The Reciprocal Theorem for Harmonic Oscillations of an Elastic, Isotropic Medium

[+] Author and Article Information
Robert I. Sann

The Bendix Corporation, Teterboro, N. J.

Bernard W. Shaffer

New York University, New York, N. Y.

J. Eng. Ind 88(4), 350-351 (Nov 01, 1966) (2 pages) doi:10.1115/1.3672658 History: Received July 26, 1965; Online December 08, 2011


Using the formulation of continuum mechanics, a dynamic reciprocal theorem is derived for sinusoidal motion of an elastic medium. It is found that, exactly as in the static case, the work of the forces of State 1 acting through the displacements of State 2, equals the work of the forces of State 2 acting through the displacements of State 1. A simple example is given, which illustrates the application of the reciprocal theorem to the analysis of forced vibrations of beams.

Copyright © 1966 by ASME
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