Nonlinear vibration of truncated conical shells : Donnell, Sanders and Nemeth theories

The formulation of nonlinear kinematics of shells in three different shell theories namely Donnell, Sanders and Nemeth including shear deformation for anisotropic materials is presented. A finite element solution for the equilibrium equations of Sander's improved first-approximation theory is developed and has been used to develop the nonlinear finite element amplitude equation of vibration of conical shells of Donnell, Sanders and Nemeth theories using generalized coordinates methods and Lagrange equations of motions. The amplitude equation of nonlinear vibration of conical shell has been solved for multiple cases of isotropic materials with neglecting the shear deformation. Linear vibration frequencies for different conical shells with different materials, geometry and boundary conditions are validated against the existing experimental data in the literature and show excellent agreement. The nonlinear vibration results have been validated against the existing data for cylindrical shells and demonstrate good accordance. The validated model has been used to investigate effect of different parameters including circumferential mode number, cone-half angle, length to radius ratio, thickness to radius ratio and boundary conditions.