The nonlinear vibrations of a vertical hard gyroscopic rotor with nonlinear characteristics

Abstract

Abstract. The paper considers an impact of viscous linear and cubic nonlinear damping of the elastic support on nonlinear vibrations of a vertical hard gyroscopic unbalanced rotor, taking into account nonlinear stiffness of the support material. Analyzing the research results shows that linear and cubic nonlinear damping can significantly suppress the resonance peak of the fundamental harmonic, eliminate the jumping phenomena of the nonlinear system. In non-resonance areas where the velocity is higher than the critical one, cubic nonlinear damping, unlike linear one, can slightly suppress amplitude of the rotor vibration. Therefore, in the high-velocity area, only nonlinear damping can maintain performance of a vibration isolator. In resonance area, an increase in linear or cubic nonlinear damping significantly suppresses the ability to absolute displacement. In non-resonance area, where the rotational velocity is lower than the critical one, they have almost no impact on ability to absolute displacement. In high velocity area, an increase in nonlinear damping may slightly increase the moment of force transmissibility, but linear damping has almost no impact on it. The obtained results can be successfully used to produce passive vibration isolators used for damping the vibrations of rotary machines, including gyroscopic ones.

Modeling the Dynamics of a Gyroscopic Rigid Rotor with Linear and Nonlinear Damping and Nonlinear Stiffness of the Elastic Support

“…For example, in [5], the parametric effect of various types of attenuation on the performance of nonlinear vibration isolators under harmonic excitation was investigated. In [6][7][8][9][10][11], the effectiveness of passive vibration isolators with linear damping and nonlinear cubic damping in resonant and non-resonant vibration regions of a system with linear and nonlinear stiffness was examined. Nonlinear damping, in contrast to linear damping, not only significantly suppresses the maximum resonant amplitude of vibrations, but also preserves the vibration isolation of the system in the region beyond the resonant frequency of vibrations.…”

“…Nonlinear damping, in contrast to linear damping, not only significantly suppresses the maximum resonant amplitude of vibrations, but also preserves the vibration isolation of the system in the region beyond the resonant frequency of vibrations. The introduction of nonlinear rigidity into an oscillatory system with purely linear rigidity [6,9] not only improves the transfer of the transmission force to the region beyond the resonant frequency (angular velocity), but also leads to the appearance of jumping effects, and nonlinear cubic damping can weaken these effects, and even completely eliminate them [7,10,11].…”

“…In [10][11][12], the effects of the linear and nonlinear vibration damping of the elastic support rubber material were experimentally confirmed. With the phenomenological model of nonlinear damping adopted in [6][7][8][9][10][11], the results of analytical studies are in satisfactory agreement with the results of experimental studies.…”

Nonlinear Dynamics of the Quadratic-Damping Helmholtz Oscillator

“…Nowadays, most nonlinear vibration techniques focus on the method of modulation of upper harmonics and sidebands, but approaches to detect nonlinear damage based on nonlinear resonances require even more investigation. us, the condition giving the relation between the amplitude of vibration and the parameters of the system is crucial for the good choice of the frequency and the amplitude of excitation to trigger a nonlinear resonance effect [34][35][36]. e most suitable techniques for finding resonances are the harmonic balance and the multiple-scale methods [18,19,37].…”

Mathematical Modeling of a Multi-Inert Oscillatory Mechanism

“…Разработаны осцилляторы с другим характером энергообмена, например, преобразованием кинетической энергии груза в энергию магнитного поля соленоида или энергию электрического поля конденсатора. Все эти колебательные системы и подобные им [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] явились предпосылкой создания биинертного осциллятора, в котором ускорение одного груза происходит за счет торможения другого, т. е. происходит обмен только кинетическими энергиями.…”