Identification of probability density function for the nonlinear response of structures with uncertain input

Abstract

A method for the identification of the probability density function of nonlinear structures subjected to the earthquake with random input is presented in this paper. In the method, the dynamic response of stochastic nonlinear structures is firstly expressed in a formal solution which is a function of random parameters. The probability density evolution equation (PDEE) is then derived according to the principle of preservation of probability. The solution of this equation can put out the instantaneous probability density function. The accuracy and efficiency of the method are demonstrated by numerical examples, including a SDOF system and a steel frame. The evolution of probability density functions of the stochastic responses is observed, and it is shown that their distribution law is much irregular and far from well-known distribution types.