Method of Inversion of Laplace Transform in Some Problems of Dynamic Elasticity

The novelty of the proposed paper is in the workingout of new analytical approach for the inversion of Laplace transform. The necessity of it is coerced by widely application of Laplace transform in many problems of mechanics, elasticity, thermoelasticity, poroelasticity etc. The theorems are formulated and proved in the general form with the help of complex analysis. The transforms are expanded in Taylor series and Laplace transform inversion is applied term-by-term. The corollaries with the proves for the series converges are done using the generalized functions theory and real analysis. The verification of proposed approach is provided by the comparison with the formulas previously known from literature.