타원형 또는 원형 단면을 가진 원형 링의 3차원적 진동해석

Abstract

A three-dimensional(3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (circumferentially closed), circular rings with an elliptical or circular cross-section. Displacement components , and 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 (strain) and kinetic energies of the circular rings are formulated, and upper bound values of the frequencies are obtained 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 for the first five frequencies of the rings. Novel numerical results are presented for the circular rings having an elliptical cross-section based upon 3-D theory. Comparisons are also made between the frequencies from the present 3-D Ritz method and ones obtained from thin and thick ring theories, experiments, and another 3-D method.攀†책임저자;정회원, 중앙대학교 공과대학 건축공학과E-mail : jhkang@cau.ac.krTel : (02)820-5342, Fax : (02)812-4150* 중앙대학교 일반대학원 건축학과攀攀