MULTIPLE-SCALE AND NUMERICAL ANALYSES FOR THE NONLINEAR OSCILLATIONS OF A GAS BUBBLE SURROUNDED BY A MAXWELL'S FLUID

2019 ◽  
Vol 46 (3) ◽  
pp. 261-275
Author(s):  
César Yepes ◽  
Jorge Naude ◽  
Federico Mendez ◽  
Margarita Navarrete ◽  
Fátima Moumtadi
Keyword(s):  
Nonlinear Oscillations ◽  
Multiple Scale ◽  
Numerical Analyses ◽  
Gas Bubble

scholarly journals A model for nonlinear oscillations of a gas bubble in liquids.

1991 ◽  
Vol 90 (4) ◽  
pp. 2317-2317
Author(s):  
Jei‐Cheong Ryu ◽  
Ho‐Young Kwak
Keyword(s):  
Nonlinear Oscillations ◽  
Gas Bubble

Nonlinear dynamic responses of electrically actuated dielectric elastomer-based microbeam resonators

2021 ◽  
pp. 1045389X2110235
Author(s):  
Amin Alibakhshi ◽  
Hamidreza Heidari
Keyword(s):  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Time Integration ◽  
Time History ◽  
Nonlinear Resonance ◽  
Multiple Scale ◽  
Dielectric Elastomer ◽  
Constitutive Law ◽  
Dynamic Responses ◽  
Governing Equations

This paper aims to investigate the chaotic and nonlinear resonant behaviors of a dielectric elastomer-based microbeam resonator, incorporating material and geometric nonlinearities. The von Kármán strain-displacement equation is utilized to model the geometric nonlinearity. Material nonlinearity is described via the hyperelastic Gent model and Neo-Hookean constitutive law. The applied electrical loading to the elastomer includes both static and sinusoidal voltages. The governing equations of motion are formulated based on an energy approach and generalized Hamilton’s principle. Employing a single-mode Galerkin technique, the governing equations are obtained only in terms of time derivatives. The governing ordinary differential equations are solved by means of the multiple scale method and a time-integration-based solver. The nonlinear resonance characteristics are explored through the frequency-amplitude plots. The nonlinear oscillations of the system are analyzed making use of visual techniques such as phase plane diagram, Poincaré section and time history, and fast Fourier transform. Based on the results obtained, the resonant behavior is the hardening type. The vibration of the dielectric elastomer based-microbeam is the quasiperiodic response.

A Time-Varying Stiffness Rotor Active Magnetic Bearings Under Combined Resonance

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
U. H. Hegazy ◽  
M. H. Eissa ◽  
Y. A. Amer
Keyword(s):  
Multiple Scales ◽  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Multiple Scale ◽  
Magnetic Bearings ◽  
Time Varying ◽  
Active Magnetic Bearings ◽  
Gyroscopic Effects ◽  
Nonlinear Equations Of Motion ◽  
Combined Resonance

This paper is concerned with the nonlinear oscillations and dynamic behavior of a rigid disk-rotor supported by active magnetic bearings (AMB), without gyroscopic effects. The nonlinear equations of motion are derived considering a periodically time-varying stiffness. The method of multiple scales is applied to obtain four first-order differential equations that describe the modulation of the amplitudes and the phases of the vibrations in the horizontal and vertical directions. The stability and the steady-state response of the system at a combination resonance for various parameters are studied numerically, applying the frequency response function method. It is shown that the system exhibits many typical nonlinear behaviors, including multiple-valued solutions, jump phenomenon, hardening, and softening nonlinearity. A numerical simulation using a fourth-order Runge-Kutta algorithm is carried out, where different effects of the system parameters on the nonlinear response of the rotor are reported and compared to the results from the multiple scale analysis. Results are compared to available published work.

Forced nonlinear oscillations of a gas bubble in a large spherical flask (resonator) filled with a fluid

1998 ◽  
Vol 39 (5) ◽  
pp. 719-728
Author(s):  
R. I. Nigmatulin ◽  
V. Sh. Shagapov ◽  
G. Ya. Galeeva
Keyword(s):  
Nonlinear Oscillations ◽  
Gas Bubble ◽  
Large Spherical

A refined model of nonlinear nonspherical oscillations of a gas bubble in liquid

2007 ◽  
Vol 5 ◽  
pp. 241-247
Author(s):  
L.A. Kosolapova ◽  
V.G. Malakhov
Keyword(s):  
Mathematical Model ◽  
Nonlinear Oscillations ◽  
Spherical Shape ◽  
Bubble Surface ◽  
Surface Shape ◽  
Gas Bubble ◽  
Refined Model ◽  
Order Model ◽  
Third Order ◽  
The Third

A mathematical model of nonlinear oscillations of a gas bubble in a liquid is proposed, in which the change of the bubble surface shape is represented as a series of spherical harmonics, and the equations are accurate up to the third order with respect to the distortion amplitudes of the bubble spherical shape. It is shown that the application of the refined model can lead to modes of oscillation that differ from those obtained using the second-order model.

Nonlinear Oscillations of a Spherically Symmetric Single Bubble in an Acoustic Field

2011 ◽  
Vol 8 (1) ◽  
pp. 45-53
Author(s):  
E.V. Volkova ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Mass Transfer ◽  
Acoustic Field ◽  
Moving Boundary ◽  
Nonlinear Oscillations ◽  
Diffusion Problem ◽  
Spherically Symmetric ◽  
Lagrangian Coordinates ◽  
Gas Bubble ◽  
Bubble Wall ◽  
Convection Diffusion

In the present paper the dynamics of a single gas bubble under the influence of an acoustic field is studied, taking mass transfer through the moving bubble wall into account. Mass transfer is calculated separately in the diffusion problem. Due to changes in the pressure inside the bubble caused by oscillations of its volume, the concentration of the gas dissolved in the liquid undergoes oscillations of large amplitude near the bubble boundary. To eliminate the computational problems associated with the moving boundary, the convection-diffusion equations describing the transport of a gas dissolved in a liquid are written in Lagrangian coordinates.

Nonlinear oscillations of non-spherical cavitation bubbles in acoustic fields

1980 ◽  
Vol 101 (2) ◽  
pp. 423-444 ◽  
Author(s):  
P. Hall ◽  
G. Seminara
Keyword(s):  
Nonlinear Oscillations ◽  
Sound Field ◽  
Spherical Shape ◽  
Multiple Scale ◽  
Hysteresis Phenomenon ◽  
Driving Frequency ◽  
Acoustic Fields ◽  
Scale Type ◽  
Shape Oscillation ◽  
Secondary Bifurcations

The nonlinear stability of gas bubbles in acoustic fields is studied using a multiple-scale type of expansion. In particular the development of a subharmonic or a synchronous perturbation to the flow is investigated. It is shown when an equilibrium non-spherical shape oscillation of a bubble is stable. If the amplitude of the sound field is ε then it is shown that subharmonic perturbations of order ε½ can exist and be stable. Furthermore synchronous perturbations of order ε can exist and be stable. It is shown that synchronous perturbations, unlike the subharmonic case where the bifurcation is symmetric, bifurcate transcritically when the driving frequency is varied and also undergo secondary bifurcations. It is further shown that, in certain cases, the latter properties of the synchronous modes cause the flow to exhibit a hysteresis phenomenon when the driving frequency is varied.

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