A METHOD OF COMPLEX SOLUTION TO DYNAMIC PROBLEMS OF PLANE ELASTICITY FOR ANISOTROPIC MEDIA

The method of functionally invariant solutions suggested by V. I. Smirnov and S. L. Sobolev [1, 2] is extended in [3] to dynamic problems of plane elasticity for anisotropic media. Since the paper [3] contains an inaccuracy, in the present paper we continue studying this problem for anisotropic media with four elastic constants without any constraints imposed on the elastic constants of real media of the class under consideration. We obtained and investigated simple solutions describing plane waves and also general complex solutions for a system of second-order differential equations describing free vibrations in the examined medium. Homogeneous zero-dimension solutions describing vibrations excited by a point source of the impulse type are obtained from the general solutions as a special case. These solutions are single-valued on Riemann surfaces, the shape of which depends on the relationships between the elastic constants. The solutions obtained differ from those of [3].