Computation Method To Forecast The Covariance Of The Earthquake Stochastic Response For Large Complicated Non-Linear Structures

Being an embranchment of modern applied mechanics, stochastic dynamic has been applied mainly study the statistical properties of dynamic systems'response in stochastic excitation. But it is not easy to compute the stochastic response especially for multi-degree of freedom non-linear systems. There is more difficulty in receiving covariance matrix of the earthquake stochastic response for large complicated non-linear structures.The dimension of the covariance matrix of the stochastic response has relation to the degree of freedom of systems. Generally, the dimension of the covariance matrix is twice of the degree of freedom of systems or much bigger. When the degree of freedom of systems is large, it's hard to putting computation in practice, and it also wastes too much storage space and computation time. So, a new reasonable and effectual resolving method is needed. In academic field, a lot of scholars pay much attention on how to deal with the problem.A computation method to forecast the covariance of the earthquake stochastic response for large complicated non-liner structures has been studied in this paper. The method can avoid the storage of the full covariance matrix. Is a deterministic integration method with the Karhunen-Loéve (K-L) expansion. The work of this paper contains the following three aspects:(1). The covariance of the earthquake stochastic response is represented by the K-L vectors, and then the following step K-L vectors can be integrated by any available and appropriate deterministic step by step integration scheme. At the same time, the smaller ones of the K-L vectors will be omitted because of the application of mode truncation. The efficiency of the computation will be increased, and the computation time will be saved.(2). There it is suggested that the high frequency modes react essentially in a static manner when exited by low frequencies. Then the number of iterative degree of freedom in the computation can be reduced. This will improved the computation efficiency further.(3). A 24 degree of freedom non-linear hysteretic system has been imported as an example ,which is shear type. The normal computation, K-L vectors'mode truncation computation and the computation of reducing the degree of freedom have been used. The results of these methods have been compared and analyzed. It indicates that it is feasible to compute the covariance of the earthquake stochastic response for large complicated non-liner structures using the deterministic integration method with the K-L expansion.