Applied Research Laboratories, University of Texas at Austin, Austin, Texas 78713-8029, USA.
J Acoust Soc Am. 2012 Sep;132(3):1346-57. doi: 10.1121/1.4730888.
Three models are considered for describing the dynamics of a pulsating cylindrical bubble. A linear solution is derived for a cylindrical bubble in an infinite compressible liquid. The solution accounts for losses due to viscosity, heat conduction, and acoustic radiation. It reveals that radiation is the dominant loss mechanism, and that it is 22 times greater than for a spherical bubble of the same radius. The predicted resonance frequency provides a basis of comparison for limiting forms of other models. The second model considered is a commonly used equation in Rayleigh-Plesset form that requires an incompressible liquid to be finite in extent in order for bubble pulsation to occur. The radial extent of the liquid becomes a fitting parameter, and it is found that considerably different values of the parameter are required for modeling inertial motion versus acoustical oscillations. The third model was developed by V. K. Kedrinskii [Hydrodynamics of Explosion (Springer, New York, 2005), pp. 23-26] in the form of the Gilmore equation