Dynamics of flexible beams undergoing overall motions

A modelling method for straight beams undergoing large overall motions as well as small elastic deformations is presented in this paper. Different from the classical linear Cartesian modelling method which employs three Cartesian deformation variables, the present modelling method uses a non-Cartesian variable along with two Cartesian variables to describe the elastic deformation. A quadratic form of the strain energy expressed with the hybrid set of deformation variables is used to obtain the generalized active forces and a geometric constraint equation relating the non-Cartesian variable and Cartesian variables is used to obtain the generalized inertia forces in the equations of motion. The present modelling method not only provides accurate simulation results but also clarifies the limit of validity of the classical linear Cartesian modelling method.