Dynamic analysis of very flexible beams

The dynamic analysis of flexible beams with large deformations is difficult and few studies have been performed. In this paper, the vibration analysis of several very flexible beams with large deflections using the finite element approach is studied. The examples were a cantilever beam and rotating flexible robot arms. The results were compared with the results available in the published literature. Several successful checks on the finite element results were performed to ensure the accuracy of the solutions. Due to the geometrical nonlinearity, several static equilibrium shapes can exist for large deflections of a cantilever beam for a given load. Nonlinear dynamic finite element analysis was implemented to investigate the stability of these shapes.