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Free Vibration Analysis of Thick Circular Ring from Three-Dimensional Analysis  

양근혁 (중앙대학교(서울캠퍼스) 공과대학 건축학부 건축공학과)
강재훈 (중앙대학교(서울캠퍼스) 공과대학 건축학부 건축공학과)
채영호 (중앙대학교(서울캠퍼스) 첨단영상대학원 영상공학과)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.15, no.4, 2002 , pp. 609-617 More about this Journal
Abstract
A three-dimensional(3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, circular rings with isosceles trapezoidal and triangular cross-sections. Displacement components u/sub s/, u/sub z/, and u/sub θin the meridional, normal, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the ψ and z directions. Potential(strain) and kinetic energies of the circular ring are formulated, and upper bound values of the frequencies we obtained by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Novel numerical results are presented for the circular rings with isosceles trapezoidal and equilateral triangular cross-sections having completely free boundaries. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the rings. The method is applicable to thin rings, as well as thick and very thick ones.
Keywords
three-dimensional analysis; free vibration; circular ring; Ritz method;
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