International Journal of Structural Stability and Dynamics

This paper examines the nonlinear dynamics of a translational functionally graded material (FGM) plate. The plate is composed of nickel and stainless steel, and its property is graded in the thickness direction that obeys a power-law distribution. By adopting the Kármán nonlinear geometrical relations, the equation of motion is derived from the D’Alembert’s principle by considering the dynamic equilibrium relationships for the out-of-plane vibration of the plate. The equation of motion is discretized by using the Galerkin method and thus a series of ordinary differential equations with mode-coupling terms are obtained. These ordinary differential equations are then solved by utilizing the method of harmonic balance. The analytical results are verified by the adaptive step-size fourth-order Runge–Kutta technique. The stability analysis of analytical solutions is also carried out by introducing small perturbation for steady state solutions. Both natural frequency and nonlinear frequency-amplitude characteristics are presented. In the translational FGM plate, strong nonlinear mode interaction phenomenon has been detected. The nonlinear frequency response shows intensive hardening-spring characteristics. Moreover, various system parameters such as power-law distribution, translating speed of the plate, in-plane tension force, damping coefficient and external excitation amplitude are selected as the controlled variables to present parametric study. Their effects on the nonlinear dynamical response of the translational FGM plate are highlighted.

Nonlinear magneto-elastic combined resonance of parametric and forced excitations is investigated for a rotating circular plate with a variable speed under alternating load. According to the magneto-elastic vibration equations of a conductive rotating thin circular plate, the axisymmetric vibration differential equations of the rotating circular plate under transverse magnetic field are obtained through the application of the Galerkin integral method. The method of multiple scales is applied to solve the differential equations of the circular plate under alternating magnetic field, and the resonance states of the system under combined parametric and forced excitations are obtained by analyzing secular terms. The respective amplitude–frequency response equations are also derived, as well as the necessary and sufficient conditions of the system to make it stable. A numerical method is adopted to acquire amplitude–frequency response curves, bifurcation diagrams of amplitude and the variation pattern of amplitude with magnetic induction intensity and radial force. The influence of parameter variation on stability of the system is also investigated. Based on the global bifurcation diagram of the system, the influence of the change of bifurcation parameters on the system dynamics is discussed.

The dynamic stability of vortex-induced vibration (VIV) of circular cylinders has been well investigated. However, there have been few studies on this topic for bridge decks. To fill this gap, this study focuses on the dynamic stability of a VIV system for bridge decks. Some recently developed techniques for nonlinear dynamics are adopted, for example, the state space reconstruction and Poincare mapping techniques. The dynamic stability of the VIV system is assessed by combining analytical and experimental approaches, and a typical bridge deck is analyzed as a case study. Results indicate that the experimentally observed hysteresis phenomenon corresponds to the occurrence of saddle-node bifurcation of the VIV system. Through the method proposed in this study, the evolution of dynamic stability of the VIV system versus wind velocity is established. The dynamic characteristics of the system are further clarified, which offers a useful clue to understanding the VIV system for bridge decks, while providing valuable information for mathematical modeling.

With the increasing threat of terrorism attack, the probability of explosion inside the subway is very large. Reinforced concrete columns are the main supporting members of subway stations. If the columns of a subway station were subjected to near-field explosions, their damages can affect the safety of the subway after explosion. By using the finite element method, this paper established a coupling “explosive-air-concrete” model and verified the feasibility of the model through experiments. This model can be used in the damage assessment of subway station columns in terms of the bearing capacity, by which the damage of a reinforced concrete column can be divided into different levels. Furthermore, the effect of different parameters on the damage and bearing capacity of the subway station is discussed. The results demonstrate that the stirrup reinforcement ratio of a reinforced concrete is the key factor in determining the column damage under blast loadings. The present study therefore provides a key reference for assessing the damage of subway structures after terrorist attack.

This paper presents a non-stationary random vibration analysis of railway bridges under moving heavy-haul trains by the pseudo-excitation method (PEM) considering the train-track-bridge coupling dynamics. The train and the ballasted track-bridge are modeled by the multibody dynamics and finite element (FE) method, respectively. Based on the linearized wheel-rail interaction model, the equations of motion of the train-ballasted track-bridge coupling system are then derived. Meanwhile, the excitations between the rails and wheels caused by the random track irregularity are transformed into a series of deterministic pseudo-harmonic excitation vectors by the PEM. Then, the random vibration responses of the coupling system are obtained using a step-by-step integration method and the maximum responses are estimated using the 3$\sigma$ rule for the Gaussian stochastic process. The proposed method is validated by the field measurement data collected from a simply-supported girder bridge (SSB) for heavy-haul trains in China. Finally, the effects of train speed, grade of track irregularity, and train type on the random dynamic behavior of six girder bridges for heavy-haul railways are investigated. The results show that the vertical acceleration and dynamic amplification factor (DAF) of the midspan of the SSB girders are influenced significantly by the train speed and track irregularity. With the increase in the vehicle axle-load, the vertical deflection-to-span ratio ($\gamma$) of the girders increases approximately linearly, but the DAF and vertical acceleration fail to show clear trend.

