International Journal of Structural Stability and Dynamics

Sandwich plates are popular in the research field of vibration damping and are widely used in numerous engineering domains. Sandwich plates have been studied extensively for their excellent performances by a large number of researchers. Due to the interaction between the out-of-plane and in-plane vibrations of the layers of sandwich plates, it is difficult to solve the displacements of each layer in all directions analytically. To deal with this problem conveniently and accurately, a novel analytical method is presented in this study for coupled out-of-plane and in-plane vibrations of sandwich plates, which can be applied to both free and forced vibrations of sandwich plates with arbitrary boundaries. In this method, the core plate is treated as a three-dimensional (3D) problem, and it is assumed that the displacement of the core plate varies linearly along the thickness. Based on the Kirchhoff hypothesis, the displacement solutions of the base and constrained plates of the sandwich plate in the $x$, $y$ and $z$ directions are expressed as a superposition of one-dimensional (1D) and two-dimensional (2D) Fourier series, respectively. By comparison to the published analytical solutions and numerical results of the finite element method, the proposed method achieves excellent accuracy and reliability. In addition, the influence of out-of-plane and in-plane vibrations of sandwich plates on each other is studied, and the effects of geometrical and material parameters on the dynamic behaviors of a sandwich plate are investigated. The result shows that the out-of-plane vibration affects the in-plane vibration significantly, which means that the coupling effect of the out-of-plane and in-plane vibrations must be taken into account when analyzing in-plane vibration.

Human-induced vibration is an important serviceability issue of modern structural designs, especially for light long-span structures. The common heel-drop impact is usually considered in evaluating the vibration of cold-formed steel (CFS) floors. This paper proposes a simplified equation for determining the peak accelerations under transient impacts, based on the Duhamel integral. The analytical results were validated with a comparison with the results from the heel-drop test results on a CFS floor of 3 900mm × 5 600mm (at both construction and completion stages). The dynamic responses of the floor, including peak acceleration, maximum transient vibration value (MTVV), and crest factor (a ratio of MTVV-to-peak acceleration) were analyzed in detail. The natural frequencies of the floor were obtained from the FFT and FRF analysis of heel-drop and hammering test results. The investigated on-site composite CFS floor with concrete topping was found to have a high fundamental frequency: 17Hz at the construction stage and 21Hz at the completion stage. In determining the fundamental frequency of the CFS floor, the hammering was thought to be more effective than the heel-drop owing to the phenomenon of human-structure interaction (HSI). Moreover, finite element analyses were performed to study the effects of profiled steel sheeting type (Types 28-100-800, 21-180-900, and 14-80-640) and concrete thickness (40, 50, 60, 70, 80, 90, and 100mm). With the SCSC condition (two opposite edges clamped and the other two edges simply-supported), the peak acceleration decreased by 50% when the concrete thickness increased from 40mm to 100mm.

To study the impact of upwarp deformation in the ballastless track on the jumping behavior of the high-speed vehicle, utilizing UM and ANSYS joint simulation, a vertical vibration model of high-speed vehicle on CRTS II slab ballastless track was developed based on the non-Hertz wheel–rail contact model of virtual penetration theory. By using the single-wave cosine curve simulating the characteristics of upwarp deformation in the track slab, we calculated the whole process of wheel jumping. This allowed us to analyze how the amplitude and wavelength of the track slab upward deformation influence the vibration response of the vehicle–track system. Our findings indicate that when a wheel passes through the arch section of the track slab, the entire wheel jumping process consists of distinct stages: “wheel–rail bonding, wheel–rail separation, wheel–rail impact (one or more times), and wheel–rail bonding.” As the amplitude of upwarp deformation increases and the wavelength decreases, significant changes occur in several parameters, including the vertical force between the wheel and rail, wheel unloading rate, wheel jump height, frequency, duration, and vertical displacement of the rail. Additionally, when the wavelength is between 2 and 6m and the amplitude is 8mm, the vertical force between the wheel and rail becomes zero, the wheel load reduction rate is one, and the wheel jumps. When the wavelength is less than 3m, the wheel jump height exceeds the flange height, increasing the risk of derailment. Meanwhile, during the first wheel–rail impact, the wheel–rail vertical force and the rail vertical displacement reach their maximum, potentially impacting rail service performance negatively. Finally, compared to the amplitude of the track slab camber deformation, its wavelength has a greater impact on the entire process of wheel jumping. It is recommended that attention be paid to the change in the wavelength of the track slab camber during the maintenance and repair of the ballastless track.

