteristics of hollowing defects are measured and analyzed using a laser self-mixing interferometer. The ceramic tile above the hollowing defect is equivalent to a thin circular plate with peripheral fixed support. According to Kirchhoff’s classical circular plate theory and the circular plate displacement function based on the improved Fourier series, a theoretical model of a circular plate is established. By solving the characteristic equation, the theoretical modal parameters of hollowing defects are obtained. Subsequently, an experimental system based on a laser self-mixing interferometer is built, and modal experiments are carried out using the hammering method. The experimental modal parameters are obtained with a professional modal analysis software. Through comparative analysis between the theoretical and experimental modal parameters, the error of the natural frequency results is found to be tiny and the mode shapes are consistent. These results provide theoretical guidance for a practical non-destructive acoustic-optic fusion method for detecting hollowing defects.

Fatigue Failure Of Steam Turbine Discs - A Centenary Tribute To Wilfred Campbell

Abstract The year 2024 marks one hundred years since Wilfred Campbell published his landmark work on vibrational analysis of rotating disc following a series of disc failures in steam turbines. Despite the absence of advanced engineering analytical tools, Campbell came up with an elegant method to visually demonstrate and capture the mode shapes in rotating discs. The first part of this paper reviews Campbell?s life and analytical and experimental work in this area. Regardless of the current advanced engineering capabilities to predict nodal shapes in turbine discs, turbine discs still experience failures related to vibration. The second part of the paper discusses a recent case study where a turbine disc failure occurred as a result of vibration. The discussion includes metallurgical root cause failure analysis and engineering analysis to predict the vibrational characteristics. Metallurgical failure analysis confirmed that the primary mode of failure was fatigue and did not have any issues with the disc material or its mechanical properties. Finite element modeling and analysis were used for the engineering analysis to predict the natural frequencies of the bladed-disc. The engineering analysis showed the evidence of potential resonance, and the failure was related to nodal vibration issues.

Experimental and numerical investigation of the modal parameters for thin laminated composite plates

In the present work, glass fiber-reinforced (GFR) composite specimens were fabricated using the vacuum-bag molding process. The properties related to the vibrational response of the fabricated composite plates, such as natural frequency, modal density, and damping loss factor (DLF), were investigated through both experimental and numerical approaches. The effects of different parameters, including boundary conditions (BCs), fiber orientations, laminate layer numbers, and aspect ratios, were comprehensively studied. It was found that the experimental and numerical results were in close agreement. For each case, finite element analysis was performed to determine the natural frequencies and mode shapes. Regarding the various BCs, the DLF was observed to be highest (0.47) for fully clamped BC and lowest (0.12) for free-free BC, whereas the modal density was highest (0.068) for cantilever BC and lowest (0.037) for fully clamped BC. In terms of different lamination schemes, the DLF was highest (0.42) for a plate with quasi-isotropic fibers and lowest (0.25) for a plate with unidirectional fibers, while the modal density was highest (0.068) for quasi-isotropic fibers and lowest (0.047) for unidirectional fibers. Regarding the plates with different laminate layers, the highest DLF (0.47) was observed for a plate with 16 layers, while the lowest DLF (0.33) was found in a plate with 8 layers. Conversely, the highest modal density (0.067) was observed for a plate with 8 layers, and the lowest (0.057) was noted for a plate with 16 layers. Lastly, considering aspect ratios, the highest DLF (0.48) was observed for an aspect ratio of 0.5, and the lowest (0.26) for an aspect ratio of 1.5. The highest modal density (0.09) was also observed for an aspect ratio of 0.5, while the lowest modal density (0.045) was for an aspect ratio of 1.5.

Free vibration analysis of Euler-Bernoulli beams modeled by spatial-fractional differential equation

In this article, a more accurate dynamic model of Euler-Bernoulli beam is proposed, based on the spatial-fractional derivatives. Firstly, the governing differential equation is derived. After that, this equation is solved by two different methods: the first method uses only the left fractional derivative, while the second method tends to use both the left and right fractional derivatives, simultaneously. In the second method, the location of the "switching point" which connects the left and right derivatives is treated as a variable parameter. The effect of this parameter is investigated by analyzing several beams. As numerical results, the natural frequencies and mode shapes of beams with different boundary conditions are presented.

