Frequency analysis of eccentric hemispherical shells with variable thickness
- Authors
- Kang, Jae Hoon
- Issue Date
- Jul-2015
- Publisher
- TECHNO-PRESS
- Keywords
- vibration; eccentric hemi-spherical shell; variable thickness; shell of revolution
- Citation
- STRUCTURAL ENGINEERING AND MECHANICS, v.55, no.2, pp 245 - 261
- Pages
- 17
- Journal Title
- STRUCTURAL ENGINEERING AND MECHANICS
- Volume
- 55
- Number
- 2
- Start Page
- 245
- End Page
- 261
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/9332
- DOI
- 10.12989/sem.2015.55.2.245
- ISSN
- 1225-4568
1598-6217
- Abstract
- A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of eccentric hemi-spherical shells of revolution with variable thickness. 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(r), u(theta), and u(z) in the radial, circumferential, and axial directions, respectively, are taken to be periodic in. and in time, and algebraic polynomials in the r and z directions. Potential and kinetic energies of eccentric hemi-spherical shells with variable thickness 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 three or four-digit exactitude is demonstrated for the first five frequencies of the shells. Numerical results are presented for a variety of eccentric hemi-spherical shells with variable thickness.
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