International Journal of Structural Stability and Dynamics

This research presents the geometrically nonlinear investigation of functionally graded saturated porous material (FGSPM) plate under undrained conditions. In conjunction with von Karman’s nonlinearity, the refined shear deformation plate theory (RSDPT) is implemented to model the FGSPM plate. The effective material characteristics of the saturated porous plate change constantly in the thickness direction. The pores of the saturated porous plate are examined in fluid-filled conditions. Thus, the constitutive equations are established using Biot’s linear poroelasticity theory. The governing equations are developed by combining a nonlinear finite element technique with Hamilton’s principle. Then, the direct iterative approach is utilized to extract the geometrically nonlinear numerical results. The emphasis is placed on exploring the effects of numerous parameters such as Skempton coefficient, volume fraction grading index, porosity volume index, porosity distributions, and boundary conditions during the extensive numerical analyses on the linear frequency, large amplitude frequencies, and nonlinear central deflections of the FGSPM plate. It is evident from the investigation that saturated fluid in the pores substantially impacts the nonlinear deflection and vibration behavior of the FGSPM plate.

Analytical solutions based on three-dimensional (3D) elasticity for the vibrations of functionally graded material (FGM) plates are valuable for assessing the validity and accuracy of various plate theories and numerical approaches. Few benchmark 3D analytical solutions for the vibrations of FGM plates are available in the literature. In this study, analytical solutions based on Fourier series and 3D elasticity were developed for the first time for the vibrations of FGM rectangular plates with two simply supported opposite edge faces. The distributions of the properties of FGMs through the thickness follow a simple power law. The proposed solutions were validated by conducting comprehensive convergence studies on the vibration frequencies of square plates with different thickness-to-side ratios and boundary conditions as well as comparisons with published results. The benchmark nondimensional frequencies were tabulated for plates with free boundary conditions on the top and bottom faces and six combinations of boundary conditions on the other two faces. Moreover, the effects of aspect ratio and gradient index on the vibration frequencies of FGM plates were investigated. The influence of the thickness ratio of the FGM layer to the homogenous layer on the vibration frequencies of sandwich plates with FGM face sheets and a homogeneous core was also studied.

To study the probabilistic distribution of maximum wheel unloading rate of high-speed trains and its temporal correlation when a train passes over a bridge, a method for the estimation of the extremal index is proposed. Using the time series threshold theory, the maximum value cumulative distribution function (CDF) when the wheel unloading rate is regarded as a time series is derived and validated. This approach can also address dependent series, which the traditional probability distribution function formulas could not. Then, the difference between treating the wheel unloading rate as a time series and independent series is investigated using Monte Carlo simulations. Finally, the influence of the number of calculation steps on the threshold is studied, and the differences between thresholds calculated by different extremal indices when considering the number of trains running during the service period of the bridge are explored. The maximum value CDFs of the wheel unloading rate for different track irregularities, bridge lengths, and vehicle speeds are investigated for a three-span simply-supported bridge. The results show that the differences in the maximum value probability density functions (PDFs) obtained by considering the wheel unloading rate as time series and independent random series cannot be ignored. However, when studying a high-confidence level problem, such as the threshold of the wheel unloading rate, the difference between the two approaches is small enough. As the number of calculation steps increases, the extremal index will gradually decrease. When considering a long-distance high-speed rail line, its shorter segment can be used to study the threshold of the wheel unloading rate.

This paper is concerned with coupled vibration of rotating composite laminated beams under hygrothermal environment. The governing equations of the coupled vibration of the beams considering hygrothermal effects and rotating motion are derived on the base of d’Alembert principle. Green’s function method is adopted to obtain the flapwise-edgewise coupled vibration characteristics of the beams. Then, a comprehensive parametric study on natural frequencies of flapwise and edgewise bending vibrations is numerically performed. Results indicate that the flapwise-edgewise coupling factors are essential for the vibration analysis of the high-speed rotating structures. Temperature variation, moisture concentration, rotating speed, and design parameters have a significant influence on the coupled vibration characters of the beams, and thermal expansion deformation is nonnegligible in the coupled vibration analysis.

