Three-dimensional vibration analysis of thick, complete conical shells

被引:20
|
作者
Kang, JH [1 ]
Leissa, AW
机构
[1] Chung Ang Univ, Dept Architectural Engn, Seoul 156756, South Korea
[2] Colorado State Univ, Ft Collins, CO 80523 USA
关键词
D O I
10.1115/1.1767843
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution. Unlike conventional shell theories, which are mathematically two-dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components u(r), u(z), and n(theta) in the radial, axial, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in theta, and algebraic polynomials in the r and z-directions. Potential (strain) and kinetic energies of the conical shells are formulated, the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the conical shells. Novel numerical results are presented for thick, complete conical shells of revolution based upon the 3D theory. Comparisons are also made between the frequencies from the present 3D Ritz method and a 2D thin shell theory.
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页码:502 / 507
页数:6
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