Unsteady deformation of anisotropic circular cylindrical shell
The unsteady deformation of a thin, infinitely long circular cylindrical shell of constant thickness under the impact of a concentrated shock load distributed over an arbitrary region on its lateral surface is being studied. The shell material is assumed to be linearly elastic, anisotropic, and symmetrical about its middle surface. The Kirchhoff-Love model is employed to describe the shell motion. The motion of the shell is being considered in a cylindrical coordinate system associated with the axis of the cylindrical shell, and the sought-for function of the normal non-stationary deflection is constructed by connecting the Green’s function with the function of the operating load using an integral operator of the convolution type in spatial variables and time. The Green’s function for an anisotropic shell is a solution to a special problem of the impact of an instantaneous concentrated load on the shell, mathematically modeled by the Dirac delta functions. Expansions in exponential Fourier series, integral Laplace transform in time and integral Fourier transform in longitudinal coordinate are being used to construct the Green’s function. The inverse integral Laplace transform is being performed analytically, and the original integral Fourier transform is being found using numerical methods for integrating rapidly oscillating functions. The integrals of the convolution of the Green’s function with the load function are being taken with quadrature formulas using the rectangle method. As an example, the unsteady dynamics of cylindrical shell was sstudied under the impact of arbitrarily time-dependent concentrated load and load distributed over the finite area belonging to the lateral surface of the shell. Several options of symmetry of the elastic medium (isotropic, orthotropic and anisotropic) herewith were analyzed, which demonstrates calculated solution versatility both in terms of influence nature and shell material. For the considered symmetry options, the study of the unsteady vibrations propagation character, which allowed evaluating the solution adequacy, was conducted.The presented approach to constructing the unsteady deflection function while transition to the dimensional values opens opportunities for the analysis of the stress-strain state of the extended cylindrical shells with account for various options of the material anisotropy and law of distribution of the unsteady loading along both coordinates and time.