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In this paper, the stationary response of a van der Pol vibro-impact system with Coulomb friction excited by Gaussian white noise is studied. The Zhuravlev nonsmooth transformation of the state variables is utilized to transform the original system to a new system without the impact term. Then, the stochastic averaging method is applied to the equivalent system to obtain the stationary probability density functions (pdfs). The accuracy of the analytical results obtained from the proposed procedure is verified by those from the Monte Carlo simulation based on the original system. Effects of different damping coefficients, restitution coefficients, amplitudes of friction and noise intensities on the response are discussed. Additionally, stochastic P-bifurcations are explored.

It was shown previously that the synergy of the multi-degree-of-freedom (multi-DOF) and the mechanical stopper techniques is an effective way to further broaden the operation bandwidth of vibration energy harvesters. Considering the stochastic factor at the same time, this paper is devoted to developing a theoretical method for analyzing the dynamical characteristics of an impact-engaged 2DOF energy harvesting system under stochastic excitation, in which the impact is modeled as a nonlinear piecewise function. The existence of the impact and multi-DOF brings complexity in analyses, and the main theoretical method utilized in this paper is the stochastic averaging method which is suitable for multi-DOF quasi-nonintegrable systems. After that, the joint and marginal probability density functions of the system are derived, and numerical examples are shown to verify the effectiveness of the theoretical method. It is noteworthy that the theoretical method has the potential to be extended to more complex multi-DOF systems with stoppers. Subsequently, the stochastic response, bifurcations in the stochastic and corresponding deterministic systems, and the relationship between the D-bifurcation and the mean square voltage are discussed. Effects of crucial system coefficients, the impact stiffness and distance on the system are investigated as well.

In this paper, a new impact-to-impact mapping is constructed to investigate the stochastic response of a nonautonomous vibro-impact system. The significant feature lies in the choice of Poincaré section, which consists of impact surface and codimensional time. Firstly, we construct a new impact-to-impact mapping to calculate the one-step transition probability matrix from a given impact to the next. Then, according to the matrix, we can investigate the stochastic responses of a nonautonomous vibro-impact system at the impact instants. The new impact-to-impact mapping is smooth and it effectively overcomes the nondifferentiability caused by the impact. A linear and a nonlinear nonautonomous vibro-impact systems are analyzed to verify the effectiveness of the strategy. The stochastic P-bifurcations induced by the noise intensity and system parameters are studied at the impact instants. Compared with Monte Carlo simulations, the new impact-to-impact strategy is accurate for nonautonomous vibro-impact systems with arbitrary restitution coefficients.

In this paper, a train–track–bridge (TTB) interaction model that can account for coach-coupler effect is presented for stochastic dynamic analysis of a train traveling over a bridge. Based on the vector form intrinsic finite element (VFIFE) method, both the bridge and non-ballasted track are discretized into a set of mass particles connected by massless beam elements, in which the fasteners that fixed the tracks on the bridge deck are modeled as a series of linear spring-dashpot units. The multi-body train car is regarded as seven mass particles (1 for car body, 2 for bogies and 4 for wheelsets) connected by parallel spring-dashpot units. Considering the random nature of rail irregularities, the Karhunen–Loéve expansion (KLE) method is used to simulate the vertical profile of the tracks. To calculate the mean and standard deviation of the stochastic response of the TTB system, the point estimated method (PEM) based on the Gaussian integration and dimension reduction method is adopted. The proposed VFIFE–TTB interaction model is then applied to stochastic resonance analyses of a train moving on a bridge. It is shown that the present VFIFE–TTB model is able to analyze the dynamic interaction of the TTB system simply and efficiently. The influence of rail irregularity-induced stochastic vibration on the train and bridge would become significant once the resonant vibration takes place on the TTB system.

Existing stochastic dynamic response analysis requires the probability distributions of all variables in the system. Some of them are difficult or even impossible to obtain, and assumed probability density functions are often adopted which may lead to potential unrealistic estimation. This error may accumulate with the dimension of the structural system. This paper proposed a strategy to address this problem in the response analysis of a high-dimensional stochastic system. Partial measurement and finite element model of the target substructure of the system are required. The stochastic responses at several unmeasured locations are reconstructed from the measured responses. Only the variability of the substructure is considered. Other parameters outside the substructure are represented by their mean values contributing to the measured responses. The proposed strategy is illustrated with the analysis of a seven-storey plane frame structure using the probability density evolution method integrated with the response reconstruction technique. Measurement noise is noted to have a large influence on stochastic dynamic responses as different from that in a deterministic analysis. The proposed stochastic substructural response analysis strategy is found more computational efficient than traditional approach and with more realistic information of the structure from the measured responses.

