Abstract
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.
Highlights
In many areas of technology, for example, in rocket and missile engineering, aircraft industry, mechanical engineering and construction, such structural element as shells is widely used
The continuous increase in the level and dynamics of improvement and development of new promising designs entails the imposition of higher requirements for knowledge of vibration propagation patterns in shells
The stress-strain behaviour of cylindrical shells under the influence of shock loads simulated by impulse functions is of theoretical and applied interest
Summary
In many areas of technology, for example, in rocket and missile engineering, aircraft industry, mechanical engineering and construction, such structural element as shells is widely used. In the works of A.E. Bogdanovich [2, 3], the author studied a wide range of problems in the dynamics of orthotropic cylindrical shells, their axisymmetric and non-axisymmetric deformation during longitudinal impact. Much attention is paid to the derivation and analysis of nonlinear equations of motion for orthotropic shells, the study of the applicability of the Kirchhoff-Love model in problems of dynamics. Methods for solving geometrically nonlinear problems of the dynamics of imperfect cylindrical shells are presented. On their basis, formulation and development of methods for analysing the strength of cylindrical shells made of laminated composites under dynamic compressive loads
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