International Journal of Structural Stability and Dynamics

Civil engineering structures will exhibit hysteretic behavior due to damage caused by dynamic loads. Identifying the hysteretic behavior of structures is a practical and challenging problem that involves observing vibration data to determine strength and stiffness degradation. This paper proposes a modified square root central difference Kalman filter (MSRCD-KF) method to track this behavior. By combining the QR decomposition and strong tracking filtering technology, the proposed method makes the recursive calculation process unconditionally stable, while enabling the tracking of abrupt changes in structural parameters. A three degree-of-freedom (3-DOF) Duffing system is used in the simulation to verify the effectiveness of the proposed method. Numerical results show that the proposed method can converge to the true value quickly and accurately. Then, the proposed method is used to identify the structural parameters of a two-story concrete frame structure under different seismic loading sequences. In the first example, the structure is simplified as a 2-DOF linear system for which the equivalent stiffness and damping under different damage levels are identified. This information is then used to obtain the stiffness variation trend, damping ratio, and frequency. The second example uses the Bouc–Wen model to consider the stiffness and strength degradation of the structure. Finally, the experimental results demonstrate that the proposed method can accurately identify the structural parameters of nonlinear systems, and the identified hysteresis curves are in good agreement with the experimental ones.

Metal lattice structures filled with a damping material such as polymer can exhibit high stiffness and good damping properties. Mechanical simulations of parts made from these composites can however require a large modeling and computational effort because relevant features such as complex geometries need to be represented on multiple scales. The finite cell method (FCM) and numerical homogenization are potential remedies for this problem. Moreover, if the microstructures are placed in between the components of assemblies for vibration reduction, a modified mortar technique can further increase the efficiency of the complete simulation process. With this method, it is possible to discretize the components separately and to integrate the viscoelastic behavior of the composite damping layer into their weak coupling. This paper provides a multiscale computational material design framework for such layers, based on FCM and the modified mortar technique. Its efficiency even in the case of complex microstructures is demonstrated in numerical studies. Therein, computational homogenization is first performed on various microstructures before the resulting effective material parameters are used in larger-scale simulation models to investigate their effect and to verify the employed methods.

Perforated composite laminates are frequently encountered in multiple engineering applications as sub-components of complicated structures. In many of these applications, the primary objective of using the panel is to resist buckling under diverse environmental and loading conditions. This paper is mainly focused on the vibration and buckling responses of composite laminates with elliptical cutouts subjected to localized edge loads under different hygrothermal environments. Toward this, a nine-noded heterosis plate element has been utilized to discretize the plate by adopting a refined meshing pattern around the elliptical cutout. The geometric nonlinearity has been incorporated to predict free vibrations under the hygrothermal environment. Considering the plethora of applications of composite laminates in hygrothermal conditions, a new temperature/moisture-dependent model is presented by taking into consideration various mechanical loadings. For a given environmental and loading condition, the stress distribution within the perforated panel is highly non-uniform in nature and hence, a novel dynamic approach has been proposed to solve buckling problems by adopting two sets of boundary conditions. A MATLAB program has been developed to investigate the effect of various parameters such as elliptical cutout size, elliptical orientation, elliptical cutout eccentricity, thickness and boundary conditions of the laminated composite plate under diverse hygrothermomechanical loading conditions. A notable difference in the critical buckling load is observed when the locally prestressed perforated panels are subjected to complex hygrothermal environments, especially at larger elliptical cutouts and hence the importance of localized edge loads under hygrothermal environment is emphasized.

A method is proposed to obtain the exact solution for the dynamic analysis of functionally graded porous (FGP) curved beams with general boundary conditions and variable curvatures. First, the model of a curved beam of variable curvature is constructed, and then the beam is divided into a number of free beam segments via a multi-segment segmentation (MSS) strategy. Second, the first-order shear deformation theory (FSDT) is adopted to obtain the displacement fields of each segment, and then the kinetic energy and potential energy of the structure are expressed by the displacement field. Finally, the exact solution is obtained by the Hamilton principle. Using the springs to simulate various boundary conditions, the frequency parameters, modal shapes and forced vibration responses of the structure with elastic boundary conditions are calculated, with the convergence and correctness verified. Finally, effects of the FGP curved beams, such as porosity distribution types, porosity ratios, boundary condition types, geometry parameters and load types, are investigated in detail.

