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Research Papers

Natural Vibration of Functionally Graded Cylindrical Shells With Infinite and Finite Lengths

[+] Author and Article Information
Zhiyuan Cao

 School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, P. R. China

Shougao Tang1

 School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, P. R. Chinatangsg@mail.tongji.edu.cn

1

Corresponding author.

J. Vib. Acoust 134(1), 011013 (Dec 28, 2011) (4 pages) doi:10.1115/1.4004900 History: Received April 27, 2005; Revised June 14, 2007; Accepted July 05, 2007; Published December 28, 2011; Online December 28, 2011

Upon the basic theory of functionally graded material cylindrical shell, the original 3-D foundational equations with variable coefficients are transformed into anisotropic and membrane-bending coupling 2-D equations with constant coefficients. The separation-of-variables mode shape functions in axial and circumferential directions for cylindrical shells with infinite and finite lengths are proposed for analytic solutions, which satisfy the basic differential equations, of natural vibration. The general approach presented in the paper for the solutions of natural frequency and mode shape of functionally graded cylindrical shells can be applied to cylindrical shells with any kind of functionally graded material, different length, and boundary conditions.

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