To investigate the stochastic characteristics of vehicle-bridge (VB) system under crosswind, an efficient method which combines AutoRegressive Moving Average with eXogenous inputs (ARMAX) model, high-order differencing (HOD) and important sample was proposed in this paper. First, the wind turbulence spectra relative to a moving vehicle and equivalent static gust load method were adopted to simplify the turbulent wind field of VB system, and a wind-vehicle-bridge (WVB) model was established and verified. Then, an analysis framework for WVB system based on ARMAX model was proposed, and HOD method and important sample were used to improve the prediction performance of the surrogate model. Prediction accuracy and calculation efficiency of proposed AMRAX model were verified and compared by Monte Carlo simulation (MCS). Finally, the impacts of vehicle speed and wind velocity on the stochastic characteristics of train response were discussed. Results indicate that the HOD method has significantly improved the prediction performance of ARMAX model for lateral response of trains, and the train responses predicted by ARMAX model based on HOD and important sample show perfect agreement with target results. Compared with MCS, the calculation efficiencies of proposed ARMAX model are improved by about two orders of magnitude. The extreme values of the train response with different vehicle speed and wind velocity gradually obey right skewness distribution, especially the lateral acceleration.

The stochastic response of base-isolated building considering the uncertainty in the characteristics of the earthquakes is investigated. For this purpose, a probabilistic ground motion model, for generating artificial earthquakes is developed. The model is based upon a stochastic ground motion model which has separable amplitude and spectral non-stationarities. An extensive database of recorded earthquake ground motions is created. The set of parameters required by the stochastic ground motion model to depict a particular ground motion is evaluated for all the ground motions in the database. Probability distributions are created for all the parameters. Using Monte Carlo (MC) simulations, the set of parameters required by the stochastic ground motion model to simulate ground motions is obtained from the distributions and ground motions. Further, the bilinear model of the isolator described by its characteristic strength, post-yield stiffness and yield displacement is used, and the stochastic response is determined by using an ensemble of generated earthquakes. A parametric study is conducted for the various characteristics of the isolator. This study presents an approach for stochastic seismic response analysis of base-isolated building considering the uncertainty involved in the earthquake ground motion.

In this paper, the quantification of uncertainty effects on stochastic responses of interior vibro-acoustic interaction systems with moderate geometry complexities and uncertain design parameters is investigated. A variational-based stochastic model is developed to predict the vibro-acoustic responses submitted to probabilistic parameters, and it is illustrated by application to a built-up system consisting of an irregular acoustic cavity backed up a plate assembly. The model is derived from the combination of the multi-domain Rayleigh–Ritz approach, used to solve the deterministic structural–acoustic equations, together with the generalized polynomial chaos expansion (gPCE) to represent propagation of uncertainty and estimate the statistical characteristics of the responses. Benchmark comparisons are made with the Monte Carlo simulations (MCS) to demonstrate the tremendous computational advantage of the present methodology. Uncertainty analysis is performed to ascertain the influence of random parameters on responses. The results reveal that system uncertainty is significant enough to affect the vibro-acoustic behaviors and hence the consideration of input uncertainties is necessary in analyses and designs to ensure the sustainable system performance.

In this paper, a stochastic dynamic analysis method for cable-stayed bridges subjected to multi-dimensional and multi-supported earthquake and waves is established based on the pseudo-excitation method. The Monte Carlo method is used to analyze the influence of excitation nonlinearity on the bridge structure response, and the applicability of this method is verified. Stochastic response characteristic of coastal cable-stayed bridges subjected to multi-dimensional and multi-supported earthquake and waves is studied. The influence of water–structure interaction on the stochastic seismic response of main components of the cable-stayed bridge is described, and the influence of key parameters is analyzed. The results show that the influence of excitation nonlinearity on the response of the cable-stayed bridge can be neglected. A greater energy input caused by the rigid additional mass of the hydrodynamic pressure is the reason for the increasing of the seismic response. The influence of stochastic response of the underwater structure of the tower is changed with the site conditions. For the ground motion acceleration input energy being distributed in the high-frequency domain, the water–structure interaction has a greater effect on stochastic seismic response of the underwater structure of the tower. The influence of water–structure interaction on the stochastic seismic response of the underwater structure of the cable-stayed bridge increases with the increasing of the wave height and water depth.