中文摘要：

振动气泡形成辐射场影响其他气泡的运动,故多气泡体系中气泡处于耦合振动状态.本文在气泡群振动模型的基础上,考虑气泡间耦合振动的影响,得到了均匀球状泡群内振动气泡的动力学方程,以此为基础分析了气泡的非线性声响应特征.气泡间的耦合振动增加了系统对每个气泡的约束,降低了气泡的自然共振频率,增强了气泡的非线性声响应.随着气泡数密度的增加,振动气泡受到的抑制增强;增加液体静压力同样可抑制泡群内气泡的振动,且存在静压力敏感区（1—2 atm,1 atm=1.01325×10~5Pa）;驱动声波对气泡振动影响很大,随着声波频率的增加,能够形成空化影响的气泡尺度范围变窄.在同样的声条件、泡群尺寸以及气泡内外环境下,初始半径小于5μm的气泡具有较强的声响应.气泡耦合振动会削弱单个气泡的空化影响,但可延长多气泡系统空化泡崩溃发生的时间间隔和增大作用范围,整体空化效应增强.

英文摘要：

The pressure wave emitted by a pulsating bubble affects the motions of other bubbles,so in an acoustic field bubbles are in a state of coupled oscillation.In this paper,a cluster with cavitation bubbles inside is considered,and a mathematical model is developed to describe the dynamics of the bubbles of the same radius inside a spherical cluster when the effects of coupled oscillation are included.Based on this new model,the nonlinear acoustic response of cavitation bubbles is analyzed numerically.Comparison of our model with those in the literature,shows that bubbles are suppressed heavily.Because of the coupled oscillations of bubbles,the motions of a bubble are affected by more constraints in the system,which cause the decrease of natural frequency of the bubbles.The nonlinear acoustical response of bubbles is improved by the coupled oscillation in a bubble cluster.With the rise in number density of the cluster,the suppression of bubble oscillation is enhanced.For a cluster of 1 mm radius,when the bubble number is below 500,the change of bubble number may cause a sharp decrease of maximum radial displacement of the bubbles.In cavitation region,there are bubble clusters and large-sized bubble,and the moving large bubble can absorb small bubbles from the surface of bubble cluster,so the bubble numbers inside a cluster varies with time,which may change the acoustic response of coupled oscillating bubbles.The increase of the liquid static pressure can suppress the oscillation of bubbles too,and there is a sensitive region（1–2 atm） that affects remarkably the acoustical response of bubbles.Driving ultrasound can affect the motion of bubble greatly.The range of cavitation bubble size is narrowed when the wave frequency increases.The bubbles whose initial radii are close to 5 μm are easy to be activated by ultrasound under given acoustic conditions,i.e.sizes of bubble cluster,surrounding liquid and inner gas.The cluster oscillation of bubbles may suppress the motion of individual bubbles,and weaken the cavitio