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


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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