Unified nonlinear dynamic model for shells of revolution with arbitrary shaped meridians

The geometric design plays a significant role in achieving lightweight and high strength for spacecraft and aircraft fuselages. By introducing the general formulas for the curvature and Lame ' coefficients in cylindrical coordinates, this work develops a unified nonlinear dynamic model for the shell of revolution with an arbitrary meridian. Based on Love's theory with the von K ' arm ' an nonlinearity and the variational method, a system of high-dimensional nonlinear equations describing the motions of the shell of revolution is formulated. Subsequently, the natural frequencies are analyzed, and the nonlinear periodic responses are obtained with the harmonic balance method and the arc-length continuation technique. The effectiveness of the developed model has been verified by comparing with the available results in the literature and FEM. The numerical results demonstrate the crucial role of the shell meridian in determining dynamic responses. Furthermore, the results indicate that the natural frequencies of shells can be designed by meridian modifications without significant volume change. Meanwhile, the nonlinear mode coupling, which amplifies the response complexity, can be avoided. This feature facilitates the attainment of controllable response amplitude in the shell of revolution. The developed model offers an intuitive method to achieve high shell stiffness while minimizing mass by optimizing the meridian geometry.