Dynamic analysis of an Euler–Bernoulli beam with nonlinear supports is receiving greater research interest in recent years. Current studies usually consider the boundary and internal nonlinear supports separately, and the system rotational restraint is usually ignored. However, there is little study considering the simultaneous existence of axial load, lumped mass and internal supports for such nonlinear problem. Motivated by this limitation, the dynamic behavior of an axially loaded beam supported by a nonlinear spring-mass system is solved and investigated in this paper. Modal functions of an axially loaded Euler–Bernoulli beam with linear elastic supports are taken as trail functions in Galerkin discretization of the nonlinear governing differential equation. Stable steady-state response of such axially loaded beam supported by a nonlinear spring-mass system is solved via Galerkin truncation method, which is also validated by finite difference method. Results show that parameters of nonlinear spring-mass system and boundary condition have a significant influence on system dynamic behavior. Moreover, appropriate nonlinear parameters can switch the system behavior between the single-periodic state and quasi-periodic state effectively.

A superconvergent isogeometric method is developed for the buckling analysis of thin beams and plates, in which the quadratic basis functions are particularly considered. This method is formulated through refining the quadrature rules used for the numerical integration of geometric and material stiffness matrices. The criterion for the quadrature refinement is the optimization of the buckling load accuracy under the assumption of harmonic buckling modes for thin beams and plates. The method development starts with the thin beam buckling analysis, where the material stiffness matrix with quadratic basis functions does not involve numerical integration and thus the refined quadrature rule for geometric stiffness matrix can be obtained in a relatively easy way. Subsequently, this refined quadrature rule for thin beam geometric stiffness matrix is conveniently generalized to the thin plate geometric stiffness matrix via the tensor product operation. Meanwhile, the refined quadrature rule for the thin plate material stiffness matrix is derived by minimizing the buckling load error. It turns out that the refined quadrature rule for the thin plate material stiffness matrix generally depends on the wave numbers of buckling modes. A theoretical error analysis for the buckling loads evinces that the isogeometric method with refined quadrature rules offers a fourth-order accurate superconvergent algorithm for buckling load computation, which is two orders higher than the standard isogeometric analysis approach. Numerical results well demonstrate the superconvergence of the proposed method for the buckling loads corresponding to harmonic buckling modes, and for those related with non-harmonic modes, the buckling loads given by the proposed method are also much more accurate than their counterparts produced by the conventional isogeometric analysis.

For rectangular thick plates with non-Levy boundary conditions, it is important to explore analytical free vibration solutions because the classical inverse and semi-inverse exact solution methods are not applicable to this category of problems. This work is to develop an extended separation-of-variable (SOV) method to find closed-form analytical solutions for the free vibration of rectangular Mindlin plates with arbitrary homogeneous boundary conditions. In the extended SOV method, characteristic differential equations and boundary conditions in two directions are obtained by employing the Rayleigh principle and the assumption that the mode functions are in the SOV form, and two transcendental eigenvalue equations are achieved through boundary conditions. But these two eigenvalue equations cannot be solved simultaneously since there are two equations and only the natural frequency is the unknown variable. Considering this, the second assumption in this method is that the natural frequencies corresponding to two-direction mode functions are independent of each other in the mathematical sense, thus there are two unknowns in two transcendental eigenvalue equations, and the closed-form solutions for plates with arbitrary boundary conditions can be obtained non-iteratively. From the physical sense, the natural frequencies pertaining to different direction mode functions should be the same, and this conclusion is validated analytically and numerically. The present natural frequencies and mode shapes agree well with those obtained by other analytical and numerical methods. Especially, for the plates with at least two opposite sides simply supported, the present solutions are exact.

