Free vibration analysis of shallow spherical dome by three-dimensional Ritz method
- Authors
- Kang, Jae-Hoon
- Issue Date
- Jun-2016
- Publisher
- SAGE PUBLICATIONS LTD
- Keywords
- Free vibration; Ritz method; shallow shell; spherical dome; three-dimensional analysis
- Citation
- JOURNAL OF VIBRATION AND CONTROL, v.22, no.11, pp 2731 - 2744
- Pages
- 14
- Journal Title
- JOURNAL OF VIBRATION AND CONTROL
- Volume
- 22
- Number
- 11
- Start Page
- 2731
- End Page
- 2744
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/6876
- DOI
- 10.1177/1077546314551446
- ISSN
- 1077-5463
1741-2986
- Abstract
- A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of a shallow spherical dome. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components u phi, u, and u(z) in the meridional, circumferential, and normal directions, respectively, are taken to be periodic in and in time, and the algebraic polynomials in the phi and z directions. Potential and kinetic energies of the shallow spherical domes are formulated, and 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. Natural frequencies are presented for different boundary conditions. The frequencies from the present 3-D method are compared with those from a 2-D exact method, a 2-D thick shell theory, and a 3-D finite element method.
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Collections - College of Engineering > School of Architecture and Building Science > 1. Journal Articles
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