The recent advances for an archetypal smooth and discontinuous oscillator

Zhang, Yuntian; Cao, Qingjie

doi:10.1016/j.ijmecsci.2021.106904

Cited by 34 publications

(6 citation statements)

References 163 publications

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“…For the traditional LR structure, an ultralow frequency bandgap means ultra-large weight or ultra-small static stiffness, which is not allowed in practical applications. Fortunately, the quasi-zero-stiffness (QZS) system [23][24][25][26][27] used for vibration isolation has the characteristics of high static stiffness and low dynamic stiffness. If the QZS system is introduced into the design of LR structures, the ultralow frequency bandgaps can be obtained without weakening the static stiffness of the structure, and the contradiction between the bandgap frequency and the static stiffness of the traditional LR structure can be overcome.…”

Section: Introductionmentioning

confidence: 99%

Tunable Ultralow-Frequency Bandgaps Based on Locally Resonant Plate with Quasi-Zero-Stiffness Resonators

Guo,

Xie,

Sheng

et al. 2024

Applied Sciences

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In order to suppress the transverse vibration of a plate, a quasi-zero-stiffness (QZS) resonator with tunable ultralow frequency bandgaps was introduced and analyzed. The resonator was designed by introducing the quasi-zero-stiffness systems into mass-in-mass resonators. The plane wave expansion method was employed to derive the bandgap characteristics of the locally resonant (LR) plate with QZS resonators, and corresponding simulations were carried out by finite element method (FEM). The results show that an LR plate with a QZS resonator can provide two bandgaps, and the ranges of the bandgaps agree well with the vibration attenuation bands calculated by FEM. Owing to the introduction of the QZS system, the bandgaps can be easily transferred to a lower frequency or even an ultralow frequency. The damping of the QZS resonators can effectively broaden the vibration attenuation bands. In addition, the differentiated design of the bandgap frequencies can be realized to obtain broadband low-frequency transverse wave suppression performance. Finally, a mechanical structure design scheme was proposed in order to achieve flexible adjustment of the bandgap frequency, which significantly increases the engineering applicability of QZS resonators.

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Section: Introductionmentioning

confidence: 99%

Tunable Ultralow-Frequency Bandgaps Based on Locally Resonant Plate with Quasi-Zero-Stiffness Resonators

Guo,

Xie,

Sheng

et al. 2024

Applied Sciences

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“…Mechanical oscillators with irrational nonlinearities have attracted much attention as they are especially suitable for kinematic energy harvesting [1,2] and the vibration isolation of precision instruments and low-fragility equipment [3,4]. These structures are simply and easily implemented as they are composed of concentrated masses and inclined springs with linear stiffness [5].…”

Section: Introductionmentioning

confidence: 99%

Global Dynamics and Bifurcations of an Oscillator with Symmetric Irrational Nonlinearities

Liu,

Shang

2023

Fractal Fract

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This study’s objective is an irrationally nonlinear oscillating system, whose bifurcations and consequent multi-stability under the circumstances of single potential well and double potential wells are investigated in detail to further reveal the mechanism of the transition of resonance and its utilization. First, static bifurcations of its nondimensional system are discussed. It is found that variations of two structural parameters can induce different numbers and natures of potential wells. Next, the cases of mono-potential wells and double wells are explored. The forms and stabilities of the resonant responses within each potential well and the inter-well resonant responses are discussed via different theoretical methods. The results show that the natural frequencies and trends of frequency responses in the cases of mono- and double-potential wells are totally different; as a result of the saddle-node bifurcations of resonant solutions, raising the excitation level or frequency can lead to the coexistence of bistable responses within each well and cause an inter-well periodic response. Moreover, in addition to verifying the accuracy of the theoretical prediction, numerical results considering the disturbance of initial conditions are presented to detect complicated dynamical behaviors such as jump between coexisting resonant responses, intra-well period-two responses and chaos. The results herein provide a theoretical foundation for designing and utilizing the multi-stable behaviors of irrationally nonlinear oscillators.

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“…Furthermore, the applications of the SD oscillator in vibration isolation and energy harvesting have been investigated [43]. In particular, Zhang and Cao provided a comprehensive review of state-of-the-art research on the SD oscillator in their recent work [44]. The presence of irrational functions in nonlinear systems leads to more complex system behavior.…”

Section: Introductionmentioning

confidence: 99%

Fast-slow dynamics analysis in an externally excited smooth and discontinuous oscillator with a pair of irrational nonlinearities

Wei,

Han,

2023

Phys. Scr.

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The study of fast-slow oscillations in systems with irrational nonlinearity that may yield abundant dynamical mechanisms is not well developed. This paper aims to investigate the fast-slow dynamics in an excited mass-spring oscillator with a pair of irrational nonlinearities, which can undergo the dynamical transition from smooth to discontinuous characteristics depending on the values of a smoothness parameter. Three different types of fast-slow oscillations are reported in this interesting smooth and discontinuous (SD) oscillator with a pair of irrational nonlinearities. Due to the smooth and discontinuous characteristics of this SD oscillator, we consider its dynamical behaviors under the smooth and discontinuous cases, respectively. Based on the fast-slow analysis and the two-parameter bifurcation analysis, the smooth fast-slow dynamics associated with fold hysteresis and its turnover are revealed. In the discontinuous case, the system can be viewed as a piecewise-smooth dynamical system governed by three different subsystems in different regions divided by two nonsmooth boundaries. In particular, the nonsmooth boundaries can be divided into parts with different dynamical behaviors, including escaping and crossing lines. Unlike the smooth case, there is no change in the stability of the equilibrium in these three subsystems. However, transitions of system trajectory induced by crossing lines can account for the generation of fast-slow oscillations in the piecewise-smooth system. As a result, the smooth and piecewise-smooth fast-slow dynamics in the excited SD oscillator with a pair of irrational nonlinearities are revealed, which deepens the understanding of fast-slow dynamics of the dynamical systems with irrational nonlinearity.

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The recent advances for an archetypal smooth and discontinuous oscillator

Cited by 34 publications

References 163 publications

Tunable Ultralow-Frequency Bandgaps Based on Locally Resonant Plate with Quasi-Zero-Stiffness Resonators

Tunable Ultralow-Frequency Bandgaps Based on Locally Resonant Plate with Quasi-Zero-Stiffness Resonators

Global Dynamics and Bifurcations of an Oscillator with Symmetric Irrational Nonlinearities

Fast-slow dynamics analysis in an externally excited smooth and discontinuous oscillator with a pair of irrational nonlinearities

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