Stochastic Analysis For The Coupling Vibration And Seicmic Responses Of Train-Bridge Systems

With the rapid development of high-speed railway and the continuous increase of train speed, the dynamic interaction between trains and the supporting system has become a problem of great importance, particularly for the coupled vibration analysis of train-bridge systems. To meet the requirements on the smoothness of track and hence the safety and stability of running trains, elevated bridges can stretch for dozens of kilometers, e.g. bridges account for about 80.5% of the length of the Beijing-Shanghai express railway. A great deal of testing data and simulation-based numerical results show that dynamic interactions between trains and bridges are essentially random due to track irregularities. Unfortunately, the complexity and low efficiency of the conventional random vibration methods has considerably restricted the development of the relevant research work. So for, not many papers in this field can be found in the literature.Moreover, the frequent use of elevated bridges in high-speed railways considerably increases the probability of earthquakes taking place when trains are crossing bridges. Therefore, the dynamic responses of train-bridge systems under the action of earthquakes and their effects on the running safety of trains have become an important research subject. The strong randomness of earthquakes certainly will make train-bridge systems vibrate randomly. However, due to the time variation of train-bridge systems and the complexity of the conventional random vibration algorithm, the non-stationary random vibration analysis of train-bridge coupled systems subjected to earthquakes is too hard to be performed.In the present thesis, based on the theoretical framework of random vibration, some advanced computational mechanics methodology, such as the pseudo excitation method (PEM) for random vibration, the precise integration methods (PIM) in the time or space domain, and others, are introduced into the present research on random vibration analysis of train-bridge coupled systems. Some innovative schemes based on the above methodology have been further developed according to the characteristics of the dynamic interaction between trains and bridges. By using these powerful analysis tools, the random vibration and seismic responses of train-bridge coupled systems are investigated accurately and efficiently, and the influences of some important factors, such as train speeds, track irregularities, earthquake soil sites, and seismic apparent velocities, are discussed in detail. The main research contents are as follows: 1. The extension of PEM to time-dependent train-bridge systemsPEM was previously used only to time-independent systems, such as tall buildings or large span structures, and some time-dependent systems subjected to single-dimension stationary random excitations, In the present paper, to carry out the random vibration analysis for time-dependent train-bridge systems, PEM is strictly proven to be also applicable to the time-dependent systems that are subjected to multi-dimension or non-stationary random excitations. And the pseudo-excitations corresponding to the single-dimension or multi-dimension, single-point or multi-point fully coherent, stationary or non-stationary, uniformly modulated or non-uniformly modulated random excitations, are constituted respectively through theoretical derivation. This research work not only establishes theoretical foundation for applying PEM into the high-speed railway field, but also powerfully promotes the wide application of random vibration theory in project fields.2. Efficient precise integration calculation for dynamic responses of FE bridges subjected to a moving massWhen solving dynamic responses of bridges due to a moving mass, generally direct integration methods, such as the Newmark method, requires the position and magnitude of the inertia force of moving mass to be invariant in each integration step, so that a very small integration step size is needed to ensure sufficient precision, which will increase computational effort considerable. In order to overcome this shortcoming, PIM is extended to deal with dynamic analysis of FE bridge model subjected to a moving mass. In each time step, an iterative linear interpolation scheme based on the accelerations at the element nodes at the beginning and end of the time interval, firstly, is adopted to generate the interaction forces that vary continuously with time. And then according to the force equilibrium principle or FEM shape functions, three precise integration forms, based on the simplified, consistent and hybrid decompositions respectively, are proposed and used iteratively to calculate the bridge responses. These methods can well simulate the continuous varying of the inertia forces of moving mass both in the time and space domains, and thus can give high precision results by using large integration steps. Numerous numerical comparisons show that each proposed method is greatly superior to the Newmark method.3. Non-stationary random vibration analysis of time-dependent train-bridge systemsWhen train cross bridges, due to track irregularity, the interaction between train and bridge will generate complicated random vibration. The mass, stiffness and damping of train-bridge system is time-dependent. For such a system, the most common analysis method is the time history method of low precision. In the present paper, by combining PEM of time-dependent system and extended PIM iterative forms, a new efficient and accurate algorithm for non-stationary random vibration analysis of time-dependent train-bridge systems is proposed, which is named as PEM-PIM. According to the principle of "From easiness to difficulty", the main research takes three steps. Firstly, PEM of time-dependent system is combined respectively with three PIM iterative forms, and then used in the one-wheel vehicle and bridge coupled system to analyse and compare their computational efficiency and precision. Secondly, for the vertical vehicle-bridge system taken phase-lags between successive wheels into account, the PEM-PIM scheme, based on simplified decomposition, is adopted to investigate the statistical characteristics of vertical random responses. Thirdly, this PEM-PIM scheme is introduced into the 3D random vibration analysis of train-bridge systems, in which three types track irregularities are considered. In the numerical examples, the proposed method is justified by comparing with Monte Carlo simulation results. Also, the influences of train speeds and track irregularities on system random vibrations are discussed.4. Earthquake induced random vibration analysis for train-bridge systemsWith more and more bridges used in high-speed railways, the probability of earthquakes taking place when trains are crossing bridges increases considerably, which establishes the importance of investigating the safety of train-bridge systems under the action of earthquakes. At present, for such a problem, the time history method is the only method to deal with it. In this thesis, the lateral horizontal earthquake is assumed to be a single-dimension uniformly modulated non-stationary random process, while the excitations due to track irregularity are assumed to be multi-dimension multi-phase stationary random ones. The non-stationary random responses of train-bridge systems due to such two random excitations are calculated by applying the PEM-PIM scheme, and their time-dependent PSD and standard deviations are obtained conveniently. Besides, a new formula to estimate maximum responses, based on the first-passage failure criterion, is suggested. The numerical results indicate its reliability.5. The random seismic responses of train-bridge coupled systems with wave passage effect consideredIt is well known that for long-span bridges subjected to earthquakes, it is very important to account for the phase-lags between ground joints, i.e. the so-called wave passage effect. The seismic responses with wave passage effect considered may be quite different from the results obtained based on the assumption of uniform ground motion. In similar fashion, it is necessary to consider the wave passage effect in the seismic response analysis of train-bridge coupled systems. However, no research on such random vibration analysis has been found up to now. The present paper, for the first time, establishes the time-dependent motion equation of the train-bridge system subjected to multi-point earthquake excitations based on the concept of pseudo-static displacement. With the horizontal and vertical earthquake excitations assumed to be 2D uniformly modulated, multi-point fully coherent random excitations, the accurate non-stationary random vibration analysis for such a system is performed successfully by using PEM of time-dependent system. The numerical results show the effectiveness and accuracy of the proposed method, and the influence of seismic apparent wave velocity is discussed.