Probability Densities of the Response of Non-Linear Structures under Stochastic Dynamic Excitation
An approximate method for determining estimates of response statistics for non-linear oscillators driven by wide-band random excitation is presented. The development is based on the theory of Markov processes. The proposed method is based on non-Gaussian closure procedures where a number of moment differential equations are used to evaluate parameters of non-Gaussian response distributions. The developments are described and illustrated by means of numerical examples. Special attention is given to the choice of types of non-Gaussian distributions. it is shown that some serious shortcomings of series approximations, particularly with respect to negative probability densities can be avoided by using generalized exponential distributions.
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