International Journal of Structural Stability and Dynamics

The core layer is very important in studying the vibration and noise problems of sandwich structures. The present paper studied the free vibration and sound insulation characteristics of FG-CNTRC sandwich plates with FG-CNT face sheets and different cores including the soft core (epoxy), hard core (aluminum) and porous metal foam core with different porosity distributions. By Hamilton’s principle the dynamic equations of FG-CNTRC sandwich plates are formulated based on the third-order shear deformation theory (TSDT), and the sound insulation expression is given under the excitation of the sound pressure. The theoretical solution of natural frequency and sound insulation are compared with the finite element simulation results and validated. The natural frequency of the square sandwich plate are compared with the rectangular case. The free vibration and sound insulation performance of FG-CNTRC sandwich plates are analyzed and discussed, and parametric studies are performed to evaluate the effects of CNT volume fraction, CNT distribution patterns, CNT orientation angles, porosity coefficient and incident angles on the vibro-acoustic characteristics of the sandwich plate. Some new results are presented to be used as references for the further research.

In this study, we investigated the effect of hygrothermal loads on the nonlinear free vibrations of a porous bi-directional functionally graded Timoshenko beam with a Winkler–Pasternak foundation. The corresponding governing equations were established according to Hamilton’s principle and von Kármán nonlinearity assumption. Using the differential quadrature and iterative methods, the nonlinear fundamental frequencies were determined. A numerical example was presented, and we showed that the discretization of nonlinear items considerably decreased the number of iterations. A series of parametric studies were performed, and we determined that (1) all the vibration mode shapes were significantly affected by the axial functionally graded index, while they were almost unchanged by the thickness-wise functionally graded index. Moreover, compared to the thickness-wise graded index, the axial functionally graded index played a more important role in the higher-order mode shapes. (2) The geometric nonlinearity considerably influenced the critical temperature rise value of the beams. Increasing the maximum deflection value increased the critical temperature rise value. (3) The influence of increase in temperature and moisture on the nonlinear fundamental frequency became stronger with increase in the functionally graded index, but it weakened with increase in the maximum deflection value.

This paper deals with the theoretical studies to investigate the in-plane eigenvalue problems and the one-to-one-to-one internal resonance behaviors of a double-cable-stayed flexible beam-structure mounted with a manipulator system (DCFBMS) under constant rotational speed. A more precise and rigorous dynamic model with proper boundary conditions has been developed in which geometric nonlinearity and coupling nonlinearity of cables and beam are considered while the manipulator has been modeled as a rigid link. The in-plane eigenvalue problem of the model considering the boundary and continuous conditions has been evaluated and graphically demonstrated. Then, the ordinary differential equations (ODEs) are obtained by Galerkin’s method and multiple scales method has been employed to further analyze the vibration attributes of steady-state responses and their stability under internal resonance condition. The nonlinear response, stability and bifurcations for one-to-one-to-one internal resonance have also been investigated by varying system parameters. Analytically obtained results have been verified by Runge–Kutta method and found to be in good agreement. The present theoretical results deliver a useful insight into the nonlinear dynamic behavior and operational stability of DCFBMS.

This paper investigates the free vibration of functionally graded material (FGM) sandwich plates supported by different boundary conditions and influenced by a three-parameter viscoelastic foundation and hygro-thermal changes. Three types of FGM sandwich plates are studied and discussed, in which the FGM layers vary according to the power law rule and consist of ceramic and metal materials. An efficient and simple four-variable integral higher-order shear deformation theory (HSDT) is employed to model the analytical solution of the considered problem. Hamilton principle is implemented to obtain the plates’ governing equations and to derive the eigenvalue equation for the free vibration study. The model is verified by comparing numerical results with previous studies on the vibration of exponentially graded plates. New results are presented in this paper showing the influences of different boundary conditions, hygro-thermal changes, viscoelastic parameters, vibration modes, material exponents, and geometric dimensions.

