Unconstrained and Constrained Mode Expansions for a Flexible Slewing Link

The linear equations of motion of a uniform flexible slewing link which were derived via Hamilton´s Extended Principle are considered. These equations account for the coupling between bending and rigid modes. Unconstrained and constrained mode expansions are investigated and a quantitative comparison is made between the frequency equations and associated mode shapes. A finite dimensional model is derived using the assumed modes method and the theoretical frequencies are verified with an experimental counterbalanced aluminum beam.