Thermoelastic damping properties in hemi-ellipsoidal shells with variable thickness

Thermoelastic damping (TED) is a fundamental dissipation mechanism that inevitably exists in shell resonators with high quality factors. Based on the thermal energy method, this paper demonstrates an effective method for the TED characterization of the hemi-ellipsoidal shells with variable thickness which manifest lower TED compared with the hemispherical shells. The equation of motion of the hemi-ellipsoidal shell under clamped-free boundary conditions is established by Hamilton's principle and the assumed mode method, and the natural frequencies and mode shape functions of the hemi-ellipsoidal shell with variable thickness are obtained by solving the eigenvalue problem. The temperature field is acquired by solving the heat conduction equation along the radial direction, and an analytical model for the TED of the hemi-ellipsoidal shell with variable thickness is presented by calculating the maximum elastic potential energy and the work lost per cycle of vibration due to irreversible heat conduction. Analysis on TED at the vibration patterns of meridional wave number m = 1 and the circumferential wave number n = 2 or 3 where the shell resonators typically operate is carried out. The analytically calculated TED results are compared with those of the finite element method (FEM) to verify the feasibility and correctness of the present method. The influences of the geometrical parameters on the TED characteristics of the hemi-ellipsoidal shells with variable thickness are analyzed in detail. A meaningful discovery is that compared with the hemispherical shell, the hemi-ellipsoidal shell with variable thickness has a smaller TED when its semiminor axis is shorter than the semimajor axis, which is particularly significant for optimizing the design of the shell resonators with high quality factors.

Impact of internal lattice structures on the weight and natural frequencies of a low pressure turbine blade

Vibration characteristics play a crucial role in the overall performance of Low-pressure (LP) turbine blades and different techniques are developed to enhance vibrational response by increasing natural frequencies. The present analysis aims to develop a new technique based on the investigation of improvement in natural frequencies and mass reduction of a topology-optimized blade design through location-based integration of lattice structures inside the blades. FE models are developed for three different lattice locations based on mode shape behavior obtained through modal analysis of two different nickel-based alloys at stressed and unstressed conditions. The results show that the internal BCC lattice at specific locations showed better vibrational characteristics compared to other incorporated lattice structures, and validates the location-based integration scheme for enhancement of natural frequencies and reduced mass in applied conditions. By this method, 5.7% mass reduction was achieved from an already 35% mass-reduced blade along with enhancement in the first and second natural frequencies by 8.2% and 5.9% respectively when unstressed. At stressed condition, the natural frequencies increased by ≈7.7% and ≈6.6%.

Physically Guided Estimation of Vehicle Loading-Induced Low-Frequency Bridge Responses with BP-ANN

The intersectional relationship in bridge health monitoring refers to the mapping function that correlates bridge responses across different locations. This relationship is pivotal for estimating structural responses, which are then instrumental in assessing a bridge’s service status and identifying potential damage. The current research landscape is heavily focused on high-frequency responses, especially those associated with single-mode vibration. When it comes to low-frequency responses triggered by multi-mode vehicle loading, a prevalent strategy is to regard these low-frequency responses as “quasi-static” and subsequently apply time-series prediction techniques to simulate the intersectional relationship. However, these methods are contingent upon data regarding external loading, such as traffic conditions and air temperatures. This necessitates the collection of long-term monitoring data to account for fluctuations in traffic and temperature, a task that can be quite daunting in real-world engineering contexts. To address this challenge, our study shifts the analytical perspective from a static analysis to a dynamic analysis. By delving into the physical features of bridge responses of the vehicle–bridge interaction (VBI) system, we identify that the intersectional relationship should be inherently time-independent. The perceived time lag in quasi-static responses is, in essence, a result of low-frequency vibrations that are aligned with driving force modes. We specifically derive the intersectional relationship for low-frequency bridge responses within the VBI system and determine it to be a time-invariant transfer matrix associated with multiple mode shapes. Drawing on these physical insights, we adopt a time-independent machine learning method, the backpropagation–artificial neural network (BP-ANN), to simulate the intersectional relationship. To train the network, monitoring data from various cross-sections were input, with the responses at a particular section designated as the output. The trained network is now capable of estimating responses even in scenarios where time-related traffic conditions and temperatures deviate from those present in the training data set. To substantiate the time-independent nature of the derived intersectional relationship, finite element models were developed. The proposed method was further validated through the in-field monitoring of a continuous highway bridge. We anticipate that this method will be highly effective in estimating low-frequency responses under a variety of unknown traffic and air temperature conditions, offering significant convenience for practical engineering applications.