The new generation of China Railway Track System III (CRTS III) ballastless track structure has been found vulnerable under high-level earthquakes. However, the seismic characteristics and the damage mechanism had not been well studied. In this paper, a 4-span high-speed railway (HSR) simply supported bridge-track system model is established to investigate the seismic response and damage mechanism of the bridge-CRTS III slab ballastless track system under transverse earthquakes by nonlinear history analysis. In accordance with the results, the piers have a good seismic performance under high-level earthquake (0.57 g). The non-uniform vibration of unequal-height piers results millimeter-level inconsistent displacements between the girders. The fixed bearing is vulnerable under the earthquakes with PGA of 0.3 g and 0.57 g, indicating that the seismic design of fixed bearing should be optimized to enhance the seismic resistance under high-intensity earthquake. After the damage of fixed bearing, the friction is not enough to pull the girders to vibrate together with piers which leads the sliding of girders. The sliding of girder exacerbates the non-uniform displacements of girders and roadbed. The non-uniform vibration and residual slips of girders lead deformation of the rail, especially forming turning angles at the girder joints which may impact the safety of train operation.

Two novel seismic metamaterials models, trophy and apple core, inspired by an ancient Chinese puzzle are proposed in this study. Bandgaps below 15Hz are achieved by exclusively using concrete as the base material in the designs. Vibration modes are investigated to clarify the bandgap formation. Through comparison, we found that under the same volume, the apple core model can provide a lower frequency bandgap than the trophy model. Results from transient simulations and band structures are in good agreement, validating the accuracy of the simulation results. To broaden the bandwidth, the radii of the apple core models are varied and arranged in a gradient pattern. Transient analyses using a Gaussian wave packet and Taiwan’s Chi-Chi earthquake dataset are conducted to verify the effectiveness of the gradient apple core seismic metamaterial.

Buckling may cause drill string damage or even drilling failure. For the 3000-m-long horizontal section drill string, a simplified analysis model of drill string in horizontal well is established, and the dynamic response results of axial displacement, angular displacement and contact force are obtained. When buckling, the closer the position of drill string is to the bottom, the later the buckling time, the smaller the buckling deformation degree, the slower the growth rate of axial displacement, and the smaller the attenuation degree of angular displacement and contact force amplitude. After buckling, drill string undergoes tensile deformation and eventually remains stable in the tensile state. After stabilization, from the top of drill string to the bottom of drill string, axial displacement increment increases first, then remains unchanged and then decreases, and the relative torsion angle between different positions gradually decreases. The drill string is always in horizontal contact with the wellbore, resulting in the same contact force values at different locations. The change of well inclination angle does not affect the change law of displacement and contact force. The absolute value of angular displacement is negatively correlated with the change of well inclination angle, and the value of axial displacement increment and contact force is positively correlated with the change of well deviation angle, but the value of contact force is quite close. The research results can provide reference for alleviating the buckling of drill string in horizontal wells.

In this paper, critical buckling analysis and nonlinear load-deflection curve for sandwich beam with functionally graded material are presented based on refined zigzag theory (RZT). By using the variational principle, the equilibrium equations in buckling analysis are given based on the RZT formulations as well as the nonlinear strain-displacement relations. The solutions are also derived for eigenvalue problems in critical buckling load calculations and for load-deflection relations with initial geometric imperfection. The solutions are presented analytically, and the mathematical properties during the derivation process have been proven in order to keep the mathematical rigor. The present analytical RZT critical buckling loads are validated by the RZT FEM, which is the finite element solutions of the sandwich beam meshed by the beam elements based on RZT. These solutions are also compared by commercial software ANSYS, resulting that this approach can obtain an accurate critical buckling load. Various parameters such as aspect ratio, thickness ratio and modulus ratio are considered to investigate their effects on the critical buckling loads. The present results are compared to the beams with higher-order shear deformation theory (HSDT). From the comparisons of the RZT and the HSDT results, it is seen that both theories approach to CBT for slender beam. The results show that the HSDT overestimates the stiffness in the load-deflection curve. It is shown that the RZT exhibits the zigzag displacements at high accuracy, resulting in accurate calculation in critical buckling loads, mode shapes and nonlinear load-deflection curves than HSDT. The superiority of the RZT solutions is presented especially for the case of FGM sandwich beam with soft middle layer.

