Study of vibrations of viscoelastic circular cylindrical panels of variable thickness

The problem of vibrations of viscoelastic cylindrical panels of variable thickness is considered. The system of integro-differential equations (IDE) in partial derivatives is applied to describe the relation between vibrations and deflections. Using the Bubnov-Galerkin method based on the polynomial approximation of deflections, the problem is reduced to the study of the system of ordinary integro-differential equations, in which time is the independent variable. The integro-differential equations are solved by the numerical method, which is based on elimination of the singularity from the relaxation kernel of the integral operator. A numerical algorithm that has been derived using this method is presented. The analysis of nonlinear vibrations of viscoelastic cylindrical panels of variable thickness has revealed a number of novel mechanical effects.