Design and demonstration of a roll-out membrane antenna based on thin-walled deployable composite booms

The thin-walled deployable composite boom (DCB) features the advantages of high deployment-to-package envelope ratio and elastic self-development, which is an enduring topic of interest in the field of lightweight aerospace structures. The structural design and performance demonstration was proposed herein for a roll-out membrane antenna (ROMA) based on DCBs. Firstly, a simplified analytical algorithm was formulated for approximate fundamental frequencies of the ROMA frame structure, and the two types of first-order torsional modal shapes of the frame structure was investigated with respect to configurational design parameters. In sequentially, the bending, swing and the two distinct torsional fundamental frequencies of the ROMA frame were estimated comparatively. Furthermore, the effects of the equilibrated tension from the membrane array on the bending fundamental frequency of the ROMA structure was investigated by assuming a simplified mass distribution model for the thin-film structures. Finally, The simplified analytical algorithm was used for structural design of an AIS/VDE (automatic identification system/VHF data exchange system) ROMA and its performance was validated through numerical simulations and ground tests. The successful deployment and operation of the AIS/VDE ROMA on the Pujiang-2 satellite further demonstrated the practical aerospace application significance of thin-walled DCBs.

Parametric Analysis of Moment-Resisting Timber Frames Combined with Cross Laminated Timber Walls and Prediction Models Using Nonlinear Regression and Artificial Neural Networks

The light weight and moderate stiffness of multistorey timber buildings make them susceptible to increased lateral displacements and accelerations under service-level wind loading. Therefore, the fulfilment of serviceability requirements is a major challenge. In this study, linear elastic finite element analysis was used to perform a parametric study of moment-resisting timber frames combined with cross laminated timber walls. In the parametric study, various mechanical and geometrical parameters were varied within practical ranges. The results of the parametric study were used to derive simplified analytical expressions and to train artificial neural networks which can be used to estimate fundamental frequency, mode shape, top floor displacement, maximum inter-storey drift, and wind-induced acceleration. The analytical expressions and the artificial neural networks can be used for the preliminary assessment of serviceability performance of moment-resisting timber frames with and without cross laminated timber walls, under service-level wind loading.

Comparative analysis of seismic response and vulnerability of laminated bamboo frame structure under near-field and far-field earthquake actions

The study offers an evaluation of seismic response and vulnerability for a five-story laminated bamboo frame structure, assessing the effectiveness of seismic intensity measures across various damage thresholds and the modeling uncertainties involved. A structural finite element model was developed in OpenSees software, utilizing the Pinching4 model to accurately represent the non-linear characteristics of T-shaped steel connections in beam-column joints. Two collections of earthquake records, one consisting of pulse-like near-field and the other of far-field events, were utilized to examine the structure's nonlinear behavior. Additionally, vulnerability curves for various damage states were generated using the multiple stripe analysis technique, applied to both ground motion datasets. The applicability of 24 seismic intensity measures was also analyzed across various damage limit states. The modeling uncertainty under different seismic actions was further estimated using a first-order second-moment method. Ultimately, the annual collapse probability of the structure are elucidated. Research indicates that due to the influence of joint stiffness, the overall structure demonstrates dynamic characteristics that are predominantly of the first mode shape. The spectral acceleration associated with the fundamental period achieves a reduced logarithmic standard deviation in the vulnerability analysis across various limit states. Other IMs considering higher mode effects or softening period actions no longer predominate. In most cases, the modeling uncertainty under far-field seismic action is higher than that under near-field, especially at the severe damage limit states by using an efficient intensity measure. The laminated bamboo frame structure faces a much higher collapse risk in near-field than in far-field conditions.

Time-convolutional network with joint time-frequency domain loss based on arithmetic optimization algorithm for dynamic response reconstruction

Structural Health Monitoring (SHM) systems provide extensive data on in-service bridges, which is crucial for evaluating structural performance. However, data loss frequently occurs due to environmental factors and technical failures. Although missing data reconstruction problem has been largely studied, the accuracy of response reconstruction in the frequency domain is often overlooked. To address this issue, this study proposes to integrate a time-frequency joint loss function within an Arithmetic Optimization Algorithm-Temporal Convolutional Network (AOA-TCN), which leverages temporal and spatial dependencies among measurement points to reconstruct missing dynamic deflection data. The time-frequency joint loss function is enhanced with linear decay weights to increase sensitivity to low-order modal contributions, with an adaptive weighting mechanism balancing loss contributions from time and frequency domains. These adaptive weight parameters are optimized through AOA to enhance the TCN's generalizability. The feasibility and effectiveness of the proposed method are first demonstrated using simulated dynamic deflection data of a finite element model of a continuous beam bridge, and then experimentally verified on a real-world simply-supported beam bridge. The results indicate that the proposed method achieves higher data reconstruction accuracy and more precise modal analysis results compared to existing methods. The Modal Assurance Criterion (MAC) between mode shapes identified using measured data and reconstructed response reached 96.9 %, proving that the proposed method is capable of reconstructing the missing structural response while retaining its frequency-domain information, which is valuable for structural integrity assessment based on modal parameter identification of operational bridges.

