Dynamical analysis of a single degree-of-freedom impact oscillator with impulse excitation

Abstract

In this article, the dynamical behavior of a single degree-of-freedom impact oscillator with impulse excitation is studied, where the mass impacts at one stop and is shocked with impulse excitation at the other stop. The existing and stability conditions for periodic motion of the oscillator are established. The effects of system parameters on dynamical response are discussed under different initial velocities. It is found that smaller shock gap than impact gap could make the periodic motion more stable. The decrease in natural frequency would consume less impact energy, make the vibration frequency smaller, and reduce the vibration efficiency. Finally, the dynamical properties are further analyzed under a special case, that is, the shock gap approaches zero. It could be seen that the larger shock coefficient and impact restitution coefficient would make vibration period smaller. Based on the stability condition, there are an upper limit for the product of shock coefficient and impact restitution coefficient, so that a lower limit of corresponding vibration period exists.

Scenarios in the experimental response of a vibro-impact single-degree-of-freedom system and numerical simulations

“…From the analysis of two-parameter bifurcation diagrams and basins of attraction, they found that the key factor to realize such control objective is to suppress the period-3 solutions that coexist with the desired small amplitude period-1 motions. Wang et al [50] investigated the dynamical behavior of a single degree-of-freedom impact oscillator that impacts at one stop and is shocked with impulse excitation at the other stop and established the existing and stability conditions for period-1 motion of the oscillator and its properties. Furthermore, they discussed the effects of system parameters on dynamical response under different initial velocities.…”

Influence of the characteristics of isolation and mitigation devices on the response of single‐degree‐of‐freedom vibro‐impact systems with two‐sided bumpers and gaps via shaking table tests

“…The mitigation of pounding induced by earthquake between steel structures through the interposition of shock absorbers between the colliding members are the focus of the papers. 15,16,[25][26][27][28][29][30] The constitutive relations between impacting systems can be modeled in different ways. A summary subdivision can be made in two general groups: hard and soft impacts.…”

“…Wang et al, 26 Mate et al, 28 Bamer et al, 29 Wang et al, 30 and Crozet et al 16 presented numerical studies devoted to the analysis of building pounding for SDOF 16,26,30 and MDOF 28,29 (Bamer et al 29 in 2-D and Mate et al 28 in 3-D) systems, under seismic 16,28,29 and impulsive excitation. 26,30…”

“…A summary subdivision can be made in two general groups: hard and soft impacts. The former is based on the concept of restitution coefficient, where the contact time is assumed to be infinitely small and the deformation in the contact zone to be negligible, whereas the latter presumes contact time of finite duration, and a penetration between colliding bodies is admitted. Therefore, linear, Hertzian, or alternative nonlinear springs and viscous dampers are used to model the contact.…”

Numerical study on the response scenarios in a vibro-impact single-degree-of-freedom oscillator with two unilateral dissipative and deformable constraints

“…The types of impact motion, and the bifurcations from one motion to the other, that can occur in the dynamics of vibro-impact systems with motion limiting constraints, with the variation of selected parameters are the subject of several studies, of mainly numerical nature [47][48][49][50][51][52][53][54][55][56][57][58][59][60]. The study of the dynamics of a two-degree-of-freedom periodicallyforced system with symmetric motion limiting constraints, with emphasis on the transition between fundamental impact motions, together with the design and implementation of an electronic circuit, describing the dynamic characteristics of the non-smooth system, are presented in [52].…”