Nonlinear vibration analysis of an axially moving thin-walled conical shell

The purpose of the current study is the nonlinear vibration analysis of an axially moving truncated conical shell. Based on the classical linear theory of elasticity, Donnell's nonlinear theory assumptions with Von Karman nonlinear terms, Hamilton principle, and Galerkin method, the nonlinear motion equations of axially moving truncated conical shells are derived. Then, a set of nonlinear motion equations has solved using the normal form method in the sub-harmonic region. Also, to validate the accuracy of the mentioned method, the fourth-order Runge-Kutta technique and arclength continuation has applied as a numerical solution. Therefore, the frequency response curves are investigated using the semi-analytical method and validated using the numerical method. The results show that by increasing the velocity up to a limited value, the system's maximum amplitude increases, and then increasing the velocity decreases the maximum amplitude. Also, the softening or hardening of nonlinear behaviour of the system's frequency responses due to change of cone angle has investigated.