Non-linear vibration and dynamic stability of a viscoelastic cylindrical panel with concentrated mass

Abstract

In the present paper, the problems of the vibration and dynamic stability of a viscoelastic cylindrical panel with concentrated mass are investigated, based on the Kirchhoff-Love hypothesis in the geometrically non-linear statement. The effect of the action of concentrated mass is introduced into the equation of motion of the cylindrical panel using the δ function. To solve integro-differential equations of non-linear problems of the dynamics of viscoelastic systems, a numerical method is suggested. It is based on the quadrature formula and eliminates the distinctions in the kernel of relaxation. With the Bubnov–Galerkin method, based on a polynomial approximation of the deflection, in combination with the suggested numerical method, the problems of non-linear vibration and dynamic stability of a viscoelastic cylindrical panel with concentrated masses were solved. The choice of the Koltunov–Rzhanitsyn singular kernel was substantiated. Results obtained using different theories are compared. 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 vibration and dynamic stability of a cylindrical panel is shown.