Transverse Beam Vibrations- Nonlinear Constraint

Free undamped transverse vibrations can occur in an infinite number of frequency ranges for a beam having one end clamped and the other end supported by a nonlinear spring. Included in the analysis is the effect of a concentrated mass at the spring supported end. The results of a forced harmonic input indicate that the response may become unstable in the frequency ranges of free vibrations. Additional solutions are obtained by considering higher order harmonic terms. The possibility that subharmonic vibrations may exist in a number of specified frequency ranges is also observed. By supplying insight into the vibration of a simple nonlinear arrangement, the analysis provides a starting point for investigations of the motion of more complex nonlinear systems.