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The purpose of this article is to investigate the process of the influence of a nonstationary load on an arbitrary region
of an elastic anisotropic cylindrical shell. The approach to the study of the propagation of forced transient oscillations
in the shell is based on the method of the influence function, which represents normal displacements in response to
the action of a single load concentrated along the coordinates. For the mathematical description of the instantaneous
concentrated load, the Dirac delta functions are used. To construct the influence function, expansions in exponential
Fourier series and integral Laplace and Fourier transforms are applied to the original differential equations. The
original integral Laplace transform is found analytically, and for the inverse integral Fourier transform, a numerical
method for integrating rapidly oscillating functions is used. The convergence of the result in the Chebyshev norm is
estimated. The practical significance of the work is that the obtained results can be used by scientists or students to
solve new problems of dynamics of cylindrical shells on an elastic basis under pulse loads. The found non-stationary
influence function opens up possibilities for studying the stress-strain state, solving nonstationary inverse and contact
problems for anisotropic shells, studying nonstationary dynamics in the case of nonzero initial conditions, and also
when constructing integral equations of the boundary element method.
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