This paper examines the deflection and vibration of the circular nanoplates made of functionally graded (FG) materials. The material properties of the system vary across the thickness based on the power-law distribution. The system is assumed to be subjected to hygro-thermo-electrical loadings based on nonlinear relations. The first-order shear deformation theory (FSDT) is applied to model the circular plate as a continuous system. The nonlocal strain gradient theory is employed to consider the small-scale impacts. The dynamic equations of the motion of the FG circular nanoplate for diverse boundary conditions are derived using Hamilton’s principle, and the differential quadrature (DQ) procedure is used to obtain the deflection and frequency of the system in a discrete state. The effects of various parameters, such as small-scale factors, FG material characteristics, external voltage, and hygro-thermal loadings, on the vibration of FG circular nanoplates are explored.

This paper is concerned with numerical simulation of both dynamic stability and responses of beams on elastic foundations under a pulsating axial parametric load in a single matrix method. First, the equation of motion of a beam on an elastic foundation with damping is derived and decoupled into a Mathieu–Hill equation. Three different elastic foundations are considered and compared: Winkler, Pasternak, and Hetenyi models. Then a novel numerical simulation algorithm is proposed to investigate both the dynamic stability and the responses of the beam simultaneously. Accurate instability diagrams are obtained by the numerical simulation and are substantiated by vibration response curves obtained from the same method. These numerically accurate diagrams are used to calibrate the approximate instability boundaries of various orders of Hill infinite determinants from the classical Bolotin method for the first time. A detailed discussion is presented on effects of various aspects including elastic foundation models, damping, and static and dynamic loads. The results provide insights into the efficient and safe application of beams on elastic foundations in engineering. The proposed numerical method can be extended to analyze dynamic stability and vibrations of systems under arbitrary parametric excitations where Mathieu–Hill equations are involved.

Random perturbations in nature described by non-Gaussian excitation models are far more widely applied and development prospects than that of Gaussian excitation models in practice. However, the stochastic dynamics research of non-Gaussian excitation is still not very mature. In this work, radial-basis-function-neural-network (RBFNN) is applied for calculating the stationary response of single-degree-of-freedom (SDOF) nonlinear system excited by Poisson white noise. Specifically, the trial probability-density-function (PDF) solution of reduced generalized-Fokker–Plank–Kolmogorov (GFPK) equation is constructed by a suitable number of Gaussian basis functions (GBFs) with a fixed set of means and standard deviations. Subsequently, an approximate squared error of the GFPK equation in a finite domain is considered. Together with the normalization condition, the approximate squared error can be minimized by establishing a Lagrangian function, and then the optimal weight coefficients associated with the approximate PDF solution are solved from a system of linear algebraic equations. For demonstrating the effectiveness of the proposed procedure, two specific examples are presented. The corresponding reduced GFPK equation is truncated with higher order for the strong non-Gaussian case. The precision of the analytical solution is verified against the Monte Carlo simulation (MCS) data. In addition, all the results indicate that RBFNN shows fairly high efficiency under the premise of ensuring high precision in the whole computational procedure.

Forced and free dynamic responses of nanobeams resting on a three-parameter foundation subjected to a moving force in magneto-hygro-thermal conditions are investigated based on the nonlocal strain gradient theory. Also, a detailed parametric study is conducted to identify the impact of slender ratio, axial and distributed tangential loads on the vibration characteristics and dynamic phenomena of the small-scale system. Comparative studies with existing results in the literature are performed to ensure the accuracy of the presented model and solution approach. Analytical and numerical methods are implemented to detect the effects of foundation coefficients, environmental conditions, geometrical and scale parameters on the dynamic amplification factor, critical moving force velocity, cancellation, and maximum free response mechanisms of the system. The outcomes revealed that the critical moving force velocity is enhanced by ascending the slender ratio, elastic, and shear moduli of the foundation. It is found that when the damping factor is considered for the foundation, it is feasible to prevent the occurrence of the cancellation phenomenon. Also, it is concluded that by fine-tuning scale parameters and environmental conditions, unwanted vibration of the system can be suppressed. The attained results of this study can be helpful in the vibration control of nanoscale actuators, switches, and resonators.

