A hybrid stochastic sensitivity analysis for low-frequency vibration and low-velocity impact of functionally graded plates

Abstract

This paper deals with the stochastic sensitivity analysis of functionally graded material (FGM) plates subjected to free vibration and low-velocity impact to identify the most influential parameters in the respective analyses. A hybrid moment-independent sensitivity analysis is proposed coupled with the least angle regression based adaptive sparse polynomial chaos expansion. Here the surrogate model is integrated in the sensitivity analysis framework to achieve computational efficiency. The current paper is concentrated on the relative sensitivity of material properties in the free vibration (first three natural frequencies) and low-velocity impact responses of FGM plates. Typical functionally graded materials are made of two different components, where a continuous and inhomogeneous mixture of these materials is distributed across the thickness of the plate based on certain distribution laws. Thus, besides the overall sensitivity analysis of the material properties, a unique spatial sensitivity analysis is also presented here along the thickness of the plate to provide a comprehensive view. The results presented in this paper would help to identify the most important material properties along with their depth-wise spatial sensitivity for low-frequency vibration and low-velocity impact analysis of FGM plates. This is the first attempt to carry out an efficient adaptive sparse PCE based moment-independent sensitivity analysis (depth-wise and collectively) of FGM plates under the simultaneous susceptibility of vibration and impact. Such simultaneous multi-objective sensitivity analysis can identify the important system parameters and their relative degree of importance in advanced multi-functional structural systems.