Control of vibroimpact dynamics of a single-sided Hertzian contact forced oscillator

Abstract

The control of vibroimpact dynamics of a single-sided Hertzian contact forced oscillator is investigated analytically and numerically in this paper. The control strategy is introduced via a fast excitation and attention is focused on the response near the primary resonance. The fast excitation is added to the basic harmonic force, either through a harmonic force applied from above, or via a harmonic base displacement added from bellow, or by considering the stiffness of the oscillator as a periodically and rapidly varying in time. The results reveal that the threshold of vibroimpact response initiated by jump phenomenon near the primary resonance can be shifted toward lower or higher frequencies of the slow dynamic system depending on the fast excitation taken into consideration. It was also shown that the most realistic and practical way for controlling the vibroimpact dynamics is the introduction of a fast harmonic base displacement.

A Design Method of Traveling Wave Rotary Ultrasonic Motors Driving Circuit under High Voltage Using Single-Sided Hertzian Contact Forced Oscillator Model

“…Considering the contact between the stator and the rotor, and the nonlinearity of the piezoceramic material, a single-sided Hertzian-contact forced oscillator model can be employed to represent this system [ 32 ]. The TRUM could be modeled as a spring-mass-damper-lumped system of a single degree of freedom with a nonlinear spring arranged in parallel, as shown in Figure 8 .…”

Dynamic analysis of elastically and plastically graded spherical and cylindrical contact

“…Some methods of controlling this vibro-impact response were presented by Bichri and Belhaq 24 and Bichri et al. 25,26 The presented control methods utilized fast harmonic load/displacement, fast harmonic modulation of contact stiffness, or introduction of electromagnetic actuator. Xiao et al.…”

“…Hertzian contact nonlinearity is one of the primary reasons for the nonlinear jump phenomenon. Some methods of controlling this vibro-impact response were presented by Bichri and Belhaq 24 and Bichri et al 25,26 The presented control methods utilized fast harmonic load/ displacement, fast harmonic modulation of contact stiffness, or introduction of electromagnetic actuator. Xiao et al 27 used the MMS and HBM and exact method to determine the natural frequency of a mass with Hertzian contact stiffness.…”

Frequency shift and hysteresis suppression in contact-mode AFM using contact stiffness modulation

“…Based on numerical simulations, analytical approximation and experimental testing [3,4], it was concluded that the loss of contact is generally initiated by jumps near the resonances. In order to control the location of such jumps, three strategies were developed recently [5,6]. The first strategy introduced a fast harmonic excitation added to the basic harmonic forcing from above, the second used a fast harmonic base displacement, while the third one considered a rapidly harmonic parametric stiffness.…”