Free Vibration of Rubber Matrix Cord-Reinforced Combined Shells of Revolution Under Hydrostatic Pressure

In this paper, the free vibration of rubber matrix cord-reinforced combined shells of revolution under hydrostatic pressure is investigated by the precise transfer matrix method. Under hydrostatic pressure, deformation and stress are generated in the rubber matrix composite shell. Based on the deformation characteristics of the rope structure, the deformation of the shell under hydrostatic pressure is analyzed. The stress of the shell under hydrostatic pressure is included in the shell differential equation of motion in the form of pre-stress. Then considering the fluid-solid coupling boundary condition, the field transfer matrix of the fluid-filled spherical shell is obtained. By the continuous condition of the state vector of the shell and the transformation relationship of the coordinate system, the transfer matrices at the position of the ring-stiffener and the connection position of the cylindrical shell and spherical shell are derived, and then the whole free vibration equation of the fluid-filled combined shells of revolution is assembled, and the natural frequencies are obtained by the boundary conditions. Eventually, the accuracy and reliability of the proposed method are verified by the results of literature and simulation results. Effects of the structural parameters of the spherical shell, the distribution of the ring-stiffeners, and the hydrostatic pressure on the natural frequencies of the fluid-filled combined shells of revolution are also discussed. Results of this paper can provide reference data for future studies in the related field.