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 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 technique 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.
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July 2001
Technical Papers
Constrained Substructure Approach to Optimal Strain Energy Analysis
Donald J. Leo, Assistant Professor, Assoc. Mem. ASME,
Donald J. Leo, Assistant Professor, Assoc. Mem. ASME
Center for Intelligent Material Systems and Structures, Mail Code 0261 Virginia Polytechnic Institute and State University, Blacksburg, VA 24061
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Eric M. Austin, Assistant Professor, Mem. ASME,
Eric M. Austin, Assistant Professor, Mem. ASME
Mechanical Engineering Department Clemson University, Clemson, SC 29632
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Christopher Beattie, Professor
Christopher Beattie, Professor
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061
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Donald J. Leo, Assistant Professor, Assoc. Mem. ASME
Center for Intelligent Material Systems and Structures, Mail Code 0261 Virginia Polytechnic Institute and State University, Blacksburg, VA 24061
Eric M. Austin, Assistant Professor, Mem. ASME
Mechanical Engineering Department Clemson University, Clemson, SC 29632
Christopher Beattie, Professor
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received Nov. 1999; revised Dec. 2000. Associate Editor: K. W. Wang.
J. Vib. Acoust. Jul 2001, 123(3): 340-346 (7 pages)
Published Online: December 1, 2000
Article history
Received:
November 1, 1999
Revised:
December 1, 2000
Citation
Leo, D. J., Austin, E. M., and Beattie, C. (December 1, 2000). "Constrained Substructure Approach to Optimal Strain Energy Analysis ." ASME. J. Vib. Acoust. July 2001; 123(3): 340–346. https://doi.org/10.1115/1.1368117
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