Dynamic stability of a viscoelastic cylindrical panel with concentrated masses

We discuss the problem of the dynamic stability of a viscoelastic cylindrical panel with concentrated masses in a geometrically nonlinear formulation that is based on the Kirchhoff-Love hypothesis. The effect of the action of concentrated masses is introduced into the equation of motion of a cylindrical panel using the Dirac δ-function. The problem is solved by the Bubnov-Galerkin method based on a polynomial approximation of deflections together with a numerical method based on the use of quadrature formulas. The choice of the Koltunov-Rzhanitsyn singular kernel is justified. Comparisons between the results obtained from different theories are presented. The Bubnov-Galerkin method convergence is investigated for all problems. The effect of the material viscoelastic properties and concentrated masses on the process of the dynamic stability of a cylindrical panel is shown. __________ Translated from Problemy Prochnosti, No. 4, pp. 132–147, July–August, 2008.