Solution of the Equation of Equilibrium of a Homogeneous and Isotropic Elastic Medium for Orthogonal Curvilinear Coordinates of Two Dimensions

Cases of Separable Coordinates for Laplace's Equation

Abstract

The equation of equilibrium of a homogeneous and isotropic elastic medium is solved for the orthogonal curvilinear coordinates of two dimensions under the condition that Laplace's equation is separable. Coordinates systems satisfying these conditions are Cartesian, cylindrical, elliptic cylindrical and parabolic cylindrical ones.
First, solutions of equation of motion is obtained. Then, making frequency in these solutions to zero, the equation of equilibrium is solved.