Principal-internal joint resonance of an axially moving beam with elastic constraints is investigated, where the beam is located in magnetic field excited by current-carrying wires. Based on the magnetoelasticity theory and Hamilton principle, the nonlinear magneto-elastic vibration equations are derived. The displacement function is obtained by the elastic constraint boundary condition, and then the equation is discretized into 2-DOF ordinary differential equations using the Galerkin integral method. The method of multiple scales is employed for obtaining the amplitude–frequency response equations with coupling of the first two vibration modes. Through examples, amplitudes varying with frequency tuning parameter, axial velocity, current intensity, and external excitation force are exhibited. Results indicate that as current intensity increases, electromagnetic damping increases and the amplitude decreases; As external excitation force increases and axial velocity decreases respectively, the amplitude increases and the system changes from single periodic motion to quasi-periodic motion and then to single periodic motion; The lower-order modes are always dominant when the principle-internal resonance occurs.

Ultra high voltage (UHV) transmission tower-lines systems (TTLSs) are responsible for the crucial function of transmitting and distributing electrical power over long distances, which inevitably traverse active tectonic faults when passing through seismic areas. This paper investigates the seismic behaviors of the fault-crossing UHV TTLSs, taking into account the traveling wave effects of fault-crossing ground motions. Furthermore, three scenarios (i.e. the fault located at the midspan, the side span, and the one side) according to the location of the faults relative to the TTLSs, are designated to investigate the effects of fault-crossing locations on the seismic behaviors of the fault-crossing TTLSs. The results indicate that the traveling wave effects may amplify or weaken the seismic responses and collapse of the near-fault and fault-crossing TTLSs, and the effects on the longitudinal displacement responses of the TTLS are significantly greater than those in the transverse direction, but they do not affect the distribution of the collapse weak position of the TTLSs across the fault. Besides, the effect of traveling waves on the seismic behaviors of the transmission tower further away from the fault is greater than that relatively closer to the fault. This study of the impact of the traveling wave effects and fault-crossing locations on the TTLSs serves as a valuable reference for seismic behaviors of the UHV TTLSs crossing faults.

In order to reveal the coupling parametric vibration characteristics of stay cables under combined excitation, considering the effects of cable geometric nonlinearity, inclination and the cooperative vibration of adjacent cables and bridge deck beams, a single-beam–double-cable coupled parametric vibration model excited by Gaussian white noise and deterministic harmonic excitation is established, and the coupled motion equations are derived. The Milstein–Platen method is used to directly obtain the coupled random vibration time history of the single-beam–double-cable structure, and an iterative method is proposed to counter the influence of the parametric diffusion coefficient on the numerical format. By comparing with the finite element method and the Monte Carlo numerical simulation method, the accuracy of the Milstein–Platen method in solving the vibration time history of cable–beam coupling parameters under combined excitation is first verified. Then the random displacement, power spectral density and probability density variation of the cable and beam under the combined excitation of different intensities are analyzed from the angle of random orbit. The results show that under the joint action of deterministic harmonics and random excitation, the time–domain, frequency, and probability characteristics of the single-beam–double-cable coupling system are greatly affected by the Gaussian white noise excitation proportion coefficient, and the degree of influence is different. In addition, compared with the single cable model, the vibration analysis results of the coupling model considering multiple stay cables are more reasonable.

This paper investigates the nonlinear free vibration of spinning pre-twisted functionally graded material (FGM) plates in thermal environment. Based on the Kirchhoff plate theory and von Kármán large-deformation theory, the nonlinear dynamic model is established via the Lagrange equation, where the warping effect is taken into account. The material properties are related to temperature and change according to a power-law exponent distribution. The theoretical solution of nonlinear-free vibration is obtained using the multiple scale method. The effects of power-law exponent, temperature difference, spinning speed, hub radius ratio, and twist angle on nonlinear-free vibration characteristics of the spinning pre-twisted cantilever FGM plates are discussed. The results show that the spinning pre-twisted cantilever FGM plate exhibits nonlinear hardening-spring vibration behavior, while the characteristics weaken with the increase of spinning speed. The twist angle and setting angle have coupling effects on the nonlinear vibration characteristics of spinning pre-twisted FGM plates.