Ice loads attached to a transmission tower-line system can not only increase the vertical loads on the insulators, but also cause flashover to occur more easily. Both effects can lead to an increased probability of insulator breakage. In this paper, a finite-element model of a transmission tower-line system with three towers and four span lines under the ice loads is established. Dynamic analyses of the tower-line system after insulator breakage are performed to study the dynamic responses of the system and its failure process. In addition, a parametric analysis is conducted to investigate the influence of span length and insulator length on the vibration of the system and the failure mode. The results show that a larger ice load can lead to more severe vibration of the tower-line system due to the insulator breakage. Moreover, as the span length increases, the insulator breakage can result in more serious consequences and even the cascading collapse of the transmission tower-line system. This study provides crucial reference for preventing the failure of transmission tower-line systems in heavy ice regions.

Wind-induced response analysis is an important process in the design of large-span roofs. Conventional time-domain methods are computationally more expensive than frequency-domain algorithms; however, the latter are not as accurate because of the ill-treatment of the modal coupling effects. This paper revisited the derivations of the frequency-domain algorithm and proposed a fast algorithm for estimating the dynamic wind-induced response considering duly the modal coupling effects. With the wind load cross-spectra modeled by rational functions, closed-form solutions to the frequency-domain integrals can be calculated by Cauchy’s residue theorem, rather than by numerical integration, thereby reducing the truncation errors and enhancing the efficiency of computation. The algorithm is applied to the analysis of a grandstand roof and a spherical dome. Through comparison with time domain analyses results, the algorithm is proved to be reliable. A criterion of the coupling modal combination was suggested based on the cumulative modal contribution rate of over 70%.

Dynamic progressive collapse analysis of building structures is usually conducted under sudden column loss conditions. The time length required for disabling the failed column is defined as the rise time. The rise-time effect on the maximum dynamic response of building frames under column loss is investigated in this study. Based on the work-energy principle, an approximate analytical formulation for the maximum dynamic response is derived considering the rise-time effect. The force- and displacement-based dynamic increase factors (DIFs) of a single degree-of-freedom model and a clamped steel beam are used to assess the accuracy and validity of the proposed formulation. Analysis results indicate that the DIFs decrease with increased rise time. Also, the rise-time effect decreases with increased ductility demand. Practical application of the analytical formulation to regular building frames subjected to column loss is illustrated. Primary factors related to the extent of the rise-time effect on the column-loss response are identified for design consideration.

Research on modeling the walking-induced dynamic load and its effects on structures has been increasing in recent years. Existing standards for estimating the acceleration response excited by crowd takes $\sqrt{N}$ ($N$ is the number of walking persons in a crowd) times the single pedestrian load as the crowd load, neglecting uncertainties in the related parameters. This paper proposes a method for predicting the crowd-induced structural acceleration response based on the Bayesian theory. Parameters of the crowd include the distribution of stepping frequency, the interval of arriving time and the weight of pedestrians. By combining the existing methods for calculating the structural response to a pedestrian load and the Bayesian theory, the root-mean-square acceleration along with the crowd parameters are obtained. A field investigation is conducted to study the walking characteristics of pedestrians, including the distribution of stepping frequency, walking velocity and step length. The case of a crowd moving across a simply supported beam bridge is taken for illustration. The acceleration response under the crowd load with different stepping frequencies is calculated. A comparison between the results from the Bayesian method and the design standards is conducted. The proposed method is found to yield acceptable results, and is then applied to estimating the acceleration response of a typical Tibetan heritage building, with the result compared with a field measurement.

This paper investigates the buckling behavior of graphene platelets (GPL) reinforced composite cylindrical shells with cutouts via finite element method (FEM) simulation. Young’s modulus of the composites is determined by the modified Halpin–Tsai micromechanics model while the mass density and Poisson’s ratio of the composites are approximated by the rule of mixture. Comprehensive parametric study is conducted to investigate the effects of the weight fraction and the shape of GPL fillers, the geometry of the shell and the position and orientation of the cutout on the buckling behaviors of the cylindrical structures. The results demonstrate that the addition of GPLs can significantly increase the load bearing capacity of the cylindrical shells. Larger sized GPLs with fewer single graphene layers are favorable reinforcing fillers in enhancing the buckling performances of the structures. The buckling load is sensitive to the location of the cutout with larger aspect ratio. Moreover, the orientation of the cutout is found to have significant effects on the buckling load when the orientation angle $\theta$ is falling within the ranges – $\pi$/2 $\le \theta \le$ – $\pi$/4 and $\pi$/4 $\le \theta \le \pi$/2.

