A novel iterative algorithm for natural frequency analysis of FG thin plates under interval uncertainty

Abstract

High-accuracy numerical method for uncertainty propagation analysis is a crucial issue in the field of structural reliability design. In this work, a novel iterative algorithm is proposed to study the free vibration of the functionally graded (FG) thin plates with material uncertainties. As a highly accurate approach distinct from the existing non-iterative model, the frequency analysis of FG thin plates can be achieved by updating the lower and upper bounds of natural frequency step by step. Based on the classic plate theory, the governing equations of the FG thin plate resting on an elastic medium are derived and the analytical formulation for the natural frequency is presented. By introducing interval parameters to quantify the material uncertainties, a non-probabilistic model for evaluating the natural frequency response of the embedded FG thin plate is developed. Subsequently, the deduction of the novel iterative algorithm for solving the non-probabilistic model is given based on interval mathematics. The developed model and the proposed iterative algorithm are validated by the Monte Carlo method, and then the detailed parametric studies are carried out to explore the combined influences of material uncertainties, power-law index, and elastic foundation parameters, as well as size parameters on the natural frequency of the FG thin plate. Numerical results can provide useful guidance in the precise design of FG structures.