Design And Analysis Of A Nonlinear Magnetic Vibration Isolator With Quasi-zero-stiffness Characteristic

Nowadays the linear vibration and isolation theory is tending to be perfect.Important applications in engineering practice solve many engineering problems.However, the vast majority of vibration systems in engineering practice havenonlinear characteristic. The design theory and application of nonlinear vibrationisolation systems are still at the exploratory stage. Low-frequency vibration isolationis still the problems faced by the engineering field.In the ideal case of a mass m supported by a linear stiffness k on a rigidfoundation, an isolator doesn’t provide efficient attenuation until a frequency of2k/m. It is evident that a smaller stiffness leads to a broadband of vibration isolationbut usually encounters a problem of larger static displacement of the supported mass.In recent years the quasi-zero stiffness (QZS) systems have been attempted toovercome the disadvantage. A quasi-zero stiffness system possesses a localized zerostiffness at equilibrium state. As deflection increases the stiffness increasesnonlinearly with the characteristics of high-static-low-dynamic stiffness. QZS systemoffers the desirable property to satisfy the requirement of a low natural frequency butsmall static displacement.This paper presents analyses of two nonlinear magnetic vibration isolatorsdesigned with the characteristic of quasi-zero stiffness (QZS). One QZS isolator isdevised by connecting a vertical coil spring with two symmetrically inclined magneticsprings. The other is the leveraged QZS isolator coupled with a lever mechanism. Anapproximate expression of magnet repulsive force is proposed for analyzing thefeature of the magnet spring. Analytical result reveals a unique relationship betweenthe stiffness of vertical spring and design parameters of magnet springs for the QZSsystems to support a mass loading. In numerical investigation, the forcetransmissibility derived by the harmonic balance (HB) method is used for theperformance evaluation of the vibration isolation systems. The QZS isolator typicallyattenuates at lower frequencies and outperforms the leveraged QZS isolator; theleveraged QZS isolator can enhance the stiffness of integrated system in the cost ofattenuation capability; both the QZS systems can outperform the linear system.A quasi-zero stiffness (QZS) vibration isolation system delivers excellentattenuation when an excitation frequency is greater than the jump-down frequency.However, the isolation effect of the system is uncertainty in the jumping frequency domain. To solve this problem, this paper proposes a damping perturbation controlmethod. When the system damping is increased to a certain extent, the jump-downfrequency will be lower than the excitation frequency. The large amplitude vibrationresponse on the resonance branch will become unstable and drop to the non-resonancebranch with small oscillation. The Von der Pol Plane is used to determine the timingof withdrawnness of the control to ensure that the vibration state ultimately rests onthe non-resonance branch. The method makes attenuation available in the jumpingfrequency domain and broadens the frequency range of effective isolation of QZSvibration isolation system.