The time-varying mean (TVM) component plays a vital role in the characterization of non-stationary winds, whereas it is difficult to extract the TVM accurately or to validate it quantitively. To deal with this problem, this paper first develops two additional conditions for the TVM extraction from the perspective of structural wind-induced vibration response, then presents an approach, based on the combination of Vondrak filter and genetic algorithm (Vondrak-G), to derive the optimal TVM from non-stationary wind speed records as well as its turbulence characteristics (i.e. gust factor, turbulence intensity, and turbulence integral length scale). Furthermore, the wind characteristics obtained by the Vondrak-G approach are compared with those by a conventional approach derived for stationary winds, demonstrating that the results by the Vondrak-G approach are evidently more accurate. This paper aims to provide an effective method for accurately extracting the TVM and then evaluating wind characteristics of the non-stationary wind.

The first studies on the dynamic behavior of railway lines go back to the 19th century, after the industrial revolution. Since then, numerous analytical solutions and numerical models have been developed toward understanding the dynamic response of moving loads. However, proposals that reproduce the vibrational behavior of subway lines remain challenging due to the complexity and number of variables involved. This paper presents two simplified numerical models built and validated with experimental data to simulate the subway dynamic behavior. The first simulated the vibration generation, whereas the other simulated the propagation throughout the soil. Analyses were conducted from 1/3 octave bands spectra, as in practice. The models showed the coefficient of friction of the wheel/rail contact does not impact the global level vibration significantly, and an estimation of this parameter (0.3) enabled an analysis of the attenuation conditions for the floating slab track (FST) system. The study of attenuations revealed FST stiffness changes are a more robust solution than changes in its mass. The wave soil propagation model has proved adequate in comparison to classic solutions, and a strategy for the estimate of error associated with two-dimensional (2D) simplifications is proposed. Despite the simplicity of the models, the numerical simulations fit the experimental data well, supporting simplified models that study subways, and promoting more vibration control evaluations at lower computational costs.

The plate-type structures are classical configurations in many engineering applications. A comprehensive understanding of the structural dynamic mechanisms is of great significance. An analytical modeling approach is established and applied to investigate the dynamic characteristics of a plate system. The model encompasses two parallel elastically restrained rectangular plates coupled through mechanical links. The linear stiffness parameters are used to simulate various structural boundary conditions and mechanical links. The wave propagation of the plate structure is considered based on the improved Fourier series method. And the theoretical formulations for the dynamic performance of the plate system are obtained by employing the energy principle and Rayleigh–Ritz method. The stability and efficiency of the proposed model are firstly validated for the plate system with classical boundary conditions by comparing the results obtained from FEM software. Subsequently, the boundary restraining parameters are analyzed to figure out their effects on the modal characteristics of the plate system. In addition, the influence of mechanical link distributions on the forced response properties of the plate system is presented and discussed. Numerical results show that the importance of both the boundary conditions and the mechanical link distributions on the dynamic behavior of the plate system. The obtained results of the dynamic investigation and parametric analysis of the plate system can be useful for the further work of vibration and noise control technology of engineering applications.

The seismic response of curved concrete bridges is complex because of the geometric irregularity and induced planar rotation of the deck, which can magnify the displacement of the deck and deformation of the bearings. To control the planar rotation and thus the seismic response of the curved bridge, an orthogonally separated isolation system (OSIS) is proposed, which consists of the upper and lower isolation parts. With this, the planar relative displacement of the common isolation system is decomposed into the relative displacement of the upper part in one direction and the relative displacement of the lower isolation part in the orthogonal direction. Therefore, the planar rotation can be restrained and the seismic demand of the isolation bearing is decoupled. The analytical models of a curved bridge and the OSIS are established in OpenSees. A suite of 118 ground motions, of which 80 are ordinary and 38 are pulse-like, is selected as input with 24 different angles of incidence so as to consider the seismic variation. Nonlinear dynamic time-history analyses of the two models are conducted to evaluate the effectiveness of the OSIS. The results show that the OSIS can effectively decrease the deck displacement, the bearing deformation and the pier column shear force, especially under the ground motions with higher intensities, while the shear force increases slightly on the abutment.

