한국전산구조공학회:학술대회논문집 (Proceedings of the Computational Structural Engineering Institute Conference)
- 한국전산구조공학회 2001년도 가을 학술발표회 논문집
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- Pages.515-522
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- 2001
중복근을 갖는 감쇠 시스템의 고유진동수와 모드의 민감도
Natural Frequency and Mode Shape Sensitivities of Damped Systems with Multiple Natural Frequencies
초록
A simplified method is presented for the computation of eigenvalue and eigenvector derivatives associated with repeated eigenvalues. In the proposed method, adjacent eigenvectors and orthonormal conditions are used to compose an algebraic equation whose order is (n+m)x(n+m), where n is the number of coordinates and m is the number of multiplicity of the repeated eigenvalue. One algebraic equation developed can be computed eigenvalue and eigenvector derivatives simultaneously. Since the coefficient matrix of the proposed equation is symmetric and based on N-space, this method is very efficient compared to previous methods. Moreover the numerical stability of the method is guaranteed because the coefficient matrix of the proposed equation is non-singular, This method can be consistently applied to both structural systems with structural design parameters and mechanical systems with lumped design parameters. To verify the effectiveness of the proposed method, the finite element model of the cantilever beam and a 5-DOF mechanical system in the case of a non-proportionally damped system are considered as numerical examples. The design parameter of the cantilever beam is its width, and that of the 5-DOF mechanical system is a spring.
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