Nonlinear dynamics of two harmonically excited elastic structures with impact interaction

Stability investigation of velocity-modulated gear system using a new computational algorithm

“…Parametric instabilities happened when harmonics of the excitation frequency are close to particular combinations of the natural frequencies, and the instability of a periodic solution can be determined by the magnitudes of the associated Floquet multipliers [56][57][58]. Because instabilities involve the discontinuous nature of the equation of motion, it could be very difficult to obtain simple expressions for the instability boundaries.…”

Periodically forced system with symmetric motion limiting constraints: Dynamic characteristics and equivalent electronic circuit realization

“…The initial values and the starting point of mapping should be emphasized, because the motion type of the system possibly depends on these initial conditions, as reported in Refs. [25,53,54]. All figures shown in ; (c) the description of mutual transition between 1-p-p and 1-(pþ 1)-(pþ 1) motions(p¼2, 3, 4, 5), including abnormal fundamental 1-(pþ 1)-p motion and subharmonic 2-(2pþ1)-2p and 3-(3pþ 1)-(3pþ1) motions in the related tongue-shaped zones; (d) saddle-note bifurcation boundaries SN 1 À p À p 1Àðp þ 1Þ À ðp þ 1Þ of 1-(pþ 1)-(pþ 1) motions (p¼ 2, 3, 4); (e) grazing bifurcation boundaries G r 1 À p À p and G b 1 À p À p of 1-p-p motions (p¼ 2, 3, 4, 5); (f) hysteresis region HR p existing between grazing boundary G r 1 À p À p and saddlenode bifurcation boundary SN 1 À p À p 1Àðp þ 1Þ À ðp þ 1Þ .…”

“…[46][47][48][49][50][51][52][53][54][55]. Stensson and Nordmark [46] investigated the effects of low-velocity impacts through experimental and numerical efforts.…”

“…[25]. Further, Long et al [54] expanded the study to two harmonically excited elastic structures with impact interaction. Through associated experiments, typical behaviors of the non-smooth system, including grazing bifurcation, jump and hysteresis, are examined, which are in good agreement with numerical results.…”

“…Although analytical and numerical results on grazing impacts and post-grazing phenomena have been reported extensively, experimental evidence of grazing impacts and post-grazing phenomena in mechanical and structural systems as reported in Refs. [25,46,50,53,54] has been limited.…”