ON ONE MATHEMATICAL METHOD FOR SOLUTION OF DYNAMICAL VISCOELASTICITY PROBLEMS

Abstract

Effective mathematical method for solution of nanstationary dynamical problems of linear ahisotropic viscoclastioity at arbitrary difference and nondifference hereditary kernels is developed in the paper. In case when the ratio of kernels of relaxation is independent on time, the known theorems are generalized and the new theorems, by means of which

the solution of fundemental dynamical problems of anisotropic inhomogeneous, viscoelasticity are reduced to solutions of corresponding problems of elastodynamics and to solutions of some one-dimensional mixed value problems for integro-differential equation in partial derivatives hyperbolic type,

are proved. The solutions of all necessary problems for arbitrary hereditary kernels are constructed. These results represent the principle of correspondence of nonstationary dynamical problems solutions of'elasticity and viscoelasticity theories in originals.

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