Abstract
In structural and mechanical engineering, problems involving unpredictable or stochastic variables or processes are frequently encountered, and in these cases a probabilistic analysis may be most rational way of approaching the problem. In many problems involving the dynamical behaviour of mechanical systems, the dominating source of uncertainty or unpredictability is the excitation. If the excitation is given in terms of a stochastic process, the response of the mechanical system is also a stochastic process. In order to assess the probability of accurance of extreme events and evaluate possible fatigue damage in the structure, it is necessary to be able to evaluate the response statistics with reasonable accuracy. In this article the stationary density of the response and the power spectral density of the response is addressed.
Keywords: Non-Linear System, Stochastic Linearization, Power Spectral Density, Probability Theory