Nonlinear dynamics of a column with a tip mass
A large number of aerospace structures and large flexible mechanical structures can be modeled as a large flexible column with a tip mass. Sometimes under certain circumstances, large deformations may be caused in the structures. The developments in the field of design have led to the use of lightweight and high strength materials in these structures. Thus, modem structures are lighter, more flexible, and provide much lower energy dissipation, leading to an intense vibration response. Hence, the dynamic analysis of these structures becomes an important criterion for design. In this study, the nonlinear dynamics of a column with a tip mass was investigated. The partial differential equations of motion were derived for two cases: one in which the truncation of the higher order terms has been done at the beginning of the derivation of the equation of motion and the other in which the truncation was performed at the end of the derivation. Galerkin's method was applied to obtain the second order nonlinear differential equation. The numerical simulation was performed for both the cases, and the results were compared. The multiple scales method was employed to obtain the analytical solution. It has then been compared with the numerical simulation results.