Abstract
System analysis of bubble oscillations in an elastic tube is important for medical applications using nano/microbubbles such as ultrasonic contrast agents and high intensity focused ultrasound. In order to investigate inuences of the bubble-bubble interaction on the natural frequencies of two bubbles, a simple bubble model combined with the springmass system for the tube wall is proposed. In this model, the bubbles are represented by point sources for volume oscillations. The natural frequencies of the system are derived by linearizing the governing equations. Two bubble resonance frequency modes are obtained from the eigenvalue analysis. The eigenvector analysis shows that the lower resonance frequency of the bubble corresponds to the mode in which both bubbles oscillate with the same phase; the tube wall also oscillates with the same phase. The higher corresponds to the mode in which one bubble oscillates with inverse phase to the other; the left-hand side of the tube wall oscillates with the inverse phase to the right-hand side of the tube wall while either side of the tube oscillates with the same phase as each nearby bubble.
