?? ???????????? ???????????? ?????????????????????????????? ???????????????????????? ???????????? ???? ?????????????????????? ???????????????????????? ?????????????????? ?? ?????????????????????? ???????????????? ?????????????? ?? ???????????????? ????????????????. ???????????? ?????????????????? ???????????????? ???????????? ????????????????????, ?? ?????????????? ?????????????????? ?????????????????????????????? ????????????????????????, ?????????????? ?????????????? ???? ??????????????. ?? ?????????????? ???? ???????????????????????? ?????????????????????????? ??????????????, ???????????????????? ???? ?????????????????????????? ?????????????????????????? ???????????????????????????? ??????????????, ???????????????????????? ?????????? ?????????????????????? ?? ???????????????????? ?????????????????????????? ???????????? ?????????????????????? ???? ??????????????. ?????? ?????????? ???????????????????????? ?????????????????????? ?????????????? ?????????????????????? ???????????????????????????????? ???????? ?? ?????????????????????? ?????????????????????????? ?????????????? ?? ???????? ??????????. ?????????? ???????????? ?????????????????? ???????????? ???????????????? ???????????? ?? ???????????????????????????????????? ?????????????????? ?????????? ?????? ?????????????????????? ?????????????????? ??????????????????????. ???????????? ?????????? ???????????? ???????????????? ?????????? ???????????????????? ???????????????? ???????????????????????? ???????????????????????????? ?????????? ?? ??????????????, ?? ?????????????????????? ???? ????????????????????. ?? ???????????????????? ???????? ???????????????? ???????????????????????? ?????????????????????????? ?????? ???????????????? ?????????????????????? ?????????? ?????????????????????? ???????????? ?????????? ?????????????????????? ?? ?????????????????? ??????????????.

?? ???????????? ????????????????????? ???????????????????????????? ?????????????????? ???????????? ?? ???????????????????? ?????????????????????? ?????????? ?? ?????????? ???????????????? ?????????????? ?? ?????????????????????? ????????????????. ?????????? ???????????? ???????????????? ?????????????? ????????????????????, ?? ???????????? ?????????????????????? ?????????????????????????????? ????????????????????????, ?????? ???????????????? ?????? ????????. ???? ?????????????? ?????? ?????????????????????? ?????????????????????? ??????????????, ???? ?????????????????????? ???? ???????????????????????? ?????????????????????????? ???????????????????????? ??????????????, ???????????????????????????? ?????????? ?????????????? ?? ???????????????????? ???????????????????????? ???????????? ???????????????? ???? ??????????. ?????? ?????????? ???????????????????????????????? ?????????????????????? ?????????? ?????????????????? ???????????????????????????????? ?????????? ???? ???????????????????? ?????????????? ??????????????????? ?? ?????? ????????????. ?????????? ???????????? ???????????????? ???????????? ?????????????? ???????????? ???? ?????????????????????????? ???????????????? ?????????? ?????? ?????????????????????? ???????????????? ??????????????????????. ?????????? ???????? ???????????? ??????????????????????????? ???????????? ???????????????????????? ???????????????????? ???????????????????????? ?????????????????????? ??????'?? ?? ?????????????? ?? ?????????????????? ???? ????????????????????. ?? ???????????????????? ???????? ???????????????? ?????????????????????? ?????????????? ?????? ???????????????? ?????????????????????? ?????????? ?????????????????? ?????????????? ?????????? ?????????????????????? ?? ?????????????? ??????????????.

This paper considers a solution to an axially symmetric dynamic problem of determining the stress-state in the vicinity of a circular crack in a finite cylinder. The cylinder lower base is rigidly fixed, and the upper one is loaded with time-dependent tangential stresses. In contrast to the traditional analytical methods based on the use of the integralLaplacetransform, the proposed one consists in the difference approximation of only the time derivative. To do this, specially selected unequally spaced nodes and a special representation of the solution in these nodes are used. Such an approach allows the initial problem to be reduced to a sequence of boundary problems for the homogeneous Helmholtz equation. Each such problem is solved by applying the finite Fourier and Hankel integral transforms with their subsequent inversion. As a result, an integral representation was obtained for the angular displacement through an unknown displacement jump in the crack plane.