Influence of nonlinear boundary conditions on the single-mode response of a cantilever beam

In this paper, we compare the experimentally and theoretically obtained single-mode responses of a cantilever beam. The analytical portion involves solving an integro-di€erential equation via the method of multiple scales. For the single-mode response, a large discrepancy is found between theory and experiment for an assumed ideal clamp model. Through some experimental detective work, it was found, and later shown through analysis, that the substitution of a torsionally elastic end for the ®xed support brought the theoretical and experimental results into excellent agreement. The torsional spring has both linear and nonlinear (cubic) sti€ness components.