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Shock and Vibration
Volume 2015, Article ID 896204, 29 pages
Research Article

Three-Dimensional Vibration Analysis of Isotropic and Orthotropic Open Shells and Plates with Arbitrary Boundary Conditions

College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, China

Received 23 December 2014; Accepted 15 April 2015

Academic Editor: Tai Thai

Copyright © 2015 Guoyong Jin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents elasticity solutions for the vibration analysis of isotropic and orthotropic open shells and plates with arbitrary boundary conditions, including spherical and cylindrical shells and rectangular plates. Vibration characteristics of the shells and plates have been obtained via a unified three-dimensional displacement-based energy formulation represented in the general shell coordinates, in which the displacement in each direction is expanded as a triplicate product of the cosine Fourier series with the addition of certain supplementary terms introduced to eliminate any possible jumps with the original displacement function and its relevant derivatives at the boundaries. All the expansion coefficients are then treated equally as independent generalized coordinates and determined by the Rayleigh-Ritz procedure. To validate the accuracy of the present method and the corresponding theoretical formulations, numerical cases have been compared against the results in the literature and those of 3D FE analysis, with excellent agreements obtained. The effects of boundary conditions, material parameters, and geometric dimensions on the frequencies are discussed as well. Finally, several 3D vibration results of isotropic and orthotropic open spherical and cylindrical shells and plates with different geometry dimensions are presented for various boundary conditions, which may be served as benchmark solutions for future researchers as well as structure designers in this field.