Dynamic stability of thin-walled structure elements considering hereditary and inhomogeneous properties of the material

Abstract

The paper is devoted to the study of nonlinear problems of the dynamics of thin-walled structures considering hereditary and inhomogeneous properties of the material. To describe the processes of strain in viscoelastic materials, the Boltzmann-Volterra integral model with weakly singular hereditary kernels was used. Using the Bubnov-Galerkin method, the problem under consideration was reduced to solving the systems of nonlinear integrodifferential equations considering hereditary and inhomogeneous properties of the material and the radius of curvature of the structure. A computational algorithm was developed based on the elimination of the features of integrodifferential equations with weakly singular kernels, followed by the use of quadrature formulas. The results of calculating a thin-walled structure with hereditary and inhomogeneous properties of the material streamlined by a gas flow are presented. Solutions are obtained in the form of graphs.