Stochastic Vibration Analyses of Laminated Composite Plates via a Statistical Moments-Based Methodology

Abstract

In the present study, stochastic vibration analyses of a symmetrically laminated composite plate having uncertain input parameters are performed via a probabilistic methodology. Here, uncertain input parameters are selected as plate thickness, specific volume (inverse of density) and structural damping. These parameters are modeled statistically as a normal distribution. The methodology carries out the closed form solution of stochastic partial differential equation governing a structural vibration by discrete singular convolution (DSC) method in terms of its first two statistical moments: mean and standard deviation. The effects of uncertain parameters (combined in six different cases) on modal and vibration displacement response due to a harmonic excitation force are investigated. In this manner, firstly, mean and standard deviation of natural frequencies of the composite plate are obtained by solving its partial differential equation using discrete singular convolution method. After that, statistics of vibration frequency response are obtained by predicted natural frequencies’ statistics. Monte Carlo simulations are also performed to test the proposed methodology. It is shown that the methodology is more reliable in higher frequencies where the uncertainty is much more considerable. Besides, the computation time is very efficient when comparing with Monte Carlo simulations.