Nonlinear Free Vibration Analysis of Laminated Composite Plates with Random Material Properties Using Micromechanical Model in Hygrothermal Environments

This paper presents the second order statistics of hygrothermal nonlinear free vibration response of shear deformable laminated composite plate with random system properties. The system properties such as material properties, coefficients of hygroscopic expansion, thermal expansion and geometric properties are modeled as independent Random Variables (RVs). The mathematical model based on Higher Order Shear Deformation Theory [HSDT] is presented. A C-0 finite element method in conjunction with first order perturbation technique is employed to derive the second order statistics for both the expected mean and the standard deviation of the hygrothermal fundamental frequency. A detailed study is carried out to highlight the characteristics of random response and its sensitivity on the plate with various support conditions. Numerical results presented are in good agreement and validated with([4]) and with an independent Monte Carlo simulation.