Moment Lyapunov exponent and stochastic stability of a vibro-impact system driven by Gaussian white noise

Hu, Dongliang; Xu, Xin; Guirao, Juan Luis García; Chen, Huatao; Liu, Xianbin

doi:10.1016/j.ijnonlinmec.2022.103968

Cited by 7 publications

(3 citation statements)

References 33 publications

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“…As it is well known, the phenomena of impacts and dry frictions exist widely in a large number of engineering devices [1][2][3], which can induce the instability and insecurity of these devices. Thus, studying the dynamical properties has been an epoch-making field for solving the relative problems of these non-smooth devices [4][5][6]. In the last few years, numerous papers have concentrated on the study of non-smooth systems [4][5][6][7][8], in particular, on vibro-impact systems.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, studying the dynamical properties has been an epoch-making field for solving the relative problems of these non-smooth devices [4][5][6]. In the last few years, numerous papers have concentrated on the study of non-smooth systems [4][5][6][7][8], in particular, on vibro-impact systems. This kind of vibro-impact system appears when a moving mass collides with a barrier and its displacement is greater than a critical value.…”

Section: Introductionmentioning

confidence: 99%

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Bifurcation Analysis of a Nonlinear Vibro-Impact System with an Uncertain Parameter via OPA Method

Huang,

Hong,

et al. 2024

Computer Modeling in Engineering &Amp; Sciences

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In this paper, the bifurcation properties of the vibro-impact systems with an uncertain parameter under the impulse and harmonic excitations are investigated. Firstly, by means of the orthogonal polynomial approximation (OPA) method, the nonlinear damping and stiffness are expanded into the linear combination of the state variable. The condition for the appearance of the vibro-impact phenomenon is to be transformed based on the calculation of the mean value. Afterwards, the stochastic vibro-impact system can be turned into an equivalent high-dimensional deterministic non-smooth system. Two different Poincaré sections are chosen to analyze the bifurcation properties and the impact numbers are identified for the periodic response. Consequently, the numerical results verify the effectiveness of the approximation method for analyzing the considered nonlinear system. Furthermore, the bifurcation properties of the system with an uncertain parameter are explored through the high-dimensional deterministic system. It can be found that the excitation frequency can induce period-doubling bifurcation and grazing bifurcation. Increasing the random intensity may result in a diffusion-based trajectory and the impact with the constraint plane, which induces the topological behavior of the non-smooth system to change drastically. It is also found that grazing bifurcation appears in advance with increasing of the random intensity. The stronger impulse force can result in the appearance of the diffusion phenomenon.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis of a Nonlinear Vibro-Impact System with an Uncertain Parameter via OPA Method

Huang,

Hong,

et al. 2024

Computer Modeling in Engineering &Amp; Sciences

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“…Vibro-impact dynamics under a Hertzian contact force is present in various engineering applications, especially in gear drive, bearing, mechanisms transforming non-resonant rotations or translations, railway wheel-rail contact, and so on [1][2][3]. The Hertzian model is just one of the existing vibro-impact models, and many different phenomena have been reported in the field of vibro-impact systems in the last 40 years, including grazing and C-bifurcations [4], Neimark-Sacker bifurcation [5], period-doubling bifurcations [6], stochastic stability [7], fractals [8], chaos [9], and many others.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of the Vibro-Impact Nonlinear Damped and Forced Oscillator under the Influence of the Electromagnetic Actuation

Herişanu

Marinca

2022

Mathematics

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The main objective of the present work is to find an approximate analytical solution for the nonlinear differential equation of the vibro-impact oscillator under the influence of the electromagnetic actuation near the primary resonance. The trigger of vibro-impact regime is due to Hertzian contact. The optimal auxiliary functions method (OAFM) is utilized to give an analytical approximate solution of the problem. The influences of static normal load and electromagnetic actuation near the primary resonance are completely studied. The main novelties of the proposed procedure are the presence of some new adequate auxiliary functions, the introduction of the convergence-control parameters, the original construction of the initial and of the first iteration, and the freedom to choose the method for determining the optimal values of the convergence-control parameters. All these led to an explicit and accurate analytical solution, which is another novelty proposed in the paper. This technique is very accurate, simple, effective, and easy to apply using only the first iteration. A second objective was to perform an analysis of stability of the model using the multiple scales method and the eigenvalues of the Jacobian matrix.

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Resonance and chaos analysis of fractional-order nonlinear systems with Rayleigh–Duffing terms

Ren,

Xie,

Yang

et al. 2024

Nonlinear Dyn

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Moment Lyapunov exponent and stochastic stability of a vibro-impact system driven by Gaussian white noise

Cited by 7 publications

References 33 publications

Bifurcation Analysis of a Nonlinear Vibro-Impact System with an Uncertain Parameter via OPA Method

Bifurcation Analysis of a Nonlinear Vibro-Impact System with an Uncertain Parameter via OPA Method

Dynamics of the Vibro-Impact Nonlinear Damped and Forced Oscillator under the Influence of the Electromagnetic Actuation

Resonance and chaos analysis of fractional-order nonlinear systems with Rayleigh–Duffing terms

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