Bending Dominated Beam Dynamics: Continuous Shape Functions, Boundary Conditions and Internal Loads

Abstract

Predicted solutions to flexible beam dynamics problems involving large overall prescribed motion are investigated using two existing continuous shape function approaches. The beam is cantilevered to a rigid rotating table at one end and attached to the table by way of a tether spring at the other end. It is demonstrated that the free-interface component mode approach provides a significantly more accurate solution than the traditional cantilever beam eigenfunction approach. The chief difference between the two approaches is the continuous shape functions used and the handling of the boundary conditions. The beam in this study, in contrast to a previous study, is oriented such that the steady-state response of the beam is dominated by its bending behavior. It is shown that the internal loads acting on the beam must be considered in order to demonstrate the distinctive differences between the two approaches. Finally, it is demonstrated that adding a new static shape function to the existing free-interface component mode synthesis approach yields a significantly more accurate solution to the problem.