A Unified Approach To Evolutionary Random Response Problems And Its Applications

This thesis is devoted to the problem of evolutionary random responses due to evolutionary random excitations, which is an important vibration problem existing widely in engineering. The so called evolutionary random process is a kind of non-stationary random processes, which is obtained through a deterministic modulation of a stationary random process. There are two typical evolutionary random excitations in engineering. One may be generated from filtering a stationary random process through a time-variant system. The other may result from nonlinear transformation of the argument of a stationary random process. Either the responses of a time-variant system (or a time-invariant one) under evolutionary random excitations, or the responses of a time-variant system under stationary random excitations, belong to evolutionary random responses. The key to solving the evolutionary random response problem lies in obtaining the modulating function of the response. A unified approach to mean square evolutionary random response problems in linear systems is suggested in this paper. It is found that to obtain the modulating function of an evolutionary random response is equivalent to finding the transient response of the original system to a certain deterministic excitation. In general, these transient responses can be obtained by the Runge-Kutta method. By introducing Runge-Kutta integration method or the high-precision integration, the problems of evolutionary random responses for nonuniformly modulated random excitations can be solved conveniently. By comparing the obtained results with the results of complex modal analysis, it is shown that the present method is accurate enough and efficient. The method has many advantages, such as simple in formulation, easy in programing, and fast in calculating. In particular, the method can be applied to many practical engineering problems. A new method is suggested to solve the problem of nonstationary random responses of elastic-viscoelastic composite structures. The correlation characteristics of responses under uniformly modulated or ununiformly modulated random excitations are obtained. The dynamic equations of a mobile flexible manipulator on the rough road are developed by using assumed mode method. The mean square responses of flexible linkages and the manipulator paw are derived. The influence of random road undulation on these mean square responses is analysed through a numerical example. In vibration analysis of the coupled vehicle and bridge, the influence of random road undulation used to be neglected. In fact, the vibration problem of the coupled vehicle and bridge can be reduced to a response problem of a time-variant system under the united action of road undulation and a moving weight. The system response consists of two parts, namely an evolutionary random one and a deterministic transient one. Based on the unified approach to the evolutionary random response problem, suggested by the authors previously, either the random response or the deterministic response in the coupled vehicle and bridge can obtained effectively by Runge-Kutta method. Numerical examples show that the influence of random road undulation to the vibration of the vehicle is much greater than the influence to the vibration of the bridge. Finally the method of the unified approach to the evolutionary random response problem is further applied to the evolutionary random response problems of multi-degree-of-freedom nonlinear systems. Based on the statistical linearization technique, the statistic characteristics of the evolutionary random response of MDOF nonlinear systems are obtained in a handy way.