Based on the modified third-order shear deformation theory, the harmonic balance method, and the pseudo-arclength continuation method with two-point prediction, the nonlinear forced vibration response of incompressible hyperelastic moderately thick cylindrical shells subjected to a concentrated harmonic load at mid-span and simply supported boundary conditions at both ends is investigated. The algorithmic procedure for solving steady-state periodic solutions of strongly nonlinear systems of differential equations is presented. The structural response characteristics of shells under different excitation amplitudes and structural parameters are analyzed. The numerical results indicate that the aspect ratio of moderately thick hyperelastic cylindrical shells has a significant effect on the natural frequency ratio. Different frequency ratios lead to varying nonlinear mode coupling effects. The coupling effects among modes result in complex nonlinear behavior in the vibration response of each mode, leading to abundant multi-valued phenomena in the response curve.

This paper deals with the vibrational frequencies of deep sandwich arches to enhance their application domain and possibly use them for energy harvesting. The circular arch with porous nanocomposite core and titanium alloy face sheets having different end conditions is numerically analyzed. The middle core of the sandwich arch is made of a six-layered porous aluminum reinforced with graphene nanoplatelets. The kinematic equations are formulated in this study based on the higher-order shear deformation theory using a logarithmic function of radius. The effective properties of the nanocomposite media are modeled by employing the Halpin–Tsai modified rule. The equations of motion are determined by applying the principle of virtual displacement. The partial differential equations are reduced using the generalized differential quadrature technique to solving an algebraic eigenvalue problem. Novel numerical results are given to show the effects of geometrical parameters, material properties, and boundary conditions on the vibrations of deep sandwich arch.

This paper introduces a biomimetic gradient hierarchical multicellular structure consisting of two tree-like fractal variants: one based on vertex connections (HCV) and the other based on wall connections (HCW). We investigate their mechanical behavior and deformation through numerical simulations. Our findings reveal that, irrespective of whether they have the same wall thickness or mass, second-order and third-order structures exhibit superior energy absorption capacity (EA) and crushing force efficiency (CFE) compared to first-order structures, resulting in significantly enhanced crashworthiness performance. In the case of HCV structures with identical wall thickness, the third-order structure outperforms the first-order structure by 79.73% in specific energy absorption (SEA) and by 38.51% in CFE. Similarly, for HCW structures, the third-order variant surpasses the first-order one by 45.57% in SEA and 28.39% in CFE. We also conduct a parametric study, exploring the influence of inner circle diameter, fractal coefficient, and fractal angle on the crashworthiness of biomimetic gradient hierarchical multicellular structures. We identify the optimal fractal coefficient and inner diameter distribution range for HCV when the fractal angle is 60${}^{\circ }$. Lastly, we compare these structures with traditional multicellular tubes, demonstrating that biomimetic gradient hierarchical multicellular tubes achieve up to 50.34% higher SEA and 55.13% higher CFE. The results of this study offer valuable design insights for developing lightweight and efficient energy-absorbing structures.

This paper addresses the investigation of axisymmetric thermally induced vibrations in Functionally Graded Material (FGM) cylindrical shells. It considers temperature-dependent (TD) properties and geometric non-linearity (the von Karman effect). The study systematically solves a transient heat conduction equation using finite differences method and the Crank–Nicolson method. During the heating stages, the evaluation of thermal forces and moments takes place. Equations of motion are derived through the application of Hamilton’s principle. Spatial dependencies are discretized using the generalized Ritz method, while temporal dependencies are approximated using the $\beta$-Newmark method with Newton–Raphson linearization. A comparative analysis validates the procedure’s efficiency and precision. Parametric studies explore the influence of parameters, including the temperature-dependency material properties, geometric nonlinearity, and shell’s power-law index, providing valuable insights into FGM shell behavior under thermal shock.

To reveal the dynamic properties of cable-stayed bridges under complex external excitations, a double-cable-stayed shallow arch model induced by multi-frequency harmonic excitations is established. The cable and shallow arch exhibit primary or subharmonic resonances by sweeping excitations simultaneously and asynchronously. Galerkin method, one/two time scales Incremental Harmonic Balance (IHB) method, and Runge–Kutta (RK) method are applied to explore the nonlinear dynamic responses. Research results demonstrate that both the cables and shallow arch present soft and hard spring properties, despite the very weak hard spring of the shallow arch; one-way dynamic interaction among the cables and the shallow arch is discovered when sweeping excitations asynchronously.

