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


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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