Stochastic Analysis For Dynamic Interaction Of Vehicles And Structures

In 1964, the successful operation of Shinkansen in Japan signifies the coming of the era of modern high speed railway transportation. Later, France and Germany develop TGV and ICE high speed train, respectively. After more than 40 years of development, such high speed transportation has become the most economical and efficient land transportation system. With the increasing of vehicle velocity, the dynamic interaction between vehicles and neighbouring structures such as the rails, groundbasis or nearby buildings, is received more and more attention. This is because, on one hand , the running of vehicles will induce vibration of surrounding structures. On the other hand, the dynamic reaction of such structures will affect the stable and safe operation of the vehicles considerable. A great deal of testing data and simulation-based numerical results show that dynamic interactions between vehicles and neighbouring structures are essentially random. Unfortunately, the complexity and low efficiency of the conventional random vibration approaches has considerably restricted the development of the relevant research work. So far, not many papers in this field can be found in the literature. In the present ph.d thesis, based on the theoretical framework of random vibration, some advanced computational mechanics methodology, such as the pseudo excitation method for random vibration, the precise integration methods in the time domain or the space domain, the symplectic geometric scheme, which is closely related to Hamiltonian duality system, and others, are introduced into the present research on dynamic analyses of various coupled vehicle-structure systems. Some innovative schemes based on the above methodology have been further developed, which can be summarized as follows:1. Vertical random vibration analysis of vehicle-track coupling systemsThe main difficulty in the random vibration analysis of vehicle-track systems is the prohibitive computational effort required when using the conventional approaches. In addition, the process is also quite complicated. In the present paper, the tack is regarded as an infinitely long periodic structure. The pseudo excitation method (PEM) and the symplectic geometric method are combined to perform the random vibration analysis. That means, the random unevenness of the rail-surfaces are firstly transformed into the summation of a series of harmonic unevenness in terms of the PEM, then the symplectic approach is used in the solution of the frequency-response characteristic of the periodic railway structure, finally the random responses of the couples vehicle-railway system are computed by means of the PEM accurately and efficiently. It is noted that analyzing a typical substructure with periodical boundary conditions will produce the frequency-response characteristic of the entire railway, therefore the efficiency of this approach is much higher that usual FEM-based approached, even reaches more than 100 times for a typical numerical example. Numerical comparisons also show the suitability of the coupled model and the traditional rigid track model, as well as the influences of track damping and vehicle velocity on the system random vibration.2. Traffic induced non-stationary random wave propagation in layered soil media.Moving vehicles will induce track random vibration, which will propagate through thenearby ground, typically layered soil media. Such kind of non-stationary random wave propagation problems is in general quite difficult to solve. In this thesis, a track-ground coupling system is set up, by which the rail is modeled as a single infinite Euler beam connected to sleepers and hence to ballast. This ballast rests on the ground, which is assumed to consist of layered transversely isotropic soil. The random wave propagation problem is introduced into a Hamiltonian duality system. First, the non-stationary power spectral density (PSD) and the time-dependent standard deviation is derived conveniently by means of PEM. Then it is proved that in the frequency-wave number domain the coefficient matrix of wave propagation state equation is Hamiltonian, which can be solve accurately by using the precise integration method (PIM). At last in order to decrease the computational effort, an improved computational procedure is proposed, which takes advantage of the transverse isotropic property of the layered soil to reduce the threefold iteration process into a twofold one. In the numerical examples, the statistical characteristic of the ground response and the effect of correlation between loads are studied.3. An accurate and efficient algorithm for dynamic analysis of FE structures subjected to moving loadsWhen dealing with moving loads, generally direct integration methods, such as the Newmark method, are used which require the position and magnitude of the load to be invariant in each integration step, so that a very small integration step size is needed to ensure sufficient precision, witch can increase computational effort considerable. In order to overcome this shortcoming, the precise integration method (PIM) is extended to deal with dynamic analysis of FE structures subjected to moving loads.In each time step, based on FEM shape functions or the force equilibrium principle, two alternative decomposition procedures, i.e. consistent decomposition and simplified decomposition, are proposed. The resulting methods allow the position of the load and its magnitude to vary with time in each integration step and thus reduce the computational error considerable. When the time step stratified some conditions, the consistent decomposition procedure can give results up to computer precision. The simplified decomposition procedure is relatively less accurate, but very convenient for using. Numerous numerical comparisons show that either proposed method is greatly superior to the Newmark method. 4. Non-stationary random vibration of bridges subjected to moving loadsIt is well know that the random vibration analysis of vehicle-bridge coupling system is a very difficult problem. As the fundamental of this problem, the dynamic analysis of bridge subjected to random moving loads is received much attention in recent years. Some research papers have been published. However, most of these papers used relatively simple bridge models and adopted analytical solution or inefficient numerical method to get stochastic response. The modal superposition is used in the analysis, but the cross-correlation between modal responses is usually neglected in order to decrease the computational effort. Moreover the investigation of the influence of the correlation between loads for multi-load problems is lacking. In the present paper, a FE bridge model is used, An efficient method based on PEM and PIM is proposed, which overcome the computation bottleneck. Numerical examples investigate the dynamic statistical characteristic of a simply supported beam and of a three non-uniform span beam, and discuss the effect of the cross-correlation between modal responses and that of between loads, and the type of random loads.5. Efficient dynamic analysis for non-stationary random vibration of vehicle-bridge systemsWhen vehicles cross bridges, due to track irregularity the interaction between vehicle and bridge will generate complicated random vibration. The mass, stiffness and damping of vehicle bridge system is time dependent. For such a system, there is no mature random vibration formulation to deal with it. According to the principle of "From easiness to difficulty", the present paper takes two steps in the research work.First, the pseudo excitation method (PEM) is extended to handle the random analysis of time-dependent systems, in which the PSD and deviation is derived. The statistical characteristics of vertical dynamic responses for vehicle bridge system are investigated. Then, the extended PEM is introduced into 3D dynamic analysis, in which three types track irregularity are considered. To reduce the computational effort a vehicle bridge interaction (VBI) element is adopted by considering the feature of stochastic analysis procedure. In the numerical examples, the proposed method is justified by comparing with Monte Carlo simulation results. Also, a method, based on the 3σrule for Gaussian stochastic processes, to estimate maximum responses is suggested. Examples include a train moving across both simply supported and three-span continuous bridges and some observed phenomena are discussed.