Response Bounds for Damped Linear Mechanical Systems Under Prescribed Motion

[+] Author and Article Information
David W. Nicholson

Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, New Jersey 07030

J. Vib., Acoust., Stress, and Reliab 109(4), 422-424 (Oct 01, 1987) (3 pages) doi:10.1115/1.3269463 History: Received April 10, 1987; Online November 23, 2009


In earlier investigations, the author used extensions of two theorems of G. Strang to derive bounds on the displacements of a symmetric damped linear mechanical system subject to prescribed periodic forces. This work is extended in the current investigation to obtain bounds under prescribed periodic motions. For prescribed periodic forces, the bounds were expressed in terms of the extreme eigenvalues of several symmetric, positive definite matrices. In contrast, in the current case the bounds also depend on several nonsymmetric matrices. The bounds under prescribed motion are evaluated in an example and comparison is made with an exact result. The results reported here are new.

Copyright © 1987 by ASME
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