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.

Issue Section:
Research Papers
Keywords:
continuum mechanics, functionally graded materials, integro-differential equations, shells (structures), stress-strain relations, structural acoustics, vibrations, functionally graded material, cylindrical shell, natural frequency, analytic solution
Topics:
Functionally graded materials, Mode shapes, Pipes, Shells, Vibration, Equations of motion, Stress-strain relations, Boundary-value problems, Membranes, Separation (Technology)

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Copyright © 2012
 by American Society of Mechanical Engineers
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