Changes in the Effective Parameters of Averaged Motion in Nonlinear Systems Subject to Noise

Landa, P. S.; Neimark, Yu. I.; McClintock, Peter V. E.

doi:10.1007/s10955-006-9209-5

Cited by 9 publications

(5 citation statements)

References 27 publications

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“…It is based on the idea [7] that the influence of noise on a nonlinear system may be quantified in terms of the resultant change in the effective parameters of the system. This general approach is applicable, not only to SR in the archetypal overdamped bistable system [23][24][25], but also to the SR that arises in weakly-damped (underdamped) bistable oscillators [7]. Note that the general approach is not restricted to the SR configuration, and it can be applied for the analysis a wide class of weak damped nonautonomous systems.…”

Section: For Discussion)mentioning

confidence: 99%

Theory of stochastic resonance for small signals in weakly damped bistable oscillators

2008

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Section: For Discussion)mentioning

confidence: 99%

Theory of stochastic resonance for small signals in weakly damped bistable oscillators

2008

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“…Bi-frequency driving force, generated by this exciter, is transmitted via nonlinear springs 4 to subsystem II. At the same time the load of the frequency of 3 ω «vibrationally transforms» the nonlinear characteristics of the spring [2,7,8,20,31,32], providing its effective rigidity c eff with respect to loads of frequency close to ω , up to a certain value c eff (3 ω , A 3 ω ), depending both on the frequency 3 ω and on the amplitude of the corresponding harmonics A 3 ω . The condition of the onset of the vibrational resonance in this case is the relation ceff/M2≈ω (where M 2 is the mass of the body 2).…”

Section: Dynamic Scheme Of An Exciter Based On the Phenomenon Of Vibrational Resonancementioning

confidence: 99%

Energy and frequency ripple in devices with inertial excitation of oscillations

Blekhman

Вайсберг

Vasilkov

2021

Phil. Trans. R. Soc. A.

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We consider vibration devices that consist of softly vibration-isolated rigid bodies subjected to vibrations transmitted by means of inertial vibration exciters (unbalanced rotors) driven into rotation by electric motors. Typically, when designing such devices, it is assumed that the rotors rotate uniformly with a certain circular frequency and the body performs small harmonic oscillations with the same frequency. The present work, using a second-order approximation of their nonlinear coupled differential equations, shows that the rotor and the oscillating body keep exchanging energy. At the same time, the angular velocity of the rotor oscillates with the working frequency as well as with its multiple frequencies during each revolution. As a result, the acceleration of the oscillating body also acquires harmonics with multiple frequencies. This may cause both unwanted and beneficial resonance phenomena. We obtain formulae describing the magnitudes of these ripples. We show that the magnitude of oscillations of the angular frequency can also be estimated using energy considerations. Such estimates are provided for the three most common schemes of dynamic devices. Available experimental data confirm the main conclusions of the theory. We discuss both the harmful effects of these phenomena as well as their possible applications. The latter include design of bi-harmonic vibration exciters and exciters based on vibrational resonance. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 2)’.

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“…One perception of SR is in terms of a noise-induced change in the system parameters, which results in the resonance-like dependence of Q on K in the overdamped oscillator described by Eq. (2.1) [24,36,46]. To calculate the effective (i.e.…”

Section: Stochastic Resonance With White Noisementioning

confidence: 99%

Nonlinear systems with fast and slow motions. Changes in the probability distribution for fast motions under the influence of slower ones

Landa

McClintock

2013

Physics Reports

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The influence of slow processes on the probability distribution of fast random processes is investigated. By reviewing four examples we show that such influence is apparently of a universal character and that, in some cases, this universality is of multifractal form. As our examples we consider theoretically stochastic resonance, turbulent jets with acoustic forcing, and two problems studied experimentally by Shnol' on the influence of the Earth's slow rotation on the probability distribution for the velocities of model Brownian particles and on alpha decay. In the case of stochastic resonance, the slow process is a low frequency, harmonic, external force. In the case of turbulent jets, the slow process is acoustic forcing. In the models based on Shnol's experiments, the slow processes are inertial forces arising from the rotation of the Earth, both about its own axis and about the Sun. It is shown that all of these slow processes cause changes in the probability distributions for the velocities of fast processes interacting with them, and that these changes are similar in form.

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Changes in the Effective Parameters of Averaged Motion in Nonlinear Systems Subject to Noise

Cited by 9 publications

References 27 publications

Theory of stochastic resonance for small signals in weakly damped bistable oscillators

Theory of stochastic resonance for small signals in weakly damped bistable oscillators

Energy and frequency ripple in devices with inertial excitation of oscillations

Nonlinear systems with fast and slow motions. Changes in the probability distribution for fast motions under the influence of slower ones

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