Nonlinear normal modes and localization in two bubble oscillators
Related Experiment Video
Updated: Mar 12, 2026

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System
Published on: May 9, 2021
Naohiro Sugita1, Toshihiko Sugiura1
1Department of Mechanical Engineering, Keio University, Yokohama 2238522, Japan.
Abstract:
We investigated a bifurcation structure of coupled nonlinear oscillation of two spherical gas bubbles subject to a stationary sound field by means of nonlinear modal analysis. The goal of this paper is to describe an energy localization phenomenon of coupled two-bubble oscillators, resulting from symmetry-breaking bifurcation of the steady-state oscillation. Approximate asymptotic solutions of nonlinear normal modes (NNMs) and steady state oscillation are obtained based on the method of multiple scales. It is found that localized oscillation arises in a neighborhood of the localized normal modes. The analytical solutions of the amplitude and the phase shift of the steady-state oscillation are compared to numerical results and found to be in good agreement within the limit of small-amplitude oscillation. For larger amplitude oscillation, a bifurcation diagram of the localized solution as a function of the driving frequency and the separation distance between the bubbles is provided in the presence of the thermal damping. The numerical results show that the localized oscillation can occur for a fairly typical parameter range used in practical experiments and simulations in the early literatures.
Related Concept Videos
Modes of Standing Waves - I
Damped Oscillations
Although friction and other non-conservative...
Oscillations about an Equilibrium Position
Modes of Standing Waves: II
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end....
Forced Oscillations
Oscillations In An LC Circuit

