This paper studies an inverse design problem of a general eigenvalue of a dynamic system where the elements of the rigidity and mass matrices are linear with respect to a design vector b. The coefficients of spring and mass of a lumped parameters structure, the length and width, the radius, etc play the role of design parameters. For some specified eigenvalues and eigenvectors, the design parameter vector can be obtained and the rigidity and mass matrices of an initially designed structure can be reconstructed by solving linear algebra equations. The theory and method can not only be used for an in-line system, but it can also be used for an inverse vibration design of a complex structure.
Direct Method of Inverse Eigenvalue Problems for Structure Redesign*
Contributed by the Design Automation Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received Aug. 2002; rev. Apr. 2003. Associate Editor: A. A. Shabana.
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Liangsheng , W. (January 22, 2004). "Direct Method of Inverse Eigenvalue Problems for Structure Redesign." ASME. J. Mech. Des. December 2003; 125(4): 845–847. https://doi.org/10.1115/1.1631575
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