Three-dimensional nonlinear coupled dynamic modeling of a tip-loaded rotating cantilever

This paper presents a general three-dimensional flexible dynamic model of a tip-loaded rotating cantilever beam. For generality, the beam tip is assumed to be loaded with a rigid body with an arbitrary center of mass position, and subject to external force and moment. The coupled longitudinal (axial), bending–bending, and twist elastic motions are considered to formulate the system dynamics. The beam structural internal damping is modeled utilizing Rayleigh’s dissipation function. As well, the influence of gravity is considered. A symbolic code is developed to derive the equations of motion, and it is subsequently used to simulate the dynamics of two numerical case studies. The time response results are found to be in an excellent agreement with those reported from the literature. The effects of internal damping and coupling among the elastic motions on the system dynamic response are then investigated.