Dynamics of impact oscillator with dry friction

Błażejczyk-Okolewska, Barbara; Kapitaniak, Tomasz

doi:10.1016/0960-0779(95)00127-1

Cited by 62 publications

(35 citation statements)

References 14 publications

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“…Since the qualitative behaviour of dry friction systems is sensitive to small changes of system parameters [19], the occurrence of special solutions can be expected in this case. The shadow, traces, or remanences of these special solutions can be detected in the perturbed and more realistic friction models, so their identification is useful to more fully understand transient or temporary dynamic behaviour in experiments.…”

Section: Asymmetric Solutionsmentioning

confidence: 99%

Sub-harmonic resonant solutions of a harmonically excited dry friction oscillator

2006

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Special sub-harmonic solutions of a harmonically forced dry-friction oscillator are analysed. Although the typical non-sticking solutions are stable and symmetric, a continuum of possible asymmetric, marginally stable solutions exist at excitation frequencies = 1/2n. We determine the explicit form of the one-parameter family of these solutions, and give the conditions under which our formulae are valid. The stability of the solutions is examined in the third-order approximation. Finally, our analytical results are checked by numerical simulations.

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Section: Asymmetric Solutionsmentioning

confidence: 99%

Sub-harmonic resonant solutions of a harmonically excited dry friction oscillator

2006

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“…It is noted that the concept of hidden attractors has been suggested in connection with the occurrence of unpredictable attractors in multistable systems [21]. Researchers have shown that multistability is connected with the occurrence of unpredictable attractors [21][22][23][24][25][26][27][28][29][30]. Recently, hidden attractor has been investigated in numerous systems such as Chua system [19], drilling system [31], Lorenz-like system [32], Goodwin oscillator [33], electromechanical systems [34], twodimensional maps [35], phase-locked loop circuits [36], and Rabinovich-Fabrikant system [37].…”

Section: Introductionmentioning

confidence: 99%

Multimedia Security Application of a Ten-Term Chaotic System without Equilibrium

et al. 2017

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A system without equilibrium has been proposed in this work. Although there is an absence of equilibrium points, the system displays chaos, which has been confirmed by phase portraits and Lyapunov exponents. The system is realized on an electronic card, which exhibits chaotic signals. Furthermore, chaotic property of the system is applied in multimedia security such as image encryption and sound steganography.

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“…Researchers have developed different friction models, starting from the basic Coulomb model [15] to more advanced models [16][17][18][19][20][21][22], which take into account various properties of friction. Overviews of friction models are presented in [23][24][25]. The choice of the model depends on the characteristics of the investigated system.…”

Section: Introductionmentioning

confidence: 99%

Synchronization in arrays of coupled self-induced friction oscillators

Marszal

Saha

Jankowski

et al. 2016

Eur. Phys. J. Spec. Top.

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Abstract. We investigate synchronization phenomena in systems of self-induced dry friction oscillators with kinematic excitation coupled by linear springs. Friction force is modelled according to exponential model. Initially, a single degree of freedom mass-spring system on a moving belt is considered to check the type of motion of the system (periodic, non-periodic). Then the system is coupled in chain of identical oscillators starting from two, up to four oscillators. A reference probe of two coupled oscillators is applied in order to detect synchronization thresholds for both periodic and non-periodic motion of the system. The master stability function is applied to predict the synchronization thresholds for longer chains of oscillators basing on two oscillator probe. It is shown that synchronization is possible both for three and four coupled oscillators under certain circumstances. Our results confirmed that this technique can be also applied for the systems with discontinuities.

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Dynamics of impact oscillator with dry friction

Cited by 62 publications

References 14 publications

Sub-harmonic resonant solutions of a harmonically excited dry friction oscillator

Sub-harmonic resonant solutions of a harmonically excited dry friction oscillator

Multimedia Security Application of a Ten-Term Chaotic System without Equilibrium

Synchronization in arrays of coupled self-induced friction oscillators

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