中文摘要：

为了研究体积形变对气泡运动状态的影响，推导了在声波激励下考虑体积粘滞作用的气泡动力学模型以及其自治方程。通过数值计算分析了考虑体积粘滞作用时气泡的动力学特性以及激励声波频谱的能量变化规律，并与Keller方程的结果进行了对比。研究结果表明：气泡在运动状态为周期三以上时，体积粘滞会阻碍气泡的无规运动，甚至改变其动力学特性，因此气泡需要更高的激励阈值才能从分岔到混沌状态。且考虑体积粘滞作用时，气泡的运动状态不同激励声波通过气泡后的频谱展宽程度也不同。为实际应用气泡的动力学特性以及激励声波频谱的能量转移方面提供了一定的理论基础。

英文摘要：

In order to investigate the effect of volume deformation on bubble motion state, the bubble dynamics mod？el and its autonomous equation taking into account the volume viscosity effect under the acoustic excitation was de？rived. The dynamic characteristics of bubbles and the spectrum energy variations of incentive sound wave when tak？ing into account the volume viscosity effect were analyzed by numerical simulation and compared with the results of the Keller equation. The results show that when the motion state of bubbles is more than period 3, the volume vis？cosity will hinder the random motion of bubble, and even change its dynamic characteristics. Indicating, the bub？bles need a higher incentive threshold from the bifurcations to chaos. When the motion states of bubbles are differ？ent, the spectrum broadening degree of the incentive wave through the bubbles are also different when considering the volume viscosity effect. It provides a theoretical basis for the practical application of the bubble dynamics and the energy transfer of incentive acoustic spectrum.