Possibility of using dual frequency to control chaotic oscillations of a   spherical bubble
  Acoustic cavitation bubbles are known to exhibit highly nonlinear and unpredictable chaotic dynamics. Their inevitable role in applications like sonoluminescence, sonochemistry and medical procedures suggests that their dynamics be controlled. Reducing chaotic oscillations could be the first step in controlling the bubble dynamics by increasing the predictability of the bubble response to an applied acoustic field. One way to achieve this concept is to perturb the acoustic forcing. Recently, due to the improvements associated with using dual frequency sources, this method has been the subject of many studies which have proved its applicability and advantages. Due to this reason, in this paper, the oscillations of a spherical bubble driven by a dual frequency source, were studied and compared to the ones driven by a single source. Results indicated that using dual frequency had a strong impact on reducing the chaotic oscillations to regular ones. The governing parameters influencing its dynamics are the secondary frequency and its phase difference with the fundamental frequency. Also using dual frequency forcing may arm us by the possibility of generating oscillations of desired amplitudes. To our knowledge the investigation of the ability of using a dual frequency forcing to control chaotic oscillations are presented for the first time in this paper. 
Sohrab Behnia, Amin Jafari, Wiria Soltanpoor, Okhtai Jahanbakhsh