A direct probabilistic method to solve state equations under random excitation

In random vibration problems, the statistical characteristics of the response, such as the mean value, correlation and variance, are often interested in by people. This paper is concerned with the statistic property of structural dynamic response under uncertain loads which are considered random processes. These random processes can either be stationary or non-stationary. A more accurate method named the direct probabilistic approach (DPA) is presented, which is proposed providing an alternative to the conventional time, frequency domain methods and the state space theory in a random vibration field. In this study, the response's statistical characteristics can be directly obtained from the statistical characteristics and the initial condition of the corresponding external loads. Finally, two examples are given to compare the DPA method with the conventional method. Good agreement is found, which strongly validates the proposed method.