Nonlinear vibrations and dynamic stability of a viscoelastic circular cylindrical shell with shear strain and inertia of rotation taken into account

We consider nonlinear vibration and dynamic stability problems for a viscoelastic circular cylindrical shell according to the refined Timoshenko theory, which takes into account the shear strain and the inertia of rotation, in a geometrically nonlinear setting. The problem data are reduced to systems of nonlinear integro-differential equations with singular relaxation kernels, which can be solved by the Bubnov-Galerkin method combined with a numerical method based on quadrature formulas. We study the numerical convergence of the Bubnov-Galerkin method. We analyze the shell dynamic behavior in a wide range of physical-mechanical and geometric parameters. We demonstrate the influence of the viscoelastic properties of the material on the nonlinear vibrations and dynamic stability of a circular cylindrical shell. We also compare the results obtained according to different theories.