Stability of large amplitude forced motion of a simply supported beam

Abstract

The large amplitude steady state forced motion of a simply supported beam with ends restrained to remain a fixed distance apart is represented by a series of linear normal modes. The validity of the assumption of single mode response is examined by investigating the stability of the unforced modes when a single mode is forced. The equations include the effects of an initial axial load and numerical examples are presented for axial loads in both the pre- and post-buckling regions. It is concluded that the approximation of single mode response is not always valid because of the possible instability of higher modes.