Rapid assessment of seismic performance of large monopile-supported offshore wind turbines under scour

This study focuses on investigating the seismic performance of a reference 15 MW offshore wind turbine (OWT) supported by a large-diameter monopile, under various scour conditions. Fully coupled nonlinear finite element models considering 3D soil continuum for seismic response analysis of monopile-supported OWTs are very complicated and computationally expensive. Therefore, it is important to have good insight on the dynamic behaviour of monopile-supported OWTs subjected to earthquake excitations before performing high-fidelity fully nonlinear 3D simulations, which will not generally be practical in cases considering various seismic loading and scouring scenarios. The purpose of this study is to provide a fast and efficient tool to understand the interaction between the seismic behaviour of emerging large-capacity OWTs when scour erosion affects the dynamic properties of the structure. The dynamic stiffness method (DSM) is applied for the free vibration analysis of the structure. Modal superposition is used to calculate the seismic responses of the OWT by using the exact mode shapes obtained from the dynamic stiffness formulations. The rotor-nacelle-assembly (RNA) is idealized as a lumped mass at the tower top. The tower and monopile are modelled as Timoshenko beam-columns under axial compressive loading. The soil-structure interaction (SSI) is modelled using the Winkler framework, whereby the soil contribution is assumed as elastic to take advantage of the modal superposition method. Two different approaches are considered for the soil stiffness; a constant profile, and a linearly-varying subgrade modulus along the embedded depth of the pile, and both are appraised in this paper. Firstly, natural frequencies obtained from dynamic stiffness formulations are validated using experimental data from literature for the case of controlled dynamic SSI experiments, and for operating OWTs. Additionally, the natural frequency provided by a technical document for the reference 15 MW OWT is compared to the result from the DSM, where a very good agreement is observed. The seismic response time-histories of the OWT model are obtained under different input earthquake conditions, and subsequently verified by comparison with the results of finite element simulations. The effects of different scour scenarios and foundation modelling approaches on the free vibration and seismic responses are subsequently investigated. A parametric analysis is also performed using different soil properties to observe the interaction between the soil stiffness, scour condition, and seismic response. Finally, the influence of the frequency content of seismic records on the dynamic response of the OWT, specifically the tower top acceleration, the mudline rotation, and the mudline stress, is investigated considering various scour scenarios. The specific numerical case study undertaken for a reference 15 MW OWT, which is supported by a large monopile in very dense sand, shows that the seismic responses are very limited and that the elastic soil behaviour assumption is reasonable. Additionally, considering the computational efficiency, the proposed combination of DSM and modal superposition can be used for rapid seismic performance assessment of large diameter monopile-supported OWTs at the preliminary design stage to gain insight to the global dynamic response of the whole vibrating system.

Framework for electrochemical-mechanical behavior of all-solid-state batteries: From the reconstruction method to multi-physics and multi-scale modeling

All-solid-state batteries (ASSBs) are high-energy, high-power batteries. To enhance the understanding of the electrochemical-mechanical behavior in ASSBs across different scales, we developed a multi-physics and multi-scale modeling framework. This framework incorporates elastoplastic finite deformation and electrode microstructures of ASSBs, and the role of gradient plasticity in the governing equation for multiple physical fields was discussed. Utilizing X-ray computed tomography, we reconstructed the microstructure through a machine learning (ML)-informed image segmentation process. Our study clarifies the impact of electrode microstructures on concentration, stress, voltage, delamination and buckling from AM to electrode scale. Comparative analysis of the Feret diameter distribution of active materials (AMs) shows that ML-informed image segmentation outperforms two traditional segmentation methods. We observed that the asynchronous diffusion saturation of AMs, varying in shape and size, significantly influences the electrochemical-mechanical behavior of ASSBs, resulting in complicated debonding indices and J-integral distribution at the interface. The proposed upscaling homogenization procedure is demonstrated to be efficient for buckling analysis, with the shape mode closely matching existing experimental observations. These results shed light on the critical multi-physics and multi-scale coupling mechanisms in ASSBs.

