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Proceedings Paper

Constrained-substructure approach to optimal strain energy analysis
Author(s): Donald J. Leo; Eric M. Austin; Christopher A. Beattie
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Paper Abstract

The chief tool for design of viscoelastic-based damping treatments over the past 20 years has been the modal strain energy (MSE) approach. This approach to damping design traditionally has involved a practitioner to vary placement and stiffness of add-on elements using experience and trial and error so as to maximize the add-on element's share of system MSE in modes of interest. In this paper we develop a new technique for maximizing strain energy as a function of stiffness for add-on structural elements modeled as rank r perturbations to the original stiffness matrix. The techniques is based on a constrained substructure approach allowing us to parameterize strain energy in terms of the eigenvalues of the perturbed structure. An optimality condition is derived that relates the input-output response at the attachment location of the add-on elements to the maximum achievable strain energy. A realizability condition is also derived which indicates whether or not the optimal solution is achievable with passive structural elements. This method has applications in the design of structural treatments for controlling sound and vibration and promises an efficient means of determining the limits of performance of passive structural treatments. An advantage of our approach over existing methods is that the maximum achievable strain energy fraction in the add-on elements is directly computable with the realizability condition then indicating whether the optimal solution is achievable.

Paper Details

Date Published: 27 April 2000
PDF: 10 pages
Proc. SPIE 3989, Smart Structures and Materials 2000: Damping and Isolation, (27 April 2000); doi: 10.1117/12.384555
Show Author Affiliations
Donald J. Leo, Virginia Polytechnic Institute and State Univ. (United States)
Eric M. Austin, Virginia Polytechnic Institute and State Univ. (United States)
Christopher A. Beattie, Virginia Polytechnic Institute and State Univ. (United States)

Published in SPIE Proceedings Vol. 3989:
Smart Structures and Materials 2000: Damping and Isolation
T. Tupper Hyde, Editor(s)

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