NATURAL VIBRATIONS OF VISCOELASTIC THREE-LAYER SHALLOW SPHERICAL SHELLS

Abstract

The development of various fields of engineering and technology is inextricably linked with the creation of new polymeric and composite materials with predetermined various physical and mechanical properties. The paper considers linear natural vibrations of a viscoelastic three-layer shallow spherical shell with the most common types of boundary conditions (sliding pinching, free support, etc.). The problem is reduced to the consideration of a single-layer spherical shell. The aim of the work is to formulate and solve the problem of natural oscillations of viscoelastic multilayer spherical shells. Based on the methods of differential equations in partial derivatives, a frequency equation with complex output parameters is obtained. The problem of natural oscillations of viscoelastic multilayer spherical shells is posed and solved. An equation of resonant frequencies is obtained, which makes it possible to implement the construction of eigenmodes and numerical results.