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RESEARCH PAPERS

Some General Orthogonality Relations

[+] Author and Article Information
H. Herman

Department of Mechanical Engineering, Newark College of Engineering, Newark, N. J.

J. Appl. Mech 37(3), 596-598 (Sep 01, 1970) (3 pages) doi:10.1115/1.3408585 History: Received December 31, 1969; Online July 12, 2010

Abstract

General orthogonality relations which are valid for all linear elastic systems are derived, one relation for systems without damping and another for systems with viscous damping. A general orthogonality relation is also derived for linear viscoelastic systems, but the proof of its validity does not extend to approximate theories with indeterminacies in the stress-strain relations. The method of utilizing the orthogonality relations to determine the coefficients in series expansions is demonstrated.

Copyright © 1970 by ASME
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