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

Algebraic techniques and perturbation methods to approach frequency response curves

“…The real dynamical behaviours of mechanical and structural systems are represented by nonlinear differential equations. For system with smooth nonlinearities (very often polynomial nonlinearities) perturbation methods have been developed to trace system responses, from them we can refer to Krilov-Bogoliubov-Mitropolski (KBM) [1,2,3,4,5,6,7,8,9], Harmonic Balance Method (HBM) [10,11,12], normal form [13,14,15,16,17,18,19,20,21,22] and multiple scale methods [6,23,24,25,26,27]. Meanwhile, many other methods exists which are omitted here [23].…”

Remarks on optimization of impact damping for a non-ideal and nonlinear structural system

“…Mikhlin et al. 5 describe it as a phenomenon in which a large part of the vibration energy is transferred from the energy source straight to the resonance vibrations. In other words, in these problems the oscillating system interacts with the source of excitation.…”

“…The first mention of a non-ideal problem presented in the literature is the well-known Sommerfeld effect, named after the first researcher to observe it in 1902. Mikhlin et al 5 describe it as a phenomenon in which a large part of the vibration energy is transferred from the energy source straight to the resonance vibrations. In other words, in these problems the oscillating system interacts with the source of excitation.…”