Constrained-substructure approach to optimal strain energy analysis

Donald J. Leo; Eric M. Austin; Christopher A. Beattie

doi:10.1117/12.384555

27 April 2000 Constrained-substructure approach to optimal strain energy analysis

Donald J. Leo, Eric M. Austin, Christopher A. Beattie

Proceedings Volume 3989, Smart Structures and Materials 2000: Damping and Isolation; (2000) https://doi.org/10.1117/12.384555
Event: SPIE's 7th Annual International Symposium on Smart Structures and Materials, 2000, Newport Beach, CA, United States

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.

Citation Download Citation

Donald J. Leo, Eric M. Austin, and Christopher A. Beattie "Constrained-substructure approach to optimal strain energy analysis", Proc. SPIE 3989, Smart Structures and Materials 2000: Damping and Isolation, (27 April 2000); https://doi.org/10.1117/12.384555

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