The effect of material property on the critical velocity of randomly excited nonlinear axially travelling functionally graded plates

Abstract

In this paper, the critical axial speeds of three types of sigmoid, power law and exponential law functionally graded plates for both isotropic and orthotropic cases are obtained via a completely analytic method. The plates are subjected to lateral white noise excitation and show evidence of large deformations. Due to randomness, the conventional deterministic methods fail and a statistical approach must be selected. Here, the probability density function is evaluated analytically for prescribed plates and used to investigate the critical axial velocity of them. Specifically the effect of inplane forces, mean value of lateral load and the material property on the critical axial speed are studied and discussed for both isotropic and orthotropic functionally graded plates. Since the governing equation is transformed to a non dimensional format, the results can be used for a wide range of plate dimensions. It is shown that the material heterogeneity palys an essential and significant role in increasing or decreasing the critical speed of both isotropic and orthotropic functionally graded plates.