Application of flügge thin shell theory to the solution of free vibration behaviors for spherical-cylindrical-spherical shell: A unified formulation

• Published in: European journal of mechanics, A, Solids Vol. 74; pp. 381 - 393
• Main Authors: Pang, Fuzhen, Li, Haichao, Cui, Jie, Du, Yuan, Gao, Cong
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Masson SAS 01.03.2019; Elsevier BV
• Subjects: A semi analytical method; Boundary conditions; Computer simulation; Cylindrical shells; Finite element method; Formulations; Fourier series; Free vibration; Functions (mathematics); Parameters study; Polynomials; Ritz method; Shell theory; Spherical shells; Spherical-cylindrical-spherical shell; Stiffness; Thin walled shells; Unified displacement functions; Vibration analysis; A semi analytical method; Spherical-cylindrical-spherical shell; Parameters study; Free vibration; Unified displacement functions
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2018.12.003

The main purpose of this paper is to provide a semi analytical method to analyze the free vibration of spherical-cylindrical-spherical shell subject to arbitrary boundary conditions. The formulations are established based on energy method and Flügge thin shell theory. The displacement functions are expressed by unified Jacobi polynomials and Fourier series. The arbitrary boundary conditions are simulated by penalty method about spring stiffness. The final solutions of spherical-cylindrical-spherical shell are obtained by Rayleigh–Ritz method. To sufficient illustrate the effectiveness of proposed method, some numerical example 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 spherical-cylindrical-spherical shell. •Free vibration of spherical-cylindrical-spherical shellstructureisinvestigated by using asemi-analytical method.•Thepaper presents a generalized and unified Jacobi−Ritz formulation.•The papergeneralizesthe selection of admissible displacement functions by using Jacobi polynomial.