Analyzing Random Responses Of Systems To Evolutionary Nonstationary Rondom Excitations

This paper is devoted to propose a general method of analyzing random responses of systems to evolutionary nonstationary random excitation. Firstly, subjected to the evolutionary nonstationary random excitation model, the evolutionary power spectrum density function (EPSD) of excitation is given by wavelet transform. Based on the EPSD, the evolutionary random responses of systems to the evolutionary nonstationary random excitations are studied. The application and validity of presented method are illustrated in numerical examples.For explaining the validity of method presented in the paper, under some different seismic models, the evolutionary random mean-square responses of a system are evaluated under the evolutionary nonstationary random excitations and then the result are compared with simulated results. In these numerical examples, it is shown that the method presented in the paper is effective. The content of the paper includes three parts as following.1) Firstly, the advantage and disadvantage of the traditional methods ofsignal analysis are explained. Then the elementary knowledge of wavelet analysis is introduced.2) In this part, the evolutionary random excitation model is introduced. The evolutionary power spectrum density function (EPSD) of a evolutionary random excitation is given by wavelet transform.3) Based on the EPSD estimated by wavelet transform, evolutionary nonstationary random responses of a SDOF and a MDOF system are analyzed. The validity and application of presented method are illustrated in numerical examples by numerical simulation. The part is a key in the paper.4) For a MDOF system, the dynamic reliability of the system is discussed to explain the application of method present.Based on EPSD of evolutionary random excitation established by wavelet transform, a general method of analyzing nonstationary random responses under systems for evolutionary non-stationary random excitations is given. The validity and accuracy of method presented have been illustrated by numerical simulation. The method presented has certain university. The evolutionary random excitation models used in this paper is non-uniformly modulated evolutionary random excitation models. The method may be not only applied to a SDOF system, also to a MDOF system, not only to a classical damping system, also to a non-classical damping system. It can also be extended to the time-dependent system and random system. Withequivalent linearization, the method can be applied to nonlinear system also. There is no question that the method presented in the paper has important theory and practical significance.