A comparative study of dynamic analysis for planar multibody systems with ball bearing joints is conducted in this study. The transmission mechanism is used as the exemplar case for illustrating the effect of ball bearing joints on the dynamic behavior of multibody systems. To reflect the energy loss, the models of continuous contact force and modified Coulomb’s friction are considered in the kinematic equations for the multibody system with ball bearing joint. With this, the dynamic characteristics of the mechanism are studied. Meanwhile, an experimental platform is built to generate the test data for demonstrating the effectiveness and correctness of the proposed method. Moreover, the effects of driving speed and clearance size on the dynamic behavior of the multibody system are investigated. The numerical results indicate that the dynamic behavior of the mechanical system is sensitive to the variation of the design parameters and the selection of parameters can affect greatly the accuracy of the mechanism with clearance joints.

The dynamic interaction between the vehicle and track is one of the most critical issues for railways, as it is closely related to running safety. Previously, many vehicle–track coupling models have been developed to study the vibration response of the system. Even though the track is periodic and infinitely extended, only a finite length of the track has often been used in the simulation, so as to reduce the effort of computation. For some special issues, it is necessary to consider the influence of long-wavelength track irregularities on the vehicle responses, and the characteristic track length can reach up to the scale of kilometer. In practice, the computational effort of using a model to accommodate kilometer-long tracks is costly and even unacceptable. To overcome this problem, this paper proposes a novel snake-like model inspired by the famous game Snake to simulate infinite tracks. In the snake-like model, each vehicle can travel on the track repeatedly via the transfer nodes installed at the end of the track. Two examples were presented to verify the accuracy and efficiency of the model proposed. The results showed that the accuracy of snake-like model is consistent with that of existing methods, but the computational effort has been reduced significantly.

The Lanzhou-Xinjiang High-speed Railway runs through a region of over 500km that is amenable to frequent winds. The strong wind and rainfall pose a great threat to the safe operation of high-speed trains. To tackle the aforementioned climate challenges, this paper investigates the dynamic response of the high-speed train-track-bridge coupling system under the simultaneous action of winds and rains for the safe operation of trains. Specifically, there are four main objectives: (1) to develop a finite element model to analyze the dynamic response of the train-track-bridge system in windy and raining conditions; (2) to investigate the aerodynamic loads posed to the train-track-bridge system by winds and rains; (3) to evaluate the effects of wind speed and rainfall intensity on the train-track-bridge system; and (4) to assess the safety of trains at different train speeds and under various wind-rain conditions. To this end, this paper first establishes a train-track-bridge model via ANSYS and SIMPACK co-simulation and the aerodynamics models of the high-speed train and bridge through FLUENT to form a safety analysis system for high-speed trains running on the bridge under the wind-rain conditions. Then, the response of the train-track-bridge system under different wind speeds and rainfall intensities is studied. The results show that the effects of winds and rains are coupled. The rule of variation for the train dynamic response with respect to various wind and rain conditions is established, with practical suggestions provided for control of the safe operation of high-speed trains.

This paper presents the free and forced vibration characteristics of a hybrid honeycomb core sandwich structure consisting of a top and bottom FG-CNT reinforced polymer composite face sheet in a thermal environment. Different thermal fields like the uniform, linear and nonlinear temperature fields in the thermal environment along the thickness direction are considered to study the dynamic characteristics of the hybrid honeycomb core sandwich structure. The mathematical model is developed using Hamilton’s principle along with the third-order shear deformation theory. Five unknown modal coefficients are found using the modal superposition principle to calculate the forced vibration response. From the free and forced vibration results, it is observed that the FG-V$\mathrm{\Lambda }$ grading pattern face sheets with lower cell size honeycomb core and with higher cell wall thickness honeycomb core show better vibration characteristics. It is noticed that the sandwich structure with honeycomb core and FG-V$\mathrm{\Lambda }$ CNT reinforced polymer composite face has a higher critical buckling temperature in the thermal environment. Furthermore, for different percentages of critical buckling temperature, the natural frequencies and vibrating patterns for uniform, linear and nonlinear temperature fields are the same for the sandwich structure with UD, FG-V$\mathrm{\Lambda }$ and FG-$\mathrm{\Lambda }$V CNT reinforced polymer composite faces. In addition, the resonant peak of the sandwich structure with FG-V$\mathrm{\Lambda }$ CNT reinforced polymer composite face in nonlinear temperature field shifts more toward the right, while that of the uniform temperature field shifts more toward the left in the velocity response.