In this paper, on the example of a five – layer conical shell, the problem of dynamic behavior of multiyear discrete reinforced conical shells of rotation is considered. The study is based on the geometrical nonlinear theory of shells and rods of the Tymoshenko type. The Reissner’s variational principle is used for deductions of the motion equations. An efficient numerical method using Richardson type finite difference approximation for solution of problems on nonstationary behavior of multiplayer shells of revolution with allowance discrete rib is constructed. The method permit to realize solution of the investigated wave problems with the use of personal computers. For the case of axisymmetric vibrations, a detailed analysis of the stress-strain state of the fiver-layer reinforced conical shell was performed
multilayered conical shells of revolution, geometrically nonlinear theory of shells and ribs, non-stationary loading, numerical method, nonstationary vibrations