The axisymmetric dynamic problems of determining the stress state in the vicinity of the delamination in a finite cylinder partly coupled with the rigid base were solved. In contrast to the traditional solution methods based on the use of the integral Laplace transform, the proposed method consists in the difference approximation only of the time derivative. As a result, the original problem is replaced by a sequence of homogeneous boundary value problems for the Helmholtz equation that reduce to the Fredholm integral equation of the second kind. The numerical solution found made it possible to obtain an approximate formula for calculating the stress intensity factor.

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