Nonlinear vibrations of viscoelastic composite cylindrical panels

This paper is devoted to mathematical models of problems of nonlinear vibrations of viscoelastic, orthotropic, and isotropic cylindrical panels. The models are based on Kirchhoff-Love hypothesis and Timoshenko generalized theory (including shear deformation and rotatory inertia) in a geometrically nonlinear statement. A choice of the relaxation kernel with three rheological parameters is justified. A numerical method based on the use of quadrature formulas for solving problems in viscoelastic systems with weakly singular kernels of relaxation is proposed. With the help of the Bubnov-Galerkin method in combination with a numerical method, the problems in nonlinear vibrations of viscoelastic orthotropic and isotropic cylindrical panels are solved using the Kirchhoff-Love and Timoshenko hypothesis. Comparisons of the results obtained by these theories, with and without taking elastic waves propagation into account, are presented. In all problems, the convergence of Bubnov-Galerkins method has been investigated. The influences of the viscoelastic and anisotropic properties of a material, on the process of vibration, are discussed in this work.