Abstract: Randomness is a basic phenomenon in nature, such as earthquake, wind, wave, high-altitude air flow, road roughness and so on. This kind of environmental load is very important for the safety and durability of structures, as well as the comfort of the people. Modern industry advances with increasing demand on mechanical analysis, and random vibration as an emerging technical discipline receives more and more attentions from the engineering and academic domain, developing rapidly and deeply while being the frontier and hotspot at home and abroad. Therefore, Applied Mathematics and Mechanics had the honor to invite Prof. Zhai Wan-ming of Southwest JiaoTong University, Prof. Li Jie of Tongji University and Prof. Lin Jia-hao of Dalian University of Technology as the guest editors, to compile this Special Issue on Random Vibration and Its Engineering Application, and from different angles to mainly reflect domestic innovations in the fields of random vibration.
Abstract: Since the first paper on the pseudoexcitation method (PEM) to compute structural random responses was published in 1985, it has gradually been accepted and applied in many industrial communities and resolved a great number of important and difficult problems. Up to date, it has not only been applied by many engineers and experts through technical papers or engineering guidelines in China, but also been introduced in detail in special chapters of some internationally published engineering handbooks, and practically used by some foreign experts. This is a review paper based on over two hundred selected papers published worldwide (mostly in China) that use or develop the PEM in eleven industrial fields, as well as some typical comments given by wellknown scholars. It is hoped that this paper may help more engineers and researchers to have a more extensive understanding of the PEM, and encourage more comprehensive and effective engineering applications of the random vibration theory and achievements.
Abstract: The governing equation and solving algorithm of the probability density evolution method for stochastic dynamical systems were outlined. On this basis, some new advances in the solution of the generalized density evolution equation were discussed, including the ensemble evolution equation and its solution, the rational criterion for partitioning of the probability space, the densification technique of point set and the information reconstruction, etc.
Abstract: System identification is inevitably affected by various uncertainties involving measurement error, modeling error, numerical error as well as environmental variation, which indicates that it is of fundamental importance to explore statistical methods to improve the robustness in identification. The Bayesian approach has attracted widespread attention in the field of system identification due to a number of advantages. On the basis of the classic Bayesian theory, this paper systematically outlined the progress of the Bayesian system identification in the context of structural dynamics. In this study, the theoretical framework for the Bayesian system identification with special emphasis on applicable conditions and the limits on the two kinds of uncertainty quantification approaches were presented. In addition, this paper reviewed some theory, implementation and practice of the Bayesian approaches applied to uncertainty quantification for modal analysis, model updating and damage detection. Finally, the trends and challenges of the Bayesian system identification were prospected.
Abstract: The marine riser is an important part connecting the undersea drilling and the offshore platform. The primary factor causing the fatigue damage of marine risers is the vortex-induced vibration. Due to the random effects of ocean currents, the vortex-induced vibration of the riser is uncertain. Quick and reliable analysis of such random vibration is of great importance for the engineering design of the riser. Compared with the deterministic excitation, the random excitation is much more difficult to analyze, and the pseudo-excitation method is an efficient tool for this problem. In recent years, the pseudo-excitation method was applied and extended by the author and his collaborators for the analysis of vortex-induced vibration of marine risers, and many achievements were made, which were briefly summarized.
Abstract: In view of the track structure as a system with stochastic parameters, the random field model for railway track systems was proposed and constructed. Then the finite element model for the track system and the multi-rigid-body model for the vehicle system were coupled based on the fundamental principle of vehicle-track coupled dynamics to establish the vehicle-track stochastic analysis model in which the temporal-spatial random variances of rail line parameters were taken into consideration. The numerical examples show that the proposed methods are reliable and efficient, and the randomnesses of railway line parameters have significant influences on dynamic responses of railway vehicle-track systems: for example, running insecurity of vehicles and damage aggravation of track structures may grow with the increases of variances of track structure parameters.
Abstract: The motion equation for wind-wave-bridge coupling systems was established, based on the combination of the finite element method and the boundary element method, to consider the characteristic parameters’ correlation of the wind-wave coupling fields. In turn, the wave induced force acting on the large-scale deepwater foundation was calculated according to the potential flow theory and the boundary element method firstly, then transferred to the finite element model of the foundation based on the finite/boundary element mapping relation; the aerodynamic forces acting on the bridge were calculated with the finite element method, including the fluctuating wind induced unsteady buffeting force and the aeroelasticity interaction induced self-excited force. By means of the pseudo-excitation method, the random vibration analysis framework for the wind-wave-bridge coupling system was developed. A sea-crossing super-large bridge scheme was taken for example. The research shows, the wind-wave coupling induced bridge foundation internal forces are significantly larger than those induced by wind alone, of which the shear forces are mainly caused by wave, and the lateral moments caused by wave are equal to those caused by wind near the seabed but are larger below. So, the wind-wave coupling effects should be considered in the design of sea-crossing bridges.
