Modeling and dynamic analysis of functionally graded porous spherical shell based on Chebyshev–Ritz approach

Abstract

Abstract This study proposes a unified modeling method to investigate the dynamic behaviors of the functionally graded porous (FGP) spherical shell with elastic boundary conditions. First, three kinds of FGP distributed patterns are defined. Then, the first-order shear deformation theory is selected to build the governing equations of the spherical shell with elastic boundary conditions, which can be solved by the Rayleigh–Ritz approach. Moreover, Chebyshev polynomials of the third kind are selected as an admissible function to express the motion equation. With the constructed model, the correctness is verified by comparing the natural frequency and forced response obtained from both open literature and finite element method. Ultimately, the parameter study is conducted to conclude the effect of the design parameter on the dynamic characteristics of the spherical shell.