Two-dimensional steady-state oscillation problems of anisotropic elasticity

Abstract

The paper deals with the two-dimensional exterior bound- ary value problems of the steady-state oscillation theory for anisotro- pic elastic bodies. By means of the limiting absorption principle the fundamental matrix of the oscillation equations is constructed and the generalized radiation conditions of Sommerfeld-Kupradze type are established. Uniqueness theorems of the basic and mixed type boundary value problems are proved. In the paper we treat the uniqueness theorems of basic and mixed type exterior boundary value problems (BVPs) for equations of two-dimensional steady-state elastic oscillations of anisotropic bodies. In this case questions regarding the correctness of BVPs have not been investigated so far. Here any analogy with the isotropic case is completely violated, since the ge- ometry of the characteristic surface becomes highly complicated and the fundamental matrix cannot be written explicitly in terms of elementary functions. This in turn creates another diculty in obtaining asymptotic estimates. As is well known, even for the metaharmonic equation v(x) + k 2 v(x) = 0; k 2 > 0; x 2R 2 ;