To investigate the stochastic characteristics of vehicle-bridge (VB) system under crosswind, an efficient method which combines AutoRegressive Moving Average with eXogenous inputs (ARMAX) model, high-order differencing (HOD) and important sample was proposed in this paper. First, the wind turbulence spectra relative to a moving vehicle and equivalent static gust load method were adopted to simplify the turbulent wind field of VB system, and a wind-vehicle-bridge (WVB) model was established and verified. Then, an analysis framework for WVB system based on ARMAX model was proposed, and HOD method and important sample were used to improve the prediction performance of the surrogate model. Prediction accuracy and calculation efficiency of proposed AMRAX model were verified and compared by Monte Carlo simulation (MCS). Finally, the impacts of vehicle speed and wind velocity on the stochastic characteristics of train response were discussed. Results indicate that the HOD method has significantly improved the prediction performance of ARMAX model for lateral response of trains, and the train responses predicted by ARMAX model based on HOD and important sample show perfect agreement with target results. Compared with MCS, the calculation efficiencies of proposed ARMAX model are improved by about two orders of magnitude. The extreme values of the train response with different vehicle speed and wind velocity gradually obey right skewness distribution, especially the lateral acceleration.

With the development of pre-fabricated composite structures, concrete filled steel tubular (CFST) columns have been widely used, and researches on T-shaped CFST slender columns have attracted much attention. Since ordinary T-shaped CFST columns have weak constraint on concrete at the sectional concave angle region and local buckling easily occurs in this region, a multi-cellular T-shaped concrete filled steel tubular (MCT-CFST) column was developed for improving the axial resistant performance. In this study, the global stability performance of MCT-CFST slender columns under uniaxial eccentric compression was investigated. Firstly, three pin-ended MCT-CFST slender columns were tested under eccentric compression with different eccentricities. Secondly, a refined finite-element (FE) model of MCT-CFST column was established, and the load–displacement curves, Mises stress and deformation diagrams from the FE analysis were compared with the experimental results to verify the validity of the FE model. Moreover, based on the validated FE model, a parametric analysis was carried out to study the effects of normalized slenderness ratio, thickness of steel plate and material strength on the global stability performance of MCT-CFST slender columns under combined axial and bending loads. Finally, $N$-$M$ interaction curves were obtained from the numerical simulations, and these results were considered to provide valuable references for designing MCT-CFST slender columns in engineering practice.

In this paper, we propose a new multicellular design of assembled multi-frusta with alternate orientations and varied taper angles for effective energy absorption applications. Extensive crush test experiments, comprehensive finite-element simulations and analytical modeling were carried out to evaluate the energy absorption performance of the newly proposed multicellular assemblies. The performances of these assemblies are calibrated against conventional assembly of uniform tubes. Two aspects of the work were parametrically examined. The first was concerned with the effect of the frusta taper angle, while the second was concerned with the multi-frusta layout on the energy absorption of the proposed multi-frusta assembled structures. The results reveal that the face centered square layout with an appropriately selected taper angle possesses the optimal high specific energy absorption, low peak force, and smooth crushing force curve, which makes it a crashworthy device.

This paper attempts to demonstrate the vibration response of porous Functionally Graded Material (FGM) plate with variable thickness. For the first time, the porous tapered FGM plate being considered is mathematically modeled and assumed to be resting on a linear, parabolic, sinusoidal, and exponential varying Winkler’s elastic foundation. The even and uneven porosity distribution as a micro-defect is assumed in a tapered FGM plate that varies according to well-defined mathematical rules. The tapered FGM plate, across the edges, is supported with various boundary conditions. Simple Power (P-) and Sigmoid (S-) Law have been chosen for the homogenization of material properties that are tailored in the thickness direction. First-order shear deformation theory (FSDT) is applied to describe the displacement function for computing the strain field. The variational approach has been used to establish the formulation for free vibration response. The equation of motion has been derived using Hamilton’s principle and solved by implementing Galerkin Vlasov’s method. Parametric studies on elastic foundations have been done to explore the results and relevance to the real problems. It was observed that variable foundation has a significant effect on the tapered FGM plate rather than the tapered homogenous plate. In addition, it was witnessed that the effect of variable foundation effect diminishes as a constraint on the edges of the tapered FGM plate increases. Also, some benchmark results based on the porosity effect and the influence of variable elastic foundations are exhibited in this study for future reference.