Relaxation oscillation patterns induced by amplitude-modulated excitation in the Duffing system

Song, Jae Hee; Han, Xiujing; Zou, Yong; Jiang, Yuexiang; Bi, Qinsheng

doi:10.1016/j.chaos.2022.112555

Cited by 11 publications

(4 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In contrast, the other branch exhibits a noticeable lag. Consequently, a slight extension in the quasistatic slow process is observed, which can be attributed to the delayed appearance of fold points, a phenomenon previously documented in [42].…”

Section: Disappearance Of Relaxation Oscillationsmentioning

confidence: 55%

“…However, to date, most of the works have focused on conventional excitations and typical scales, with relatively few reports on low-frequency amplitude modulation, especially in the context of fast-slow dynamics [38,39]. The initial exploration of this topic was presented by Yu et al [40,41], who discovered mixed-mode relaxation oscillations induced by amplitude modulation near the Melnikov curve, and recently, Song et al [42] observed that low-frequency amplitude modulation with an initial phase can extend the duration of the slow process and increase the number of bifurcation points, sparking our interest in further examining amplitude modulation effects. However, these studies primarily focus on the modulation frequency and index in the context of an initial phase difference, neglecting the impact of variations in the initial phase on dynamical behavior.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Amplitude modulation leads to the disappearance of relaxation oscillations in the Duffing system

Song,

Jiang,

Han

et al. 2024

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

Relaxation oscillations are pervasive in diverse areas of natural sciences and engineering, and exploring the dynamical mechanisms of relaxation oscillations is one of the most significant issues. Typical relaxation oscillations can be observed in the Duffing system. Recently, amplitude modulation has emerged as a novel control mechanism for investigating the behavior of fast-slow dynamics in systemic tension oscillations. It has demonstrated the ability to prolong the quasi-static slow process of the system and increase the number of bifurcation points. However, the exploration of the mechanistic aspects of amplitude modulation is still in its early stages, with many unreported dynamical mechanisms. Among these, investigating the modes of relaxation oscillations induced by amplitude modulation is one of the most important issues. Therefore, this manuscript focuses on studying the effect of amplitude modulation on relaxation oscillations, using the classical forced Duffing system as a representative model. Significantly, we report an intriguing finding for the first time, revealing a new amplitude-modulated mechanism by which the disappearance of relaxation oscillations can be induced. By employing the fast-slow analysis, we have examined the underlying dynamical mechanisms, revealing a strong correlation with the modulation index of amplitude modulation. Notably, when the system operates under low amplitude modulation, an extension of the quasi-static process is observed, manifesting as a prolonged slow process. Conversely, under high amplitude modulation, relaxation oscillations suddenly disappear. Our results serve to enrich the potential mechanisms of amplitude modulation, and our analysis provides a reference for investigating the dynamical behavior induced by amplitude modulation in other dynamical systems.

show abstract

Section: Disappearance Of Relaxation Oscillationsmentioning

confidence: 55%

Section: Introductionmentioning

confidence: 99%

Amplitude modulation leads to the disappearance of relaxation oscillations in the Duffing system

Song,

Jiang,

Han

et al. 2024

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Besides, Shi et al [42] proposed a method to predict synchronization bandwidth and frequency stability through phase delay, thereby enabling oscillators to maintain optimal performance. Moreover, Song et al [43,44] and Han et al [45] investigated modulation effects on relaxation oscillations in Duffing and forced van der Pol systems, respectively. They also pioneered phase modulation analysis on relaxation oscillations, showing how modulation can trigger both emergence and dissipation of these oscillations [46].…”

