Transverse vibrations of circular solid and annular plates of generalized anisotropy

Abstract

The classical theory of vibrating circular plates has been successfully implemented in the case of isotropic, orthotropic and circularly anisotropic continuous media. This is not the case when dealing with circular plates of generalized anisotropy when an approximate analytical solution is sought since the classical approach for constructing co-ordinate functions fails to behave properly in view of the fact that inevitably some of the components of the energy integral functional cancel out. On the other hand, exact, analytical solutions appear to be out of the question. Specially constructed co-ordinate functions are presented in this paper and they allow for the solution of some basic problems accomplished in the present investigation: vibrating clamped and simply supported solid circular plates, and the case of annular plates with a free inner edge using the co-ordinate functions employed in the case of simply connected plates.