Abstract: The seismic performance of isolated bridges requires that the bridge piers should remain elastic under seismic action. The system mainly dissipates earthquake energy through nonlinear isolation bearings, so presents a typical locally nonlinear problem for seismic analysis. At present, the response spectrum method and the nonlinear timehistory method are normally used for seismic analysis of this kind of structures. In this paper, the application of the power spectrum method in seismic analysis of isolated bridges was studied. According to the design acceleration response spectrum, the compatible design acceleration power spectrum was generated at first, and then the seismic response analysis with the power spectrum method through an iteration process was carried out. The results show that the calculated seismic responses of the structure with the power spectrum method and the response spectrum method are in good agreement with each other.
Abstract: The vibration of coupled vehicle-bridge systems subjected to random deck or track irregularities exhibits typical non-stationary stochastic features. The explicit expressions for the dynamic responses of the vehicle and the bridge subsystems were first established. Based on the motion compatibility condition between the vehicle and the bridge, the explicit expression for the vehicle-bridge contact force in terms of deck irregularities was then derived. Such explicit formulation reflects the physical evolution mechanism of the coupled vehicle-bridge system. Subsequently, the evolutionary statistical moments of the vehicle-bridge contact force were obtained through direct application of the statistical moment operation rules, thereafter the evolutionary statistical moments for critical responses of the vehicle and the bridge subsystems could be calculated. In addition, a random simulation method (i.e. the Monte Carlo simulation method) was put forward based on that the contact force was explicitly expressed in terms of deck irregularities. In turn, the evolutionary statistical moments or the other statistical properties of the critical responses of the coupled vehicle-bridge system could be easily achieved. Since the physical and probabilistic evolution processes of the coupled system were coped with in a relatively separate manner, the proposed method avoided repeated solution of the motion equations for the system. Moreover, a dimension-reducing scheme was involved for the calculation of the statistical moments of the contact force and other related responses as well. All these merits enable the proposed method to be more effective for random vibration analysis of coupled vehicle-bridge systems, as compared with the previous methods. Numerical examples indicate that the proposed method has high accuracy and superior computational efficiency.
Abstract: The stochastic responses of non-linearly damped friction oscillators with viscoelastic forces under Gaussian colored noise excitation were investigated. The stochastic averaging method, which is applicable to smooth systems, was extended to non-smooth friction systems, and the stationary probability density functions of the amplitude, displacement and velocity of the system were obtained. In view of the material viscoelastic properties, the effects of friction and Gaussian colored noise on the responses of the system were studied. The study shows that the parameters of friction force, viscoelastic force and noise may induce stochastic P-bifurcations, and the system responses are very sensitive to the friction force in a certain range. In addition, the theoretical results are in good agreement with the Monte Carlo simulation results, which verifies the rationality of the proposed method.
Abstract: To investigate the influences of non-stationary earthquake excitations on the random seismic responses of composite beam cable-stayed bridges, the non-stationary random seismic responses of a composite beam cable-stayed bridge were analyzed with the multi-dimensional and multi-support pseudo excitation method to directly solve the absolute displacements by means of general FEM software. The results demonstrate that the non-stationary random seismic responses of the composite beam cable-stayed bridge under multi-support and multi-dimentional earthquake excitations can be calculated efficiently with the pseudo-excitation method based on the absolute displacement solution. The stationary assumption for the structural design will usually lead to conservative results. The traveling wave effects are significant for the responses of the large-span composite beam cable-stayed bridge and will be favorable to the displacement at the tower top and the internal force at the tower bottom, instead will be adverse to the displacement and the internal force at the main beam centre.
Abstract: The stochastic bifurcation in the saccadic system driven by noise was investigated. Firstly, the stochastic dynamic model was established by adding the additive white Gaussian noise into the existing bilateral model for the horizontal saccadic system. Secondly, the stationary joint probability density of the system displacement and velocity and the stationary probability density of the displacement with different parameters were obtained with the numerical method. Then, the results show that noise intensity and inhibitory strength of omnipause neurons may induce the stochastic P bifurcation and the number of peaks on the stationary probability density curve of displacement changes from 1 to 3 and intermittent nystagmus occurs. It is also shown that when the inhibitory strength of omnipause neurons is large enough, the stationary probability density is always unimodal and the intermittent nystagmus disappears, which has some significance for the disease treatment.