Geometrically non-linear dynamic model of a rotating flexible arm

In this paper, a mathematical model for a rotating flexible arm undergoing large planar flexural deformations is developed. The position of a typical material point along the span of the arm is described by using the inertial reference frame via a transformation matrix from the body co-ordinate system which is attached to the root of the rotating arm. The condition of inextensibility is employed to relate the axial and transverse deflections of the material point. The position and velocity vectors obtained, after imposing the inextensibility conditions, are used in the kinetic energy expression while the exact curvature is used in the potential energy. The Lagrangian dynamics in conjunction with the assumed modes method is utilized to derive directly the equivalent temporal equations of motion. The resulting non-linear model is discussed, simulated and the result of simulation are presented and compared to those obtained from the linear theory for different arm parameters.