International Journal of Structural Stability and Dynamics

To accurately and rapidly predict seismic responses, including the maximum displacement (MaxD) and maximum acceleration (MaxA), of the isolated structure considering the soil–structure interaction (SSI), five ensemble learning models, i.e. random forest (RF), gradient boosting regression tree (GBRT), extreme gradient boosting (XGBoost), light gradient boosting machine (LightGBM) and stacking model, are constructed. Firstly, a total of 96 000 nonlinear time history analyses of the isolated structure considering the SSI are conducted with the aid of OpenSees. The generated database is used for training and testing ensemble learning models. The ensemble learning models have 12 input variables in four categories, i.e. ground motion parameters, structural parameter, isolation parameters and soil parameter, and two output variables, i.e. MaxD and MaxA. The study shows that all ensemble learning models have excellent prediction performance for both training and testing datasets. The determination coefficients are larger than 0.96 and root-mean-square errors (RMSEs) are relatively small. Among the five ensemble learning models, the stacking model exhibits the best performance. In addition, the calculation method of feature importance score for the stacking model is provided. According to the feature importance analysis, the ground motion parameters have greater impact on seismic responses than other three categories of inputs. Finally, six ground motions are randomly selected to verify the generalization ability of the proposed ensemble learning models. The results show that the stacking model has a favorable generalization ability with relatively small prediction errors.

This work deals with the damping and vibration characteristics evaluation of sandwich beams based on higher-order shear deformation theories (HSDT’s). The studied sandwich beams are composed of composite materials at faces and homogeneous, isotropic viscoelastic material in the core layer. This latter (viscoelastic material) is described by complex Young’s modulus in the frequency domain. Indeed, the real part represents the stiffness, and the imaginary one describes the damping property. Nonlinear damping parameters and frequency curves are obtained using the nonlinear equation of frequency amplitude governed by multiple complex coefficients. In conjunction with a one-mode Galerkin’s procedure, the harmonic balance method is employed to obtain the nonlinear loss factor and the response frequency curves. The nonlinear frequency value and, in turn, the system loss factor ratio are obtained for various amplitudes to examine the impacts of the ply angle of fiber-reinforced composite faces, the viscoelastic shear modulus, the shear deformation model, for considering different geometric and material parameters. In the framework of this study, one attempt is to describe a better way to achieve satisfactory passive vibration control of the laminated beams.

In this paper, an improved stochastic averaging method is introduced to solve a monostable piezoelectric vibration energy harvester (VEH) model subject to basal Gaussian white and colored noises. First, the electric voltage is expressed as perturbations to the linear stiffness term and the damping term of the vibrational equation. Second, the original model is simplified into an Itô differential equation by the improved stochastic averaging method. Third, stationary solution of the Fokker–Plank–Kolmogorov function driven from the Itô equation is obtained, so that the stationary probability density functions (PDFs) of the displacement, velocity, and electrical voltage are obtained. With the help of the Monte Carlo, the effectiveness of these theoretical predictions is verified. Finally, the impacts of the nonlinear stiffness coefficient and nonlinear inertia coefficient on the responses are compared. It is found that the stiffness nonlinearity has stronger effect on the outputn electric voltage than the inertia nonlinearity.

As a critical characteristic curve of bridge structures, the influence line (IL) is effective in evaluating the bridge damage and bearing capacity. Contrary to conventional methods using static loading to obtain IL, this study proposes a methodology to determine the rotation influence line (RIL) based on the vehicle–bridge interaction (VBI) under random traffic loads. A key feature is the employment of the machine learning algorithm to determine the RIL from the upper and lower bridge response data induced by traffic flow, which is simulated using the cellular automata (CA) approach. Subsequently, by establishing a relationship between the RIL difference and the structural damage coefficient, this study identifies the bridge damage location and degree effectively. The numerical example results validate the accuracy in identifying both single- and multi-damage cases. The parameter analysis indicates that larger vehicle speed induces higher errors in identifying the RIL and the bridge damage.

The nonlinear buckling response of laminated composite cylindrical shells reinforced with graphene nanoplatelets (GNPs) is studied in this paper. The functionally graded (FG) shell reinforced by GNPs is analytically studied under external pressure and uniform temperature rise loadings. It is also assumed that the GNP-reinforced laminated composite shell is in contact with an elastic foundation. Various types of profiles are employed for the GNP distribution patterns in the shell thickness including 10 nanocomposite layers. The nonlinear strain-displacement relations of the shallow cylindrical panel are established utilizing the third-order shear deformation shell theory. Governing equilibrium equations of the laminated GNP-reinforced composite shell are formulated employing the principle of virtual displacement. The coupled system of nonlinear differential equations is solved analytically for the hinged–hinged and fixed–fixed boundaries of the shell using a perturbation-based technique. Correctness of presented formulations and obtained solutions is proved by comparisons with results from previous studies for an isotropic cylindrical shell. Novel numerical results reveal that the material properties, geometrical characteristics and load parameters significantly affect on the buckling behavior of laminated composite cylindrical shells.

