The axisymmetrical response of a circular cylindrical double-shell system with internal damping

The axisymmetrical response of a circular cylindrical double-shell system with internal damping to a time-dependent surface load is determined by the matrix analysis method. For this purpose, the equations of vibration of the system based upon the Goldenveizer-Novozhilov theory are written as a coupled set of first order differential equations by the use of the state vector of the system. Once the vector has been determined by quadrature of the equations, the steady state response is calculated numerically together with the natural frequencies in terms of the elements of the transfer matrix of the system under any combination of boundary conditions. By the application of the method, the dynamic response and the resonant frequencies (the natural frequencies) are calculated numerically for a double-shell system simply supported at the edges.