Numerical modeling of nonlinear vibrations of viscoelastic shallow shells

Abstract

This paper presents a mathematical model of nonlinear supersonic flutter of viscoelastic shells. To describe the strain processes in shallow shells, the Boltzmann-Volterra integral model is used. Based on linear integral models in geometrically nonlinear formulations, equations of nonlinear oscillations of shallow shells are derived. The Koltunov-Rzhanitsyn kernel is used as a relaxation kernel. The equations of motion of shallow shells after applying the Bubnov-Galerkin method in axial coordinates are reduced to solve a system of nonlinear integro-differential equations (IDE) with variable coefficients relative to the time function. The IDE solution is found numerically using quadrature formulas.