Section: Introductionmentioning

confidence: 99%

Overmodulation causes a variation in the number of jumps in the Duffing system

Song,

Sun,

Han

et al. 2024

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

Amplitude modulation, involving normal and overmodulation scenarios, is crucial for information transmission. However, the complex dynamics of how modulation phase shift affects relaxation oscillations, especially under overmodulation conditions, has not been fully elucidated. Thus, this paper aims to explore the dynamical mechanism of relaxation oscillations affected by modulation phase shift under overmodulation conditions. The result shows that minor phase adjustments in low overmodulation phases can change the time series of the signal. Notably, at critical modulation phase thresholds, the number of transitions in each period of relaxation oscillations increases, and this phenomenon can be observed across a range of parameter values. However, further increase in phase will lead to the decrease in the number of transitions in relaxation oscillations, which demonstrates a clear correlation between phase adjustments and fold bifurcations affecting oscillation patterns. Based on the tri-parametric and bi-parametric bifurcation analysis, we explore the effect of overmodulation index on the number of transitions, and find that higher indices induce complex variations in it. These findings highlight the intricate interplay between modulation phase and modulation index in determining relaxation oscillation patterns, which are crucial for understanding amplitude modulation diversity and can serve as a reference for future research on other modulation scenarios.

show abstract

“…Adding nonlinearity to the system is one of the most appropriate strategies for enhancing the frequency bandwidth of a harvester [ 41 , 42 ]. Several techniques for exploiting nonlinearity have been studied, including duffing [ 43 , 44 , 45 , 46 ], impact [ 47 , 48 , 49 , 50 , 51 , 52 ], and bistable oscillator designs [ 53 , 54 , 55 , 56 , 57 , 58 ]. Recently, vibro-impact has been applied to vibration energy harvesters to boost harvesting efficiency.…”

Section: Introductionmentioning

confidence: 99%

Magnetic Bistability for a Wider Bandwidth in Vibro-Impact Triboelectric Energy Harvesters

Qaseem

Ibrahim

2023

Micromachines

View full text Add to dashboard Cite

Mechanical energy from vibrations is widespread in the ambient environment. It may be harvested efficiently using triboelectric generators. Nevertheless, a harvester’s effectiveness is restricted because of the limited bandwidth. To this end, this paper presents a comprehensive theoretical and experimental investigation of a variable frequency energy harvester, which integrates a vibro-impact triboelectric-based harvester and magnetic nonlinearity to increase the operation bandwidth and improve the efficiency of conventional triboelectric harvesters. A cantilever beam with a tip magnet was aligned with another fixed magnet at the same polarity to induce a nonlinear magnetic repulsive force. A triboelectric harvester was integrated into the system by utilizing the lower surface of the tip magnet to serve as the top electrode of the harvester, while the bottom electrode with an attached polydimethylsiloxane insulator was placed underneath. Numerical simulations were performed to examine the impact of the potential wells formed by the magnets. The structure’s static and dynamic behaviors at varying excitation levels, separation distance, and surface charge density are all discussed. In order to develop a variable frequency system with a wide bandwidth, the system’s natural frequency varies by changing the distance between the two magnets to reduce or magnify the magnetic force to achieve monostable or bistable oscillations. When the system is excited by vibrations, the beams vibrate, which causes an impact between the triboelectric layers. An alternating electrical signal is generated from a periodic contact-separation motion between the harvester’s electrodes. Our theoretical findings were experimentally validated. The findings of this study have the potential to pave the way for the development of an effective energy harvester that is capable of scavenging energy from ambient vibrations across a broad range of excitation frequencies. The frequency bandwidth was found to increase by 120% at threshold distance compared to the conventional energy harvester. Nonlinear impact-driven triboelectric energy harvesters can effectively broaden the operational frequency bandwidth and enhance the harvested energy.

show abstract

Relaxation oscillation patterns induced by amplitude-modulated excitation in the Duffing system

Cited by 11 publications

References 19 publications

Amplitude modulation leads to the disappearance of relaxation oscillations in the Duffing system

Amplitude modulation leads to the disappearance of relaxation oscillations in the Duffing system

Overmodulation causes a variation in the number of jumps in the Duffing system

Magnetic Bistability for a Wider Bandwidth in Vibro-Impact Triboelectric Energy Harvesters

Contact Info

Product

Resources

About