On deriving exact probability density functions for functionally graded exponential profile orthotropic plates driven by laterally random excitation

In this article, the exact probability density function for a nonlinear exponential functionally graded orthotropic plate under lateral random excitation is investigated. After that, a study on the probability density function (PDF) is done to examine the dynamic instability and bifurcation. Using nondimensional parameters, the results are justified for a wide range of plates. The outcomes are studied with respect to the variation of both mean value of lateral loads and in-plane forces. The famous Monte Carlo simulation is employed to validate the obtained analytical PDFs. An analogical study is done between the behaviors of homogenous plates with their corresponding functionally graded material ones. Finally, it is shown how the exponential profile functionally graded orthotropic material can affect the quality of instability and bifurcation.