Vibrations of Complex Shells with Variable Thickness
Publication: Journal of Engineering Mechanics
Volume 143, Issue 8
Abstract
Natural frequencies and mode shapes of a complex shell composed of a circular cylindrical shell and hemispherical shell with variable thickness are determined by the Ritz method using a mathematically three-dimensional (3D) analysis instead of two-dimensional (2D) thin-shell theories or higher-order thick-shell theories. The present analysis is based upon the circular cylindrical coordinates, whereas in traditional shell analyses, 3D shell coordinates have usually been used. Using the Ritz method, Legendre polynomials, which are mathematically orthonormal, are used as admissible functions instead of ordinary simple algebraic polynomials. Natural frequencies are presented for different boundary conditions. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the combined shell. The frequencies from the present 3D method are compared with those from three types of 2D thin-shell theories found by previous researchers. The present method is applicable to very thick shells as well as thin shells and complex shells with variable thickness.
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 8 • August 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Aug 4, 2016
Accepted: Jan 6, 2017
Published online: Apr 10, 2017
Published in print: Aug 1, 2017
Discussion open until: Sep 10, 2017
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