Dynamic stability of viscoelastic orthotropic shells with concentrated mass

Abstract

Viscoelastic thin-walled structures such as plates, panels and shells, with mounted objects in the form of additional masses are widely used in modern technology. The role of such additional masses is often played by longitudinal and transverse ribs, tie-plates and fixtures. When designing such structures, it is relevant to study their dynamic behavior depending on the mass distribution, viscoelastic and inhomogeneous properties of the material, etc. In this paper, the dynamic stability of a viscoelastic shell carrying concentrated masses is considered, taking into account the nonlinear and inhomogeneous properties of the material. A mathematical model of the problem is described by a system of integro-differential equations in partial derivatives. With the Bubnov-Galerkin method, the problem is reduced to solving a system of ordinary nonlinear integro-differential equations. To solve the resulting system with the Koltunov-Rzhanitsyn singular kernel, a numerical method based on the use of quadrature formulas is applied. The effect of the viscoelastic and inhomogeneous properties of the shell material, location, and the amount of concentrated masses on stability is studied.