Designing for Optimal Energy Absorption, 1: Lumped Parameter Systems

[+] Author and Article Information
S. J. Cox

Department of Computational and Applied Mathematics, Rice University, PO Box 1892, Houston, TX 77251

J. Vib. Acoust 120(2), 339-345 (Apr 01, 1998) (7 pages) doi:10.1115/1.2893836 History: Received June 01, 1995; Online February 26, 2008


Given a conservative dynamical system we determine where, and in what quantity, dissipative mechanisms should be placed in order to best absorb an initial disturbance. We work in the context of linear vibrating systems described by constant mass, M, stiffness, K, and damping, D, matrices. We suppose that M and K are fixed and proceed to minimize, with respect to D, two measures of energy absorption: (i) the least exponent for which the energy exhibits exponential decay and (ii) the maximum over initial disturbances of unit energy of the infinite time integral of the energy. We construct a general setting and provide explicit solutions in the special case of normal mode systems.

Copyright © 1998 by The American Society of Mechanical Engineers
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