Open AccessNonlinear forced oscillations of gaseous bubbles in elastic microtubules
Author(s) -
Chenghui Wang,
Jianchun Cheng
Publication year - 2013
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.62.114301
Subject(s) - oscillation (cell signaling) , physics , nonlinear system , bubble , resonance (particle physics) , amplitude , nonlinear resonance , mechanics , harmonic , nonlinear oscillations , harmonic oscillator , classical mechanics , optics , atomic physics , acoustics , quantum mechanics , biology , genetics
The wall of elastic microtubules can be described as a membrane-type elastic structure. An oscillating system driven by ultrasound consists of liquid columns, a bubble and elastic wall of the tube. The nonlinear properties of this system are explored. Based on the successive approximation method, the nonlinear resonance frequencies, the amplitude response of fundamental and third oscillations to driving acoustic wave, and the mechanism of resonance response related to the driving wave whose frequency is lower than the resonant frequency are analyzed theoretically. The nonlinear system is oscillating in two directions: the axial and radial directions of the bubble in the microtubule. Numerical results show that the resonance responses cannot be present simultaneously. It has been found that the amplitudes of the fundamental and third harmonic oscillation are multivalued, which may lead to instable response. The third harmonic oscillation is stronger in the region of lower frequencies.