Mode Tracking Issues in Structural Optimization

Within the context of optimization of the structural dynamics properties of finite element models, methodology is developed for the tracking of eigenpairs through changes in the structural eigenvalue problem. The goal is to eliminate difficulties caused by "mode switching" (i.e., frequency crossing). Out of several candidate methods, two methods for mode tracking are successful. The first method, the higher order eigenpair perturbation algorithm, is based on a perturbation expansion of the eigenproblem. It iteratively computes changes in the eigenpairs due to parameter perturbations with the important feature of maintaining the correspondence between the baseline and perturbed eigenpairs. The second method is a cross-orthogonality check method, which uses mass orthogonality to reestablish correspondence after a standard reanalysis. Modified eigenpair extraction routines (Lanczos, subspace iteration, inverse power) were unsuccessful in tracking modes. Applications of mode tracking technology that are presented are frequency-constrained optimization and optimization with mode shape constraints. Each application procedure is outlined and examples are given. Recommendations are made based on method efficiency and robustness in the example problems.

[1]  Sean P. Kenny,et al.  Eigenvalue and Eigenvector Approximate Analysis for Repeated Eigenvalue Problems , 1992 .

[2]  Roger C. E. Tan,et al.  Computation of derivatives of repeated eigenvalues and corresponding eigenvectors by simultaneous iteration , 1996 .

[3]  J. A. McGrew,et al.  Orthogonalization of measured modes and calculation of influence coefficients. , 1969 .

[4]  V. B. Venkayya,et al.  Evaluation of Eigenvalue Routines for Large Scale Applications , 1994 .

[5]  H. Saunders.  Book Reviews : NUMERICAL METHODS IN FINITE ELEMENT ANALYSIS K.-J. Bathe and E.L. Wilson Prentice-Hall, Inc, Englewood Cliffs, NJ , 1978 .

[6]  Zhiping Qiu,et al.  Simplified calculation of eigenvector derivatives with repeated eigenvalues , 1996 .

[7]  Edward L. Wilson,et al.  Numerical methods in finite element analysis , 1976 .

[8]  Higher order eigenpair perturbations , 1992 .

[9]  T. Ting,et al.  An automated mode tracking strategy (dynamic structural analysis of helicopter structures) , 1995 .

[10]  I. U. Ojalvo,et al.  Efficient computation of modal sensitivities for systems with repeated frequencies , 1988 .

[11]  Michael Scott Eldred.  Full-order eigenpair perturbations with mode tracking applications in aeroelasticity and optimization. , 1993 .

[12]  W. J. Anderson,et al.  New mode tracking methods in aeroelastic analysis , 1995 .

[13]  T. Chen,et al.  An automated mode tracking strategy , 1993 .

[14]  R. Lane Dailey,et al.  Eigenvector derivatives with repeated eigenvalues , 1989 .

[15]  W. C. Mills-Curran,et al.  CALCULATION OF EIGENVECTOR DERIVATIVES FOR STRUCTURES WITH REPEATED EIGENVALUES , 1988 .

[16]  Warren C Gibson.  ASTROS-ID: Software for System Identification Using Mathematical Programming , 1992 .

[17]  W. P. Targoff.  Orthogonality Check and Correction of Measured Modes , 1976 .