A Semianalytical Approach for Free Vibration Characteristics of Functionally Graded Spherical Shell Based on First-Order Shear Deformation Theory

Fuzhen Pang,Hongcheng Wang,Haichao Li,Cong Gao,Yi Ren,Jie Cui

doi:10.1155/2019/7352901

Abstract

This paper describes a unified solution to investigate free vibration solutions of functionally graded (FG) spherical shell with general boundary restraints. The analytical model is established based on the first-order shear deformation theory, and the material varies uniformly along the thickness of FG spherical shell which is divided into several sections along the meridian direction. The displacement functions along circumferential and axial direction are, respectively, composed by Fourier series and Jacobi polynomial regardless of boundary restraints. The boundary restraints of FG spherical shell can be easily simulated according to penalty method of spring stiffness technique, and the vibration solutions are obtained by Rayleigh–Ritz method. To verify the reliability and accuracy of the present solutions, the convergence and numerical verification have been conducted about different boundary parameters, Jacobi parameter, etc. The results obtained by the present method closely agree with those obtained from the published literatures, experiments, and finite element method (FEM). The impacts of geometric dimensions and boundary conditions on the vibration characteristics of FG spherical shell structure are also presented.

Highlights

Academic Editor: Marco Gherlone is paper describes a unified solution to investigate free vibration solutions of functionally graded (FG) spherical shell with general boundary restraints. e analytical model is established based on the first-order shear deformation theory, and the material varies uniformly along the thickness of FG spherical shell which is divided into several sections along the meridian direction. e displacement functions along circumferential and axial direction are, respectively, composed by Fourier series and Jacobi polynomial regardless of boundary restraints. e boundary restraints of FG spherical shell can be simulated according to penalty method of spring stiffness technique, and the vibration solutions are obtained by Rayleigh–Ritz method
To verify the reliability and accuracy of the present solutions, the convergence and numerical verification have been conducted about different boundary parameters, Jacobi parameter, etc. e results obtained by the present method closely agree with those obtained from the published literatures, experiments, and finite element method (FEM). e impacts of geometric dimensions and boundary conditions on the vibration characteristics of FG spherical shell structure are presented
Introduction e functionally graded (FG) spherical shells have been widely used in many engineering fields such as marine and aviation due to their unique mechanical properties. ese structures are usually taking a variety of excitations which leads to structure vibration or even damage in the course of usage. erefore, the investigations of dynamic features of FG spherical shell structures are meaningful, and it is really necessary to establish a unified method for vibration solutions of FG spherical shell structures to improve applications in engineering

Summary

Introduction

Academic Editor: Marco Gherlone is paper describes a unified solution to investigate free vibration solutions of functionally graded (FG) spherical shell with general boundary restraints. e analytical model is established based on the first-order shear deformation theory, and the material varies uniformly along the thickness of FG spherical shell which is divided into several sections along the meridian direction. e displacement functions along circumferential and axial direction are, respectively, composed by Fourier series and Jacobi polynomial regardless of boundary restraints. e boundary restraints of FG spherical shell can be simulated according to penalty method of spring stiffness technique, and the vibration solutions are obtained by Rayleigh–Ritz method. E impacts of geometric dimensions and boundary conditions on the vibration characteristics of FG spherical shell structure are presented.

Results

Conclusion