This paper investigates the stability behavior of a mechanically coupled bi-stable mechanism made of two parallel and initially curved microbeams with focus on the influence of the coupled beams’ initial curvatures on the system. First, the nonlinear and coupled force–displacement equation is derived. Then, a parametric study of the coupled beams system is studied with the system categorized into different structural compartment types according to the initial curvature of the coupled beams. It is concluded that the snap-through of such a coupled bi-stable system is governed by the beams’ initial curvatures difference. The simulation results showed that these two parameters (the beams’ initial curvatures) essentially govern the structural behavior of the coupled system in satisfying the necessary structural stability condition. It is found that the smallest (critical) value of the minimum force amplitude occurs only when both initial beams’ mid-point elevations are equal to each other. Furthermore, it is shown that any probability to increase or decrease the curvature of any beam will alter the nonlinear behavior of the coupled beam system from a simple regular snap-through to a constrained-snap-through, and even to the disappearance of the snap-through. Finally, a finite element method is conducted to investigate the stability of the coupled mechanism, of which the results show a good agreement with the analytical results of this paper.

An analytical solution is proposed for the free flexural vibration of a finite cylindrical shell submerged in half-space bounded by a free surface in the low frequency range. The motion of the shell is described by the Flügge shell theory and the fluid surrounding the shell is assumed to be an acoustic media. The free surface effect is considered by satisfying the pressure release boundary condition. The accuracy of the present method is verified through comparison with the finite element solution. To throw light on the influence mechanism of free surface on the coupled modal frequencies, a modal added mass is introduced and calculated. Numerical results show that when the shell is close to the free surface, the presence of free surface will make a negative contribution to the modal added mass and finally result in the corresponding increase of the coupled modal frequencies. But the free surface effect will decrease when the immersion depth of the cylindrical shell increases. Finally, the free surface effect can be neglected if the immersion depth is higher than four times the shell radius. This conclusion is helpful to select proper test environment for an experiment on the dynamic characteristics of submerged cylindrical shells.

This paper presents a dynamic analysis procedure for predicting the responses of large, highly nonlinear, discontinuous structural systems subjected to seismic loading. The concept of equivalent nodal secant stiffness is adopted to diagonalize the conventional stiffness matrix of the structure. With the lumped-mass idealization, the decoupled equilibrium equations of the structure are then solved by the implicit Newmark integration method. Additionally, an incremental-iterative procedure is performed to ensure that the equilibrium conditions are satisfied at the end of each time step. The proposed analysis procedure has the advantages of both the conventional explicit and implicit integration procedures, but with their disadvantages removed. Through extensive applications, the results demonstrate that the proposed procedure is simple and robust for analyzing practical structural systems in terms of computational efficiency and stability.

This paper presents a new family of explicit time integration algorithms with controllable numerical dissipation for structural dynamic problems by utilizing the discrete control theory. Firstly, the equilibrium equation of the implicit Yu-$\alpha$ algorithm is adopted, and the recursive formulas of velocity and displacement for the explicit CR algorithm are used in the algorithms. Then, the transfer function and characteristic equation of the algorithms with integration coefficients are obtained by the $Z$ transformation. Furthermore, their integration coefficients are derived according to the poles condition. It was indicated that the proposed algorithms possess the advantages of second-order accuracy, self-starting, and unconditional stability for linear systems and nonlinear systems with softening stiffness. The numerical dissipation of the algorithms is controlled by the spectral radius at infinity ${\rho }_{\infty }$. It was also shown that the proposed algorithms have the same poles as the Yu-$\alpha$ algorithm, and thus the same numerical properties. Compared with the implicit Yu-$\alpha$ algorithm, the proposed algorithms are explicit in terms of both the displacement and velocity formulas. Finally, the effectiveness of the proposed algorithms in reducing the undesired participation of higher modes for solving the dynamic responses of linear and nonlinear systems has been demonstrated.

This study presents two hybrid methods, the full combination method and the simplified expression, for evaluating the fatigue life of linear structures with uncertain-but-bounded parameters subjected to stochastic excitations. First, approximate expressions of the spectral moments and spectral bandwidth parameters are derived based on the improved interval analysis via extra unitary interval and the interval Taylor expansion. Then, the lower and upper bounds of the interval expected fatigue damage rate and fatigue life are evaluated by fully or properly combining the two bounds of the spectral moments and spectral bandwidth parameters by the Tovo–Benasciutti method. Through the numerical study, the full combination method is recommended for the accurate assessment of the interval fatigue life, and the simplified expression is recommended for rapid evaluation of the two bounds of the interval fatigue life using the explicit expression. Finally, three numerical examples are adopted to illustrate the accuracy and efficiency of the proposed methods via comparison of the present results with the exact ones.

This paper is concerned with the development of the Hencky bar-net model (HBM) for free vibration analyses of rectangular plates with mixed boundary conditions and point supports. The HBM is a two-dimensional discrete net system composed of rigid segments connected by frictionless hinges and rotational springs. In the model, bending is accommodated by rotational springs at each joint while the twisting by a diagonal spring system in each grid cell. The total mass of the plate is distributed as lumped mass at each joint and the continuous boundary stiffness of plate is simulated by springs located at the edge joints. Owing to the discrete property of HBM, it is able to readily handle any boundary conditions of plates including mixed boundary conditions and point supports. The HBM is herein used to solve some vibration problems of rectangular plates with mixed boundary conditions and point supports to demonstrate its accuracy and convenience for plate analyses.