Free Vibration Analysis of Composite Plates via Refined Theories Accounting for Uncertainties

Abstract

The free vibration analysis of composite thin and relatively thick plates accounting for uncertainty is addressed in this work. Classical and refined two-dimensional models derived via Carrera's Unified Formulation (CUF) are considered. Material properties and geometrical parameters are supposed to be random. The fundamental frequency related to the first bending eigenmode is stochastically described in terms of the mean value, the standard deviation, the related confidence intervals and the cumulative distribution function. The Monte Carlo Method is employed to account for uncertainty. Cross-ply, simply supported, orthotropic plates are accounted for. Symmetric and anti-symmetric lay-ups are investigated. Displacements based and mixed two-dimensional theories are adopted. Equivalent single layer and layer wise approaches are considered. A Navier type solution is assumed. The conducted analyses have shown that for the considered cases, the fundamental natural frequency is not very sensitive to the uncertainty in the material parameters, while uncertainty in the geometrical parameters should be accounted for. In the case of thin plates, all the considered models yield statistically matching results. For relatively thick plates, the difference in the mean value of the natural frequency is due to the different number of degrees of freedom in the model.