Eigenfrequencies of thin plates and layer potentials

Abstract

In this paper the authors represent a general solution of the homogeneous plate equation, valid on both the domain of the plate and its plane complement, in terms of potentials which are generated by source layers, located on the plate boundary, of two different orders. From the conditions that describe the physical properties of the plate boundary, system of integral equations for the layer densities is obtained. It may be shown, using layer potentials of order ⩽3, that this integral formulation of the problem is equivalent to the differential one: in particular, the integral system has the same eigenfrequencies as the differential one. Two examples are given which reveal that the numerically computed eigenfrequencies of the integral system are in good agreement with experimental results.