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.
The Reciprocal Theorem for Harmonic Oscillations of an Elastic, Isotropic Medium
Robert I. Sann
The Bendix Corporation, Teterboro, N. J.
Bernard W. Shaffer
New York University, New York, N. Y.
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Sann, R. I., and Shaffer, B. W. (November 1, 1966). "The Reciprocal Theorem for Harmonic Oscillations of an Elastic, Isotropic Medium." ASME. J. Eng. Ind. November 1966; 88(4): 350–351. https://doi.org/10.1115/1.3672658
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