Increasing the number of closely packed air bubbles immersed in water changes the frequency of the Minnaert resonance. The collective interactions between bubbles in a small ensemble are primarily in the same phase, causing them to radiate a spherically symmetric field that peaks at a frequency lower than the Minnaert resonance for a single bubble. In contrast, large periodic arrays include bubbles that are further apart than half of the wavelength such that collective resonances have bubbles oscillating in opposite phases, ultimately creating a fundamental resonance at a frequency higher than the single-bubble Minnaert resonance. This work investigates the transition in resonance behavior using a modal analysis of a mass-spring system and a boundary element method. The computational complexity of the full-wave solver is significantly reduced to a linear dependence on the number of bubbles in a rectangular array. The simulated acoustic fields confirm the initial downshift in resonance frequency and the strong influence of collective resonances when the array has hundreds of bubbles covering more than half of the wavelength. These results are essential in understanding the low-frequency resonance characteristics of bubble ensembles, which have important applications in diverse fields such as underwater acoustics, quantum physics, and metamaterial design.

中文翻译：

---

用边界元法模拟集体气泡共振的频移

增加浸入水中的紧密堆积的气泡数量会改变 Minnaert 共振的频率。小型整体中气泡之间的集体相互作用主要处于同一相位，导致它们辐射出一个球对称场，该场的峰值频率低于单个气泡的 Minnaert 共振频率。相比之下，大型周期性阵列包含的气泡比波长的一半更远，因此集体共振会使气泡以相反的相位振荡，最终在高于单气泡 Minnaert 共振的频率下产生基本共振。这项工作使用质量弹簧系统的模态分析和边界元法研究共振行为的转变。全波求解器的计算复杂性显着降低为与矩形阵列中气泡数量的线性相关性。模拟声场证实了共振频率的初始下移以及当阵列有数百个气泡覆盖超过一半波长时集体共振的强烈影响。这些结果对于理解气泡集合体的低频共振特性至关重要，气泡集合体在水下声学、量子物理学和超材料设计等不同领域具有重要应用。模拟声场证实了共振频率的初始下移以及当阵列有数百个气泡覆盖超过一半波长时集体共振的强烈影响。这些结果对于理解气泡集合体的低频共振特性至关重要，气泡集合体在水下声学、量子物理学和超材料设计等不同领域具有重要应用。模拟声场证实了共振频率的初始下移以及当阵列有数百个气泡覆盖超过一半波长时集体共振的强烈影响。这些结果对于理解气泡集合体的低频共振特性至关重要，气泡集合体在水下声学、量子物理学和超材料设计等不同领域具有重要应用。