A meshfree formulation for size-dependent thermal buckling and post-buckling behaviour of porous microplates on elastic foundation subjected to localized heating

The semi-analytical framework is developed for in-plane thermal stresses within the microplates under localized heating. Localized heating is modelled using Fourier Series expansions over the complete domain of the plate. These stresses within the plate are estimated after solving the in-plane thermoelasticity problem using Airy's stress approach. Utilizing these stresses, present work also studies the buckling and post-buckling behaviour of a porous metal foam microplate resting on Winkler and Pasternak elastic foundations. The plate is modelled using Reddy's third-order shear deformation theory (TSDT) and von Kármán geometric nonlinearity, and the size-dependent effects are included using the modified strain gradient theory (MSGT). Galerkin's weighted residual method converts the partial differential equations (PDEs) into algebraic equations. The post-buckling equilibrium path is obtained using the modified Newton-Raphson method. The mode shapes of the microplate for the various configurations of the plate with different boundary conditions due to localized thermal loading are plotted. Also, these mode shapes are compared with the mode shapes of the microplate due to in-plane mechanical loading. The parametric effect of porosity, elastic foundation parameters, thickness of plate, size of plate, boundary conditions and loading concentrations on the buckling and post-buckling behaviour of the plate is studied.

Finite Element Modelling for the Dynamic Behaviour Analysis of a Structure with Hi-Lok Fasteners

The number of Hi-Lok fasteners used in the assembly of aircraft structures is very high. For this reason, an efficient modelling technique is required to accurately analyse the dynamic behaviour of the structures. In this study, a modelling technique with special emphasis on Hi-Lok modelling is proposed to analyse the dynamic behaviour of a test structure with Hi-Lok fasteners. Four different finite element (FE) models to represent the test structure with the Hi-Lok fasteners were developed using MSC Software packages. The natural frequencies and mode shapes obtained from the FE models are compared with those of the Experimental Modal Analysis (EMA) in terms of total error, computational time and memory disk usage. It was found that the model D with the simplified beams representing Hi-Lok predicts the dynamic behaviour of the test structure with an accuracy of 96.6% and with comparatively low computational time and memory disk usage. This proposed modelling scheme may provide useful approaches to aircraft researchers and engineers for the dynamic analysis of the structures.

Inductive mode selective damping of structural vibrations

AbstractStructural vibrations pose significant challenges in various engineering applications and require effective damping strategies to improve the overall performance and longevity of systems. While some oscillations can significantly reduce the longevity of systems, others might contribute positively to the overall system performance. Thus, this contribution presents a novel method of an inductive damping concept, that targets only specific vibrational modes based on their mode shapes. By analyzing the used inductive damping element in the context of a single degree of freedom oscillator, it is shown, that it functions as an ideal viscous damper only if the dynamics of the electric part of the system are neglected. The concept of mode selective damping is presented, using two of these damping elements in an oscillator chain with three masses. By altering the wiring configurations connecting the two damping elements in the electrical domain, the damping behavior can be manipulated to selectively damp only specific modes according to their mode shapes.

[formula omitted]-space physics-informed neural network (k-PINN) for compressed spectral mapping and efficient inversion of vibrations in thin composite laminates

The vibrational response of structural components carries valuable information about their underlying mechanical properties, health status and operational conditions. This underscores the need for the development of efficient physics-based inversion algorithms which, given a limited set of sensing data points and in the presence of measurement noise, can reconstruct the response at locations where measurement data is not available and/or identify the unknown mechanical properties. Addressing this challenge, Physics-Informed Neural Networks (PINNs) have emerged as a promising approach. PINNs seamlessly integrate governing equations into their architecture and have gained significant interest in solving inversion problems. In the context of learning and inversion of multimodal, multiscale vibrational responses, this paper introduces a novel spectral extension of PINNs, utilizing Fourier basis functions in the wavenumber domain, commonly known as k-space. The proposed method, referred to as k-space PINN (k-PINN), offers a robust framework for adjusting complexity and wavenumber composition of the response. Notably, the spectral formulation of k-PINN, coupled with the generally sparse representation of vibrations in k-space, facilitate efficient reconstruction and learning of broadband vibrations and alleviate the spectral bias associated with standard PINN. Additionally, the spectral solution space introduced by k-PINN substantially reduces the computational cost associated with computing physics-informed loss terms. We evaluate the effectiveness of the proposed methodology on reconstructing the bending vibrational mode shapes of a thin composite laminate and identifying its effective bending stiffness coefficients. Mode shapes are initially obtained from finite element simulation, and virtual test data with added noise are generated for evaluation purposes. It is shown that the proposed k-PINN methodology outperforms the standard PINN in terms of both learning and computational efficiency. The performance of k-PINN is further demonstrated by show casing its capability in learning different selections of symmetric, anti-symmetric and asymmetric mode shapes.