Hysteretic Nonlinearity in Inverted Pendulum Problem

Determining the regions of stability in the motion regimes and parameters of vibratory machines for different technological purposes

“…Similar to the previous work, there are no data on measurement methods of the degree of influence exerted by hysteresis nonlinearities. The use of a hysteresis loop to assess dissipative properties was described by the authors of study [14]. However, the proposals are aimed at ensuring an increase in the vibration protective properties only in a narrow field of spring mass resonance.…”

“…We solved equations (13) and (14) using the Mathcad software in a wide range of parameters of the system «vibration installation -concrete mixture».…”

Broadband frequency response of a nonlinear resonator with clearance for energy harvesting

“…Flexible nonlinear beam systems have been already discussed in the previous works [14][15][16]. In particular, Tang and Ren [14] and Xu and Yu [15] examined a control algorithm to stabilize the pendulum in the upright position.…”

“…In particular, Tang and Ren [14] and Xu and Yu [15] examined a control algorithm to stabilize the pendulum in the upright position. On the other hand, Semenov et al [16] discussed of a concept of elastic inverted Kapica like pendulum with the vertical excitation. Interestingly, their pendulum was also exposed on backlash following the hysteretic switching coupling.…”

Resonance Phenomena in Systems With Hysteretic Nonlinearities

“…Examples of such systems are the oscillations of the ferromagnetic ball in a magnetic field, oscillations of the system of coupled oscillators when the "connection force" has a hysteretic nature [7]. It should also be pointed out that these systems can be considered as an effective models in the solid state physics in the modeling of interatomic interactions taking into account various types of dislocations that arise due to material's aging.…”