Periodic Graze Phenomena Caused by Energy Transfer between Two Globally Coupled Vibro-Impact Oscillators

Takata, Soichiro; Kotake, Shigeo; Suzuki, Yasuyuki

doi:10.1299/kikaic.77.1911

Cited by 3 publications

(1 citation statement)

References 17 publications

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“…Since the algorithm can be applied to the classical wave phenomena of the oscillators, it is called wave algorithm, instead of quantum. The phenomenon of energy transfer in the oscillators has been studied by S. Takata et al as almost periodical oscillation [12] and Graze phenomena in the impact oscillator [13]. K. Yagi et al have derived the function of enforced displacement for steady vibration of a 1DOF oscillator [14] from the algorithm.…”

Section: B Grover Algorithm In Three-vibro-impact Oscillatorsmentioning

confidence: 99%

Vibration manipulation function as general lifting function for discrete sampled-data tracking control of 1DOF oscillator

Kotake

2015

2015 IEEE/SICE International Symposium on System Integration (SII)

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Intermittent lifting function, termed vibration manipulation function (VMF), is proposed as a general formula of inverse problem to manipulate a linear one-degree-of-freedom (1DOF) oscillator. Discrete sampled-data tracking control is realized by using the continuous intermittent feedforward control and discrete sampled-data feedback decided from previously determined discrete aimed states in every operating instant. Since VMF can be modified repeatedly from the discrete error deviation, we can minimize error deviation between discrete sampled output and discrete aimed value in order to make the system robust.

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Section: B Grover Algorithm In Three-vibro-impact Oscillatorsmentioning

confidence: 99%

Vibration manipulation function as general lifting function for discrete sampled-data tracking control of 1DOF oscillator

Kotake

2015

2015 IEEE/SICE International Symposium on System Integration (SII)

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Manipulation of Energy Transfer between Internally Resonant Globally Coupled Two Vibro-Impact Oscillators by Wave Algorithm

Kotake

Hanai²,

Suzuki

2011

Trans.JSME(C)

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In this paper, we have proposed wave algorithm for manipulating energy transfer between globally coupled two harmonic oscillators with internal resonance by intermittent perfect elastic impacts at balanced point. When the temporal interval of the impacts, Δt, is the same of the periodic time, 2π, the coupled oscillators exchange their energies slowly and periodically. Its periodicity depends on the ratio between the mass of the oscillators. By skipping an impact, we can reverse the direction of energy flow. And by skipping an impact in every 2nπ period, the system shows 4nπ-periodic recurrence phenomena. By controlling the intermittent of the impacts, we can keep maximizing or minimizing the amplitude of one certain oscillator. We can analytically explain these phenomena from the combinations of unitary operators under wave algorithm. Moreover, under the periodic 2π impacts, the system shows periodic recurrence phenomena, only when the rational ratio between the mass of two coupled oscillators, γ =1, 1/3 or 3; otherwise, it shows strictly ergodic behavior in velocity space.

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Wave Algorithm Analysis of Damping Energy Transfer between Two Globally Coupled Vibro-Impact Oscillators with Proportional Viscous Damping (In Case of Perfect Elastic Collision at Balanced Position)

Takata

2012

Trans.JSME(C)

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In this paper, we study periodic energy transfer in multiple vibro-impact oscillators under proportional viscous damping by using wave algorithm. Internal resonance frequency is obtained by the condition that some off-diagonal elements become to 0 in state transition matrix. Under equivalent modal damping rate, we derive the condition of periodic damped and periodic energy transfer that contains sub-harmonic resonance which depends on mass ratio between the impact and non-impact small oscillators. Under non-equivalent modal damping rate, modulation of the frequency in imperfect damped energy transfer is observed. We obtain a state transition matrix of non-equivalent modal damping rate as the perturbation of that in equivalent. The modulation of periodic damped energy transfer depends on the decay of the modal damping rate in the small impact oscillator.

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Periodic Graze Phenomena Caused by Energy Transfer between Two Globally Coupled Vibro-Impact Oscillators

Cited by 3 publications

References 17 publications

Vibration manipulation function as general lifting function for discrete sampled-data tracking control of 1DOF oscillator

Vibration manipulation function as general lifting function for discrete sampled-data tracking control of 1DOF oscillator

Manipulation of Energy Transfer between Internally Resonant Globally Coupled Two Vibro-Impact Oscillators by Wave Algorithm

Wave Algorithm Analysis of Damping Energy Transfer between Two Globally Coupled Vibro-Impact Oscillators with Proportional Viscous Damping (In Case of Perfect Elastic Collision at Balanced Position)

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