NON-STATIONARY INFLUENCE FUNCTION FOR AN UNBOUNDED ANISOTROPIC KIRCHHOFF-LOVE SHELL
Abstract
The continuous increase in the level and dynamics of improvement and the creation of new promising designs entails the imposition of higher requirements for knowledge of propagation patterns of vibrations in shells. A special place is occupied by the analysis of the propagation of non-stationary oscillations due to the fact that in such problems the variability of the required solution is substantially inhomogeneous in time and coordinates. The stress-strain behaviour of cylindrical shells under the influence of shock loads simulated by impulse is of theoretical and applied interest. 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. As an example, the spatial distributions of the influence function are constructed.
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