Energy Balance for Random Vibrations of Piecewise-Conservative Systems

Iourtchenko, D. V.; Dimentberg, M. F.

doi:10.1006/jsvi.2001.3853

Cited by 23 publications

(3 citation statements)

References 4 publications

(13 reference statements)

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“…The influence of random excitation on the dynamical behavior of a vibroimpact dynamical system has caught the attention of many researchers. Many effective methods have been developed, for example, linearization method used by Metrikyn [2], quasistatic approach method used by Stratonovich [3], exponential polynomial fitting method proposed by Zhu [4], Markov process method used by Jing and Young [5], stochastic averaging method used by Xu et al [6,7], variable transformation method used by Zhuravlev [8], energy balance method used by Iourtchenko and Dimentberg [9], mean impact Poincaré map method used by Feng and He [10], path integration method used by Iourtchenko and Song [11], and numerical simulation method used by Dimentberg et al [12]. In [13], the authors tried to review and summarize the existing methods, results, and literature available for solving problems of stochastic vibroimpact systems.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations

Huang

Wang

et al. 2014

Journal of Applied Mathematics

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The erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system's Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo and Runge-Kutta methods, the erosion of the safe basins is also discussed. The sudden change in the character of the stochastic safe basins when the bifurcation parameter of the system passes through a critical value may be defined as an alternative stochastic bifurcation. It is founded that random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation, and make the parametric threshold for motions vary in a larger region, hence making the system become more unsafely and chaotic motions may occur more easily.

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Section: Introductionmentioning

confidence: 99%

Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations

Huang

Wang

et al. 2014

Journal of Applied Mathematics

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“…The influence of the random excitation on the dynamical behavior of an impact dynamical system has caught the attention of many researchers. Some analysis methods, e.g., the linearization method [3] , the quasistatic approach method [4][5] , the Markov process method [6][7] , the stochastic averaging method [8][9] , the variable transformation method [10][11] , the energy balance method [12] , the mean impact Poincaré map method [13] , and the numerical simulation method [14] have been developed. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Subharmonic response of single-degree-of-freedom linear vibroimpact system to narrow-band random excitation

Huang

Wang

Luo

et al. 2011

Appl. Math. Mech.-Engl. Ed.

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The subharmonic response of a single-degree-of-freedom linear vibroimpact oscillator with a one-sided barrier to the narrow-band random excitation is investigated. The analysis is based on a special Zhuravlev transformation, which reduces the system to the one without impacts or velocity jumps, and thereby permits the applications of asymptotic averaging over the period for slowly varying the inphase and quadrature responses. The averaged stochastic equations are exactly solved by the method of moments for the mean square response amplitude for the case of zero offset. A perturbation-based moment closure scheme is proposed for the case of nonzero offset. The effects of damping, detuning, and bandwidth and magnitudes of the random excitations are analyzed. The theoretical analyses are verified by the numerical results. The theoretical analyses and numerical simulations show that the peak amplitudes can be strongly reduced at the large detunings.

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“…The influence of random excitation on the dynamical behaviour of an impact dy-namical system has caught the attention of many researchers. Many effective methods have been developed, e.g., linearization method, [13] quasistatic approach method, [14,15] Markov process method, [16,17] stochastic averaging method, [18,19] variable transformation method, [20] energy balance method, [21] mean impact Poincaré map method, [22] and numerical simulation method. [23] In Ref.…”

Section: Introductionmentioning

confidence: 99%

Resonance response of a single-degree-of-freedom nonlinear vibro-impact system to a narrow-band random parametric excitation

Min-Bang¹,

Huang²

2011

Chinese Phys. B

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The resonant response of a single-degree-of-freedom nonlinear vibro-impact oscillator with a one-sided barrier to a narrow-band random parametric excitation is investigated. The narrow-band random excitation used here is a bounded random noise. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, thereby permitting the applications of random averaging over "fast" variables. The averaged equations are solved exactly and an algebraic equation of the amplitude of the response is obtained for the case without random disorder. The methods of linearization and moment are used to obtain the formula of the mean-square amplitude approximately for the case with random disorder. The effects of damping, detuning, restitution factor, nonlinear intensity, frequency and magnitude of random excitations are analysed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak response amplitudes will reduce at large damping or large nonlinear intensity and will increase with large amplitude or frequency of the random excitations. The phenomenon of stochastic jump is observed, that is, the steady-state response of the system will jump from a trivial solution to a large non-trivial one when the amplitude of the random excitation exceeds some threshold value, or will jump from a large non-trivial solution to a trivial one when the intensity of the random disorder of the random excitation exceeds some threshold value.

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Energy Balance for Random Vibrations of Piecewise-Conservative Systems

Cited by 23 publications

References 4 publications

Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations

Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations

Subharmonic response of single-degree-of-freedom linear vibroimpact system to narrow-band random excitation

Resonance response of a single-degree-of-freedom nonlinear vibro-impact system to a narrow-band random parametric excitation

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