Basins of attraction in a harmonically excited spherical bubble model.

Hegedűs, Ferenc; Kullmann, Lajos

doi:10.3311/pp.me.2012-2.08

Cited by 16 publications

(15 citation statements)

References 12 publications

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“…Methods of nonlinear dynamics (e.g. resonance curves and bifurcation diagrams) have been extensively applied to investigate bubble behavior [1][2][3][4][5][6][7][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. It has been shown that the bubble oscillator can exhibit 1 2 , 1 3 , 1 4 , 1 5 or higher order SHs, as well as period doubling route to chaos [1][2][3][4][5][6][7][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]…”

Section: Introductionmentioning

confidence: 99%

A simple method to analyze the super-harmonic and ultra-harmonic behavior of the acoustically excited bubble oscillator

Sojahrood

Wegierak

Haghi

et al. 2019

Ultrasonics Sonochemistry

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Acoustically excited bubbles are involved in a wide range of phenomena and applications ranging from oceanography to sonoluminescence; they have applications in chemistry, medical imaging, and therapeutic ultrasound. The complexity of bubble dynamics and the limited understanding of their behavior restricts the exploration of their full potential. The bubble oscillator is a highly nonlinear system, which makes it difficult to generate a comprehensive understanding of its oscillatory behavior. One method used to investigate such complex dynamical systems is the bifurcation analysis. Numerous investigations have employed the method of bifurcation diagrams to study the effect of different control parameters on the bubble behavior. These studies, however, focused mainly on investigating the subharmonic (SH) and chaotic oscillations of the bubbles. Super-harmonic (SuH) and ultra-harmonic (UH) bubble oscillations remain under-investigated. One reason is that the conventional method used for generating bifurcation diagrams cannot reliably identify features that are responsible for the identification of SuH and UH oscillations. Additionally, the conventional method cannot distinguish between the UHs and SHs. We introduce a simple procedure for the generation of bifurcation diagrams to address this shortcoming. This method selects the maxima of the bubble oscillatory response and plots them alongside the traditional bifurcation points for the corresponding control parameter. Through applying this method, the oscillatory behavior of the bubble oscillator is analyzed, and stable SuH and UH bubble oscillations are investigated. Based on this new analysis, the conditions for the generation and amplification of UH and SuH regimes are discussed.

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Section: Introductionmentioning

confidence: 99%

A simple method to analyze the super-harmonic and ultra-harmonic behavior of the acoustically excited bubble oscillator

Sojahrood

Wegierak

Haghi

et al. 2019

Ultrasonics Sonochemistry

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“…Observe that these assumptions are exactly the same as in case of Behnia's condition (30), see also Eqs. (28) and (29). The resonant frequency ω 0 in Equation (33) is also known as the Minnaert frequency [51].…”

Section: The Linear Resonance Frequency Of the Bubblementioning

confidence: 99%

“…The accumulated knowledge of this nonlinear behavior has been summarized in many reviews [18][19][20] and papers [1,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. The most important findings are the existence of period-doubling cascades in the bifurcation structure [1,21,30,31,35], the appearance of resonance horns in the amplitude-frequency plane of the driving [24,27,34] or the alternation of chaotic and periodic windows [21,23,33].…”

Section: Introductionmentioning

confidence: 99%

Classification of the bifurcation structure of a periodically driven gas bubble

Varga

Hegedűs

2016

Nonlinear Dyn

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The bifurcation structure of a periodically driven spherical gas/vapour bubble is examined by means of methods of nonlinear analysis. The study of Behnia and his coworkers [1] revealed that the bifurcation structures with the pressure amplitude of the excitation as control parameter are structurally similar provided that R E ω is kept constant. In the present paper, this problem is revisited. Analytical and numerical investigations of the bubble oscillator, which is the Keller-Miksis equation, are presented. It is shown that the validity range of Behnia's condition is governed by the viscosity and the surface tension, and holds only for relatively large bubbles. In water, the effect of viscosity is negligible, and the surface tension plays significant role at bubble size lower than approximately 5 µm.

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“…AUTO is capable of tracking down whole bifurcation curves including the unstable part even if they contain multiple turning points, and it can detect the bifurcations and their types. This is the reason why AUTO is commonly used to study the bifurcation structure of nonlinear systems [5,53,[55][56][57][58][59][60][61]. In Fig.…”

Section: Coexisting Period-1 Solutionsmentioning

confidence: 99%

Non-feedback technique to directly control multistability in nonlinear oscillators by dual-frequency driving

et al. 2018

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A novel method to control multistability of nonlinear oscillators by applying dual-frequency driving is presented. The test model is the Keller-Miksis equation describing the oscillation of a bubble in a liquid. It is solved by an in-house initial-value problem solver capable to exploit the high computational resources of professional graphics cards. Dur-Electronic supplementary material The online version of this article (

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Basins of attraction in a harmonically excited spherical bubble model.

Cited by 16 publications

References 12 publications

A simple method to analyze the super-harmonic and ultra-harmonic behavior of the acoustically excited bubble oscillator

A simple method to analyze the super-harmonic and ultra-harmonic behavior of the acoustically excited bubble oscillator

Classification of the bifurcation structure of a periodically driven gas bubble

Non-feedback technique to directly control multistability in nonlinear oscillators by dual-frequency driving

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