The effect of nonlinear damping on vibrational resonance and chaotic behavior of a beam fixed at its two ends and prestressed

Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator

“…Note that the effective resonance frequency can play a direct and significant role analogous to the effective nonlinear dissipation reported in Refs [7] , [10] , [54] , [53] in the enhancement of signals by modulating the parameters of the fast signal. The effective resonance frequency parameters, which can be computed from the second term of Eq.…”

“…The net flow of heat energy is characterised by a thermal viscosity that has been reported to influence the free oscillations of the bubble strongly, particularly during the transition between the adiabatic and the isothermal states [103] , [104] , [105] . Recently, the impact of non-linear damping/dissipation on the occurrence of VR in nonlinear systems has also gained considerable research attention [7] , [10] , [53] , [54] . In view of this, and to account for the roles of all the individual factors contributing to damping of the bubble dynamics, and their influence on the VR phenomenon, it is essential to treat the liquid and thermal viscosities, as well as the acoustic radiation, independently in the derivation of the equation of motion.…”

“…The phenomenon has gained enormous research attention in the last two decades and has been extensively investigated due its several potential industrial and biomedical applications in a wide range of contexts including bistable systems [45] , [46] , [47] , [48] , multistable systems [19] , [49] , systems with various forms of potential structures [13] , [15] , linearly damped systems [1] , [50] , electrical circuits and time-delayed systems [5] , [6] , [51] , [52] , as well as plasma models [10] , [53] . Although earlier VR studies focused on the parameters of the high-frequency component of the bi-harmonic force, some recent VR research has explored the effects of parameters such as nonlinear damping/dissipation [7] , [10] , [53] , [54] , the complementary roles played by system’s innate bifurcation parameters [13] , [48] , [55] , the effect of time-delay [52] , [56] and fractional derivatives [57] , [58] , [59] , antiresonance [60] , the depth of a potential and the location of its minimum [61] , the effects of potential deformation [62] and potential roughness [53] , and mass-dependent VR [63] , amongst others. More importantly, VR has been realized experimentally in vertical cavity surface emitting lasers and optical systems [45] , [46] , [49] , [64] , [65] .…”

Research on a Multinode Joint Vibration Control Strategy for Controlling the Steering Wheel of a Commercial Vehicle

“…Consequently, it can be ignored in the analysis and used as a scattered composite rigid body for resonance suppression analysis [1]. In the last two decades, researchers have performed many studies on the approaches for the resonance suppression of structure, not only simple design models [2][3][4][5][6][7][8][9] to adjust vibration control parameters, but also dynamic vibrational behaviour of the structure [10,11]. In addition, other methods have been studied to regulate vibration responses.…”

Vibrational resonance in an oscillator with an asymmetrical deformable potential

“…Such amplification takes place when the response amplitude becomes minimum at the bifurcation of the effective potential. Following the foundational studies on VR [11,13,15], vibrational resonance has attracted a lot of research attention and has been reported in bistable systems [11,15,19], multistable systems [20][21][22], excitable systems [23], ratchets [24], quintic oscillators [25], overdamped systems [11,21,24], coupled oscillators [21,26], delayed systems [21,[26][27][28], asymmetric Duffing oscillators [29], fractional order damped oscillators [30][31][32], feedback networks [33], neuron models [23,34,35], a synthetic gene network [36], biological nonlinear maps [37], and systems with nonlinear dissipation [38][39][40], as well as in harmonically trapped potential systems [41]. In addition, experimental evidence for VR has been reported in bistable and multistable vertical-cavity surface-emitting lasers (VCSELs) [19,22,42,43].…”