This research study aims to delve into the effects of carbon nanotubes (CNTs) agglomeration on the dynamic characteristics of smart functionally graded (FG) porous sandwich plates. The structure of the sandwich plate comprises a core layer that incorporates dispersed CNTs within a polymer matrix. In addition, two layers are equipped with piezoelectric sensors and actuators. The agglomeration of CNTs is mathematically modeled using the Eshelby–Mori–Tanaka approach, accounting for both complete and partial agglomeration states. Moreover, the study takes into account the thermal-dependent behavior of CNTs. Subsequently, an optimal nonlinear proportional-integral-derivative (PID) control scheme based on the Bat optimization algorithm is applied to mitigate vibrations within the composite structure. Unlike the fixed gains of the classical PID, the nonlinear version dynamically adjusts its parameters in real time, ensuring enhanced responsiveness and stability. Furthermore, a comprehensive numerical investigation is conducted to assess the impact of several parameters on the natural frequencies in the frequency domain. These parameters encompass porosity distributions, porosity coefficients, reinforcement patterns, weight fractions of nanofillers, temperature, and the agglomeration of CNTs. The vibration attenuation performance of both nonlinear and classical PID controllers is evaluated through numerical simulations. The findings indicate the robustness and rapid disturbance rejection of the proposed control scheme.

In this paper, we solve the vibration problem of a finite bar with a viscously damped boundary in conjunction with a spring on the same side subject to the support motion on the other side. To avoid the computation of complex modes and the difficulty of orthogonal conditions for the partial differential equation (PDE) of a continuous system, two alternatives are employed. One is the analytical derivation by using the diamond rule of the method of characteristics. The advantage is that this method can yield an analytical solution. However, the disadvantage is that the method can be only applied to some simple problems such as a linear system and the one-dimensional (1D) wave equation. The other numerical method, finite element method (FEM), is incorporated into a general-purpose program to solve this problem. The advantage of the FEM is that this methodology can be applied to solve various problems such as different PDEs. Therefore, the solution obtained by using the FEM is compared with that of the analytical solution. Two special cases, only a spring and a damper alone, are also considered by using the FEM. Interestingly, the same silent area is captured in the displacement profile by using the FEM for the three cases. We also find that the displacement profiles have slope discontinuity which only occurs on the characteristic line. After the wave front arrives at the boundary, various responses appear due to different boundaries, spring, damper and both. It is found that the displacement amplitude of the general case is smaller than the other two special cases. This result matches the application of engineering practice.

The subharmonic resonances of an axially moving graphene-reinforced laminated composite plate are studied based on the Galerkin and multiscale methods. Graphene nanoplatelets (GPLs) are added into matrix material which acts as the basic layer of the plate, and a graphene-reinforced nanocomposite plate is thus obtained. Different GPL distribution patterns in the laminated plate are considered. The Halpin–Tsai model is selected to predict the physical properties of the nanocomposite. Hamilton’s principle is utilized to conduct the dynamic modeling of the plate and the von Kármán deformation theory is used. The velocity is assumed to be a combination of constant and harmonically varied velocities. The natural frequencies of the linear system with constant velocity can be obtained using the eigenvalues of the coefficient matrix of the ordinary differential equations after the governing partial differential equations of motion are discretized through the Galerkin method. The instability regions of the linear system and the amplitude–frequency relations of the nonlinear system considering the harmonically varied velocity are obtained based on the multiscale analysis. The effect of GPL reinforcement on the subharmonic resonances of the linear and nonlinear systems is analyzed in detail.

The deflection behavior of the fiber-metal laminated structures is envisaged in this research using higher-order deformation kinematics and large (finite) deformations of geometries via Green–Lagrange strain. The panel governing equation is derived using variational principle and solved numerically considering the nonlinear finite element (FE) steps. The necessary responses are obtained using in-house MATLAB computer code and compared with an in-house simulation model (prepared in ANSYS) and experimental data (using in-house experimental set-up). The results are verified and agree with the published data available in the open domain. The proposed model results show better consequences compared to the simulation results. The detailed responses are computed for the variable geometrical conditions (i.e. aspect ratio, end support, side-to-thickness ratio), loading and stacking sequences, including the metal layer placing. The inferences indicate the importance of nonlinearity in the framework of a higher-order kinematic model for analysing the metal laminated structure.