A sensitivity‐based approach to solving the inverse eigenvalue problem for linear structures carrying lumped attachments

Summary This paper presents an efficient algorithm for designing dynamical systems to exhibit a desired spectrum of eigenvalues. Focusing on combined systems of linear structures carrying various lumped element attachments, we apply the assumed‐modes method and the implicit function theorem to deriv...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2019-11, Vol.120 (5), p.537-566
Main Authors: Dawson, Charles B., Cha, Philip D.
Format: Article
Language:English
Subjects:
Accessories
Adaptive algorithms
Algorithms
eigenvalue sensitivity
Eigenvalues
inverse problem
Mathematical analysis
Sensitivity analysis
structural design
structural dynamics
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Summary:Summary This paper presents an efficient algorithm for designing dynamical systems to exhibit a desired spectrum of eigenvalues. Focusing on combined systems of linear structures carrying various lumped element attachments, we apply the assumed‐modes method and the implicit function theorem to derive analytical expressions for eigenvalue sensitivities, which are used to efficiently determine the minimal set of structural modifications needed to achieve a set of desired eigenvalues. The proposed algorithm employs an adaptive step size, performs significantly better than existing approaches, and can be easily applied to a broad range of structures. Convergence properties and limitations on achievable eigenvalues are also discussed, and a number of case studies demonstrating the performance of the algorithm in a wide variety of different applications are also included.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.6147