Vibration analysis of functionally graded porous cylindrical shell with arbitrary boundary restraints by using a semi analytical method

Abstract

The main purpose of this paper is to provide a new semi analytical method to analyze the free vibration of functionally graded porous (FGP) cylindrical shell with arbitrary boundary restraints. According to the distributions of porous along thickness direction of the structure, two typical types of symmetric and non-symmetric porosity distributions are performed in this paper. The formulations are established on the basis of energy method and first-order shear deformation theory (FSDT). The displacement functions are expressed by unified Jacobi polynomials and Fourier series. The arbitrary boundary restraints are realized by penalty method. The final solutions of FGP cylindrical shell structure are obtained by Rayleigh–Ritz method. To sufficient illustrate the effectiveness of proposed method, some numerical examples about spring stiffness, Jacobi parameters etc. are carried out. In addition, to verify the accuracy of this method, the results are compared with those obtained by FEM, experiment and published literature. The results show that the proposed method has ability to solve the free vibration behaviors of FGP cylindrical shell.