It is well known that non-stationary response probability density function(PDF) plays an important role in the reliability and failure analysis. With current approximate or numerical methods, non-stationary approximat...
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It is well known that non-stationary response probability density function(PDF) plays an important role in the reliability and failure analysis. With current approximate or numerical methods, non-stationary approximate PDF is generally obtained in terms of the ones at discrete time instants. Repeated computation has to be conducted for the ones at other time instants since response PDF at only one time instant can be obtained after performing the solution procedure. Thus, computational efficiency suffers a major setback. In this paper, the exponential polynomial closure(EPC) method is further improved and enhanced to obtain the completely non-stationary PDF solution, which are distributed continuously in the time domain. It takes temporal base function into the PDF approximation. Unknown coefficients in the EPC solution are generalized to be explicit functions of time parameter. With the least square method, the explicit time functions can be determined based on the few simulated response PDF values. Such implementation makes continues PDF distribution in the time domain available, which greatly improves the computational efficiency without repeating computation. Two typical nonlinear systems under stationary and non-stationary random excitations are taken as examples to illustrate the efficiency of the proposed method. Numerical results show that results obtained by the proposed method agree well with the simulated ones. Besides, the relation between explicit time function and modulate function is discussed.
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