DYNAMICAL POTENTIAL FOR NONLINEAR VIBRATIONS OF CANTILEVERED BEAMS

Recently it was shown that averaged characteristics of non-linear vibr ations are potential functions of load parameters in the limit of smal l dissipation. The question of the range of dissipation for which pote ntiality takes place remained open. In this paper, we study this quest ion for the case of non-linear vibrations of a cantilever beam excited harmonically at the unclamped end. We develop a non-linear one-degree -of-freedom beam model and show that the existence of a dynamical pote ntial of beam vibrations can be guaranteed with acceptable accuracy ev en for sufficiently large dissipation.