Dynamic stabilization of an asymmetric nonlinear bubble oscillator

Hegedűs, Ferenc; Kalmár, Csanád

doi:10.1007/s11071-018-4360-5

Cited by 24 publications

(20 citation statements)

References 91 publications

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“…To analyze the potential structure, we first revisit briefly the well-known theory of bubbles dynamics in relation to our model as shown in Fig. 1 (a) [116] , [117] , [118] , [119] , [120] , [121] . Accordingly, the oscillation of gas bubbles can be classified into three distinct regions relative to the special threshold which we summarise below.…”

Section: Equilibrium and Stabilitymentioning

confidence: 99%

“… (I) If the ambient pressure is higher than the vapour pressure of the liquid, the freely oscillating bubble posses only one stable equilibrium state, denoted as case I in Ref. [120] . (II) When the ambient pressure falls below the so-called Blake’s critical threshold or is in its neighbourhood, there exist two equilibria, one of which is stable while the other is unstable.…”

Section: Equilibrium and Stabilitymentioning

confidence: 99%

“…This condition was classified as case II in Ref. [120] . (III) The trajectory of the system could tend to infinity whenever the ambient pressure is lower than the Blake’s critical threshold so that the dynamics is neither stable nor unstable, and without any local/global maxima/minima.…”

Section: Equilibrium and Stabilitymentioning

confidence: 99%

See 2 more Smart Citations

Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator

Omoteso

Roy-Layinde

Laoye

et al. 2021

Ultrasonics Sonochemistry

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Section: Equilibrium and Stabilitymentioning

confidence: 99%

Section: Equilibrium and Stabilitymentioning

confidence: 99%

See 1 more Smart Citation

Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator

Omoteso

Roy-Layinde

Laoye

et al. 2021

Ultrasonics Sonochemistry

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“…The final, optimized code is approximately 50 times faster on the aforementioned card than on a four core Intel Core i7-4790 CPU. For further details on GPU accelerated ODE solvers, the interested reader is referred to the publications [10,21,[32][33][34][35][36].…”

Section: The Bubble Model and The Numerical Methodsmentioning

confidence: 99%

High Dimensional Parameter Fitting of the Keller–Miksis Equation on an Experimentally Observed Dual-Frequency Driven Acoustic Bubble

Varga

Mettin

2019

Period. Polytech. Mech. Eng.

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A parameter identification technique of an underlying bubble model of an experimentally observed single bubble in a cluster under dual-frequency external forcing is presented. The measurements are carried out via high-speed camera recordings at a rate of 162750 frames per second. The used frequencies during the experiment are 25 kHz and 50 kHz. With a digital image processing technique, the measured bubble radius as a function of time is determined. The employed governing equation for the parameter fitting is the Keller–Miksis equation being a second order ordinary differential equation. The unknown four-dimensional parameter space is composed by the two pressure amplitudes, the phase shift of the dual-frequency driving and the equilibrium size of the bubble. In order to obtain an optimal parameter set within reasonable time, an in-house initial value problem solver is used running on a graphics processing unit (GPU). The error function measuring the distance between the numerical simulations and the measurement is based on the identification of the maximum bubble radii during each subsequent period of the external forcing. The results show a consistent estimation of both pressure amplitudes. The optima of phase shift and equilibrium bubble size are less significant due to a valley-like shape of the error function. Nevertheless, reasonable values are found that lead to estimations of pressure and temperature peaks during bubble collapse.

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“…In , the Adomian decomposition method (ADM) is used to predict the trajectory of the bubble. In Hegedűs and Kalmár (2018), the authors discuss the stabilization of bubble movement by adding harmonic force to the Rayleigh-Plesset equation. They also analyzed the effect of liquid viscosity on the bifurcation structure of the bubble dynamic.…”

Section: Introductionmentioning

confidence: 99%

Robust Nonsingular Terminal Sliding Mode Control of Radius for a Bubble Between Two Elastic Walls

Badfar

Ardestani

Beheshti

2020

J Control Autom Electr Syst

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In many industrial and medical systems, there is a bubble between two elastic walls. On the other hand, the collapse of bubbles is considered a constant source of energy lost and causes system damage. This research is the first attempt to prevent from bubble collapse between two elastic boundaries by using control algorithms. In this paper, first, the nonlinear dynamic model of the bubble between two elastic walls is introduced and then rewritten into a state-space form. The second part of this paper is devoted to the design of the sliding mode controller, where the ultrasonic pressure plays the role of control input and the output is bubble radius. At first, terminal sliding mode control is proposed. Although this method ensures finite-time convergence, its main drawback is singularity in the control input signal. The nonsingular terminal sliding mode control is proposed to solve the problem of singularity in the control input signal. A rigorous stability analysis is also presented using the Lyapunov theory to demonstrate the stability of nonsingular sliding manifold. The effect of controller parameters on the performance of the closed-loop system is investigated. Finally, some simulation results including the case of parametric uncertainty are also presented to demonstrate the efficiency of the proposed scheme. The results of this study are of immediate interest for industrial applications such as designing pumps and valves and medical applications such as targeted ultrasound imaging and cancer treatment.

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Dynamic stabilization of an asymmetric nonlinear bubble oscillator

Cited by 24 publications

References 91 publications

Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator

Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator

High Dimensional Parameter Fitting of the Keller–Miksis Equation on an Experimentally Observed Dual-Frequency Driven Acoustic Bubble

Robust Nonsingular Terminal Sliding Mode Control of Radius for a Bubble Between Two Elastic Walls

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