Nonlinear oscillations of a viscoelastic cylindrical panel with concentrated masses

Abstract

The problems of oscillations of a viscoelastic cylindrical panel with concentrated masses are investigated, based on the Kirchhoff-Love hypothesis in the geometrically nonlinear statement. The effect of the action of concentrated masses is introduced into the equation of motion of the cylindrical panel using the δ function. To solve integro-differential equations of nonlinear problems of the dynamics of viscoelastic systems, a numerical method is suggested. With the Bubnov-Galerkin method, based on a polynomial approximation of the deflection, in combination with the suggested numerical method, the problems of nonlinear oscillation of a viscoelastic cylindrical panel with concentrated masses were solved. Bubnov-Galerkin's convergence was studied in all problems. The influence of the viscoelastic properties of the material and concentrated masses on the process of oscillations of a cylindrical panel is shown.