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.
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On Fundamental Solutions and Green’s Functions in the Theory of Elastic Plates
Department of Mechanics, Lehigh University, Bethlehem, Pa.
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Kalnins, A. (March 1, 1966). "On Fundamental Solutions and Green’s Functions in the Theory of Elastic Plates." ASME. J. Appl. Mech. March 1966; 33(1): 31–38. https://doi.org/10.1115/1.3625022
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