Dynamic characteristics of functionally graded porous beams with interval material properties

Abstract

This paper presents a new computational approach named hybrid Chebyshev surrogate model with discrete singular convolution (CSM-DSC) method to study the nondeterministic dynamic characteristics of functionally graded (FG) porous beams with material uncertainties. In the proposed approach, interval analysis can be directly applied in hybrid CSM-DSC computational framework, then the upper and low bounds of the dynamic responses of FG porous beams with various boundary conditions can be readily obtained. Based on Hamilton's principle and Timoshenko beam theory, the governing equation is established and solved by DSC method. By utilizing the higher-dimensional Chebyshev surrogate (HDCS) model, the approximate performance function involving uncertainty in three critical material properties, such as Young's modulus, mass density and porosity coefficient, is developed numerically. In order to verify the validity and accuracy of the proposed method, deterministic analysis and nondeterministic analysis are implemented to compare the present results against the published ones, and those obtained by the finite element method (FEM) and quasi-Monte Carlo simulation (QMCS) method. A comprehensive parametric study is then conducted to examine the influences of material parameter uncertainties, porosity distribution patterns, porosity coefficient, boundary conditions, and aspect ratio on the bounds of frequencies. The results show that the uncertainty of Young's modulus has the most significant effect on beam's dynamic responses, followed by that of mass density whereas the influence of the uncertain of porosity coefficient is much less pronounced.