Dynamical potential for non-linear vibrations of cantilevered beams

Abstract Recently it was shown that averaged characteristics of non-linear vibrations are potential functions of load parameters in the limit of small dissipation. The question of the range of dissipation for which potentiality takes place remained open. In this paper, we study this question 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 potential of beam vibrations can be guaranteed with acceptable accuracy even for sufficiently large dissipation.