Resonance behavior of the system with a limited power supply having the Mises girder as absorber

Abstract

Three-DOF system with a limited power supply (or non-ideal system) having the Mises girder as absorber is considered. Stationary resonance regimes of vibrations near stable equilibrium positions of the system are constructed in two approximations of the multiple scales method. Namely, vibrations near the resonance 1:1 between the motor rotation frequency and the linear sub-system frequency and vibrations near the resonance 1:1 between the motor and absorber frequencies are analyzed. This analysis near the first resonance is made as in supposition that elastic springs of the Mises girder are weak and have an order of the small parameter, as well as in supposition that these springs are not weak. It is obtained that the effective absorption of the elastic vibrations can be obtained in the second case. Additional numerical simulation permits to find regimes of absorption when it is possible to guarantee also the fast outcome from the first resonance region. The most appropriate for absorption and such outcome from the first resonance are vibrations near the second resonance and the snap-through motions.