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Structural Engineering and Mechanics
  Volume 55, Number 2, July25 2015, pages 245-261

Frequency analysis of eccentric hemispherical shells with variable thickness
Jae-Hoon Kang

    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 ur, uo, and uz in the radial, circumferential, and axial directions, respectively, are taken to be periodic in o 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.
Key Words
    vibration; eccentric hemi-spherical shell; variable thickness; shell of revolution
Jae-Hoon Kang: Department of Architectural Engineering, Chung-Ang University, Seoul, 156-756 South Korea

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