To reduce the instability region in the nonlinear transverse vibration of randomly excited plates using orthotropic P-FG material

In this paper, the instability region and border curves of bifurcation for a power-law functionally graded orthotropic plate subjected to lateral white noise excitation are obtained analytically. The instability region is computed and drawn as a function of load and the material properties of orthotropic power-law functionally graded material. First the governing equation for a general power-law functionally graded plate is derived with respect to assumed material property. After that, it is rewritten by introducing some non-dimensional parameters such that the results are applicable and usable for a wide range of plates. Then using Fokker–Planck–Kolmogorov equation, an exact relation for the probability density function of response is derived. A root locus study is done on the roots of probability density function to obtain a three-dimensional instability region whose borders specify the occurrence of bifurcation. Without any loss of generality and using an example, the correctness of the method to predict the instability and bifurcation is checked. Also the role of material property is investigated when some analogical figures are drawn that compare the behavior of homogenous plates with their corresponding functionally graded ones. Finally, the outcomes are validated by both the Monte Carlo simulation and the numeric bifurcation analysis of the plate.