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A sensitivity‐based approach to solving the inverse eigenvalue problem for linear structures carrying lumped attachments
Author(s) -
Dawson Charles B.,
Cha Philip D.
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6147
Subject(s) - eigenvalues and eigenvectors , sensitivity (control systems) , convergence (economics) , mathematics , set (abstract data type) , inverse , range (aeronautics) , algorithm , function (biology) , mathematical optimization , variety (cybernetics) , finite element method , computer science , engineering , geometry , structural engineering , statistics , physics , quantum mechanics , electronic engineering , aerospace engineering , evolutionary biology , economics , biology , programming language , economic growth
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.