中文摘要：

考虑了非球形气泡在声场中的形状振动,推导了非球形气泡和球形气泡之间的次Bjerknes力方程,数值模拟了声场中非球形气泡和球形气泡之间的次Bjerknes力和两个球形气泡之间的次Bjerknes力,并对非球形气泡和球形气泡之间的次Bjerknes力的影响因素进行了分析讨论.研究结果表明：当驱动声压振幅大于非球形气泡的Black阈值且又能使得非球形气泡稳定振动时,在第一个声驱动周期内,非球形气泡和球形气泡之间的次Bjerknes力和两个球形气泡的次Bjerknes力方向差异较大,在大小上是两个球形气泡次Bjerkens力的数倍,且有着更长的作用距离.非球形气泡和球形气泡之间的次Bjerknes力取决于非球形气泡的形状模态、两个气泡初始半径的比值、驱动声压振幅、气泡间距和两个气泡的相对位置.

英文摘要：

The secondary Bjerknes force between bubbles in an acoustic field is a well-known acoustic phenomenon. The theoretical researches of the secondary Bjerknes force mainly focus on the case of two spherical bubbles. The secondary Bjerknes force between two spherical bubbles, calculated based on the linear equations, is very small and negligible.Therefore these theoretical researches donot give a good explanation for the phenomenon, such as ＂streamer formation＂and multi-bubble sonoluminescence（MBSL）. Experiments of sonoluminescence show that the shapes of the bubbles in a sound field are not entirely spherical. Nonspherical effects have an important influence on the secondary Bjerknes force when two bubbles come close to each other in a strong acoustic field（〉 1.0 × 10^5Pa）. How the shape distortion of a nonspherical bubble causes the secondary Bjerknes force between two bubbles to change, and how the secondary Bjerknes force affects the oscillations and movements of bubbles are major problems which we are to solve in the present research.The expression of the secondary Bjerknes force between a nonspherical bubble and a spherical bubble is obtained by considering the shape oscillation of a nonspherical bubble. We numerical simulate the secondary Bjerknes force between a nonspherical bubble and a spherical bubble based on the nonlinear oscillation equations of two bubbles, and compare the secondary Bjerknes force between a nonspherical bubble and a spherical bubble with the secondary Bjerknes force between two spherical bubbles in the same condition. We discuss the influence of nonspherical effects on the secondary Bjerknes force between two bubbles. The results show that when the amplitude of driving pressure is greater than the Blake threshold of a nonspherical bubble and makes the bubble oscillate stably, the secondary Bjerknes force between this nonspherical bubble and a spherical bubble is different from the secondary Bjerknes force between two spherical bubbles in direction and magnitude. The seco