Vibration behaviors of elastically supported functionally graded (FG) sandwich beams resting on elastic foundations under moving loads are investigated. The transformed-section method is first applied to establish the bending vibration equations of FG sandwich beams, then the Chebyshev collocation method is used to study free and forced vibrations. Two types of sandwich beams with FG faces-isotropic core and isotropic faces-FG core are considered. The material properties of FG materials are assumed to vary across the beam thickness according to a simple power function. Regarding the free vibration analysis, bending vibration frequencies are calculated numerically by forming a matrix eigenvalue equation. As for the forced vibration analysis, the backward differentiation formula method is employed to solve the time-dependent ordinary differential equations to obtain the dynamic deformations of the beam. To ensure the accuracy of the proposed model, some calculated results are compared with those in the published literature. Parametric studies are then performed to demonstrate the effects of material gradient indexes, stack types, layer thickness ratios, slenderness ratios, excitation frequency and speed of moving loads, and foundation and support stiffness parameters on the dynamic characteristics of FG sandwich beams.

As the frequency variation in a moving mass-plate system is seldom discussed in the previous work, this study first formulates the semi-analytical solutions of a system consisting of a moving mass on a square plate. Based on the moving mass-plate system, several finite element models with designed plate-type bridges are established to further investigate the effect of moving mass on a plate, the influence of bridge local modes, and the influence of moving loads on a bridge. The numerical results have shown that the frequency variation of a plate-type bridge can reach 30% for the first three modes. The unique phenomenon of wave propagation is exhibited in the acceleration responses of the plate-type bridge, while it is uncommon for a beam-type bridge. For design purpose, the following are remarked: (1) The use of Rayleigh damping on the stiffened bridge can effectively suppress the influence of local modes on the bridge deck. (2) The high stiffness in the moving load can be served as the damper to reduce the dynamic responses of a vehicle. (3) In the design stage of a plate-type bridge subjected to moving loads, the moving force is the most conservative one among the three moving loads.

In order to study isolation measures for plate-shell integrated concrete liquid storage structure (PSICLSS), shaking table tests were carried out to investigate the seismic responses of PSICLSS. The isolation performance of rubber isolation and sliding isolation bearings for PSICLSS was studied and shape memory alloy (SMA) was used to reduce the residual displacement of sliding isolation PSICLSS. The results show that the sliding isolation bearing can effectively reduce the seismic response of PSICLSS; however, there is a large residual displacement in the isolation layer. On the other hand, SMA-sliding isolation can provide a reliable recentering capability for isolating PSICLSS and does not cause amplification of structural response.

Real-time hybrid simulation (RTHS) is an economical and reliable method for the evaluation of structural dynamic performances, and the fixed analytical substructure model is often used in RTHS which may affect the accuracy of results. In this study, a real-time hybrid simulation platform (RTHSP) developed by configuring a generic National Instruments (NI) controller with hybrid programming strategy is presented in detail. The dynamic performances of a scaled base isolated structure, where the unscented Kalman filter (UKF) was used to update the analytical substructure Bouc–Wen model during the RTHSs was evaluated by presented RTHSP. RTHS of a base-isolated structure was performed where a lead rubber bearing (LRB) was tested physically as the experimental substructure of a part of the isolation layer and the superstructure with the rest of the isolation layer model updated by UKF was considered as the analytical substructure. Under the excitation of three natural earthquakes, the RTHSs with and without UKF updating were compared and analyzed the differences between the two. The results indicated that the displacements of experimental substructure generated by RTHS with UKF updating are the largest, while the relative displacements and acceleration of superstructure are the smallest overall, and the dynamic characteristics of the isolation layer of the analysis substructure updated by UKF are different from that without updated, which reflected the more authentic dynamic mechanical performance of the base-isolated structure under earthquake excitation. In addition, the RTHSP and the hybrid programming strategy are verified to be reliable in tests and experiments, and the components and implementation of a RTHSP for base-isolated structures is described in detail, providing a reference for research on RTHS method.

A split-type two-axle vehicle for bridge indirect measurement is proposed to address the deficiencies of single-axle and conventional two-axle vehicles. At first, the conceptual design of the split-type two-axle vehicle is put forth, and the analytical solution for the vehicle-bridge interaction (VBI) system response is derived. After that, the regularity of the vehicle frequency response function is studied, and the numerical analysis method is utilized to validate the analytical solution. Based on the theoretical findings, the vehicle frequency and speed are studied to investigate their impacts on extracting bridge frequencies from vehicle responses. The results indicate that a peak will form in the frequency response function (FRF) curves when the input frequency is near to the vehicle frequency. The single peak phenomenon will occur when the zero-point condition of the FRF from the contact point to the vehicle body is remarkably close to the second vibration frequency of the vehicle. It is preferable for the first frequency of the vehicle to be higher than that of the bridge since this helps to extract the bridge frequency. On the other hand, at low speeds ($\le$ 43.2km/h), higher vehicle speeds will result in a greater distance between the peaks of the left- and right-shifted frequencies of the bridge, wider frequency bands, and lower spectral resolution, which is not conducive to bridge frequency identification.

This paper studies electro-thermal buckling in a flexoelectric microbeam. This first-of-a-kind study focuses on two case-specific types of buckling in microbeams, which are essential to microstructures. Because of the electric fields and high temperatures in their environments, microbeams are susceptible to electro-thermal buckling more often than mechanical buckling. In addition, microstructures can exhibit flexoelectricity. As such a thorough understanding of electro-thermal bucking is extremely important. In this paper, we begin with extracting the equations governing flexoelectric microbeams from size-dependent flexoelectric theories. We then derive closed-form solutions for said equations. We explore various boundary conditions and, with respect to the load, analyze the various pre-buckling and buckling modes. Our study shows that buckling does not occur in some boundary conditions, and electrical curvature is very important in isotropic and homogeneous flexoelectric microbeams. In the end, the paper presents electro-thermal buckling results for specific boundary conditions as well the probability of buckling.

The Bouc–Wen nonlinear hysteretic model is widely used in nonlinear systems, and it is difficult to identify the parameters of Bouc–Wen model because of its high nonlinearity. In the paper, a hybrid genetic algorithm combined with sequential quadratic programming is proposed to solve the problem about the parameter identification of Bouc–Wen model. Sequential quadratic programming method has good local convergence and superlinear convergence rate. Therefore, compared with the genetic algorithm, the proposed identification method can accelerate the convergence speed in parameter recognition of Bouc–Wen model and achieve excellent recognition accuracy. Through the function test and the numerical simulation of the shear structure, it is proved that the proposed method has high convergence speed and accurate identification. In addition, the theory and method proposed in this paper are combined with Bouc–Wen model to identify parameters of overall restoring force model of the energy-dissipation structures, the identification results are in good agreement with the experimental results, verifying reliability and accuracy of the model and robustness of the proposed identification method.

Storage tanks are extensively used containers in various industries for storing diverse liquids. The sloshing of liquid in these containers, often caused by earthquakes, is an emerging issue in the context of damage sustained by tanks. Thus, the seismic resilience of a tank is a critical performance criterion in tank design. Given the complexity of liquid sloshing, the fundamental characteristics of this phenomenon must be examined to gain insights into fundamental sloshing behavior. Liquid sloshing typically involves a combination of fundamental and higher sloshing modes, and the modes and frequencies of liquid sloshing are therefore crucial for assessing this complex behavior. In this study, a shaking table test was employed to analyze the characteristics of liquid sloshing modes. The shapes of the first three sloshing modes under unidirectional excitation were determined and used to validate their symmetry. The findings indicate that the first sloshing mode exerts a more pronounced influence on liquid sloshing during free oscillation induced by unidirectional and horizontal excitation. The modal contribution factor of the first sloshing mode escalates with an increase in the ratio of the liquid level to the length of the tank parallel to the shaking direction, eventually converging toward a constant value.

Flexible lightweight arched structures are finding increasing use as components in smart engineering applications. Such structures are prone to various types of instability under moving transverse loads. Here, we study deformation and vibration of a hinged circular arch under a uniformly moving point load using geometrically-exact rod theory to allow for large pre- and post-buckling deformations. We first consider the quasi-statics problem, without inertia. We find that for arches with relatively large opening angle ($\sim$160${}^{\circ }$) a sufficiently large traversing load will induce an out-of-plane flopping instability, instead of the in-plane collapse (snap-through) that dominates failure of arches with smaller opening angle. In a subsequent dynamics study, with full account of inertia, we then explore the effect of the speed of the load on this lateral buckling. We find speed to have a delaying (or even suppressing) effect on the onset of three-dimensional bending–torsional vibrations and instability. Based on numerical computations we propose a power law describing this effect. Our results highlight the role of inertia in the onset of elastic instability.