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RESEARCH PAPERS

On Fundamental Solutions and Green’s Functions in the Theory of Elastic Plates

[+] Author and Article Information
A. Kalnins

Department of Mechanics, Lehigh University, Bethlehem, Pa.

J. Appl. Mech 33(1), 31-38 (Mar 01, 1966) (8 pages) doi:10.1115/1.3625022 History: Received January 21, 1965; Revised June 30, 1965; Online September 15, 2011

Abstract

This paper is concerned with fundamental solutions of static and dynamic linear inextensional theories of thin elastic plates. It is shown that the appropriate conditions which a fundamental singularity must satisfy at the pole follow from the requirement that the reciprocal theorem is satisfied everywhere in the region occupied by the plate. Furthermore, dynamic Green’s function for a plate bounded by two concentric circular boundaries is derived by means of the addition theorem of Bessel functions. The derived Green’s function represents the response of the plate to a harmonically oscillating normal concentrated load situated at an arbitrary point on the plate.

Copyright © 1966 by ASME
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