Uncertainty qualification for the free vibration of a functionally graded material plate with uncertain mass density

Abstract

This work studies the response variability in the eigenvalue of free vibration of functionally graded material (FGM) plates with uncertain mass density. The mass density of plates is assumed to be a Gaussian random field on the plane of the plate. The formulation of free vibration of FGM plates is derived using isogeometric analysis based on higher-order shear deformation theory. The stochastic isogeometric analysis is established based on standard isogeometric analysis and a perturbation approach. Also, the formulation for variation of the eigenvalue of free vibration of the plate is issued. The present approach is validated with Monte Carlo simulation (MCS) based on a spectral representation method. The numerical examples investigated show good agreement between the present approach and Monte Carlo simulation. Based on the numerical results, the effect of a parameter of uncertain mass density on variability in the natural frequencies is drawn with respect to FGM plates.