고유 진동수와 모우드의 민감도를 계산하기 위한 효율적인 기법

학위논문(박사) - 한국과학기술원 : 기계공학과, 1996.8, [ xv, 135 p. ]An efficient sensitivity analysis method with guaranteed numerical stability is developed for calculation of the derivatives of vibration natural frequencies and the corresponding mode shapes of the undamped systems, as well as of the damped ones, with both distinct natural frequencies and multiple ones. For the distinct natural frequencies, the natural frequency and mode shape derivatives of both structural systems with structural parameters and mechanical systems with lumped parameters can be obtained consistently by solving algebraic equations with symmetric coefficient matrix whose order is (n+1)×(n+1), where n is the number of equations, for the multiple natural frequencies, by solving the coefficient matrix of order (n+m)×(n+m), where m is the number of multiplicity of a multiple natural frequency. In this case the adjacent mode shapes must be first calculated, which lie adjacent to the m distinct mode shapes which appear when design parameters vary, and then can be used in the algebraic equation defined in the proposed sensitivity analysis method as side conditions. Some datum are represented to prove the efficiency of the proposed method and its accuracy; analysis time, sensitivity analysis results of some eigenpairs and their errors. The analysis time of the proposed method for calculating the eigenpair sensitivities of the systems with distinct natural frequencies is compared with that of Nelson``s method. For multiple natural frequencies, the analysis time of the proposed method is compared with that of Dailey``s method. The analysis time of the proposed method can be reduced dramatically. Furthermore, the method can be saved the computer space (when the number of design parameters is one, Dailey``s method needs the space for the matrices K, M, K``, M`` , K" and M" whereas in the proposed method space for only the matrices K, M, K`` and M`` is needed). In conclusion, the proposed sensitivity analysis method is an analytic one. The algorithm of the...한국과학기술원 : 기계공학과

An Iterative Method for Natural Frequency and Mode Shape Sensitivities

A numerical method is presented for computation of eigenvector derivatives used an iterative procedure with guaranteed convergence. An approach for treating the singularity in calculating the eigenvector derivatives is presented, in which a shift in each eigenvalue is introduced to avoid the singularity. If the shift is selected properly, the proposed method can give very satisfactory results after only one iteration. A criterion for choosing an adequate shift, dependent on computer hardware is suggested: it is directly dependent on the eigenvalue magnitudes and the number of bits per numeral of the computer. Another merit of this method is that eigenvector derivatives with repeated eigenvalues can be easily obtained if the new eigenvectors are calculated. These new eigenvectors lie Uadjacent" to the m (number of repeated eigenvalues) distinct eigenvectors, which appear when the design parameter varies. As an example to demonstrate the efficiency of the proposed method in the case of distinct eigenvalues, a cantilever plate is considered. The results are compared with those of Nelsons method which can find the exact eigenvector derivatives. For the case of repeated eigenvalues, a cantilever beam is considered. The results are compared with those of Daileys method which also can find the exact eigenvector derivatives. The design parameter of the cantilever plate is its thickness, and that of the cantilever beam its height