VIBRATIONS OF GEOMETRICALLY NONLINEAR VISCOUS-ELASTIC CYLINDRICAL SHELLS INTERACTING WITH AN ELASTIC MEDIUM

Abstract

This article examines the nonlinear vibrations of a thin-walled structure such as a cylindrical shell interacting with the ground. On the basis of the seismodynamic theory of underground structures, the nature of the movement of the structure is revealed depending on the stiffness coefficient and rheological properties of the soil, as well as on the frequency of external influences. When solving specific problems, seismic waves in the form of a sinusoid are considered. Nonlinear integro-differential equations describing the vibrations of structures laid in the ground are solved approximately in the following sequence:
 - The method of decomposition of displacements in rad by coordinate functions is applied, which are selected depending on the boundary conditions. Using the approximate Bubnov-Galerkin method, the original nonlinear integro-differential equations in partial derivatives of the fourth order are reduced to ordinary equations of the second order;
 - The obtained nonlinear integro-differential equations are solved by the averaging method, as well as numerically.
 - The nature of the change in stress and amplitude of oscillation in time in an elastic and viscoelastic shell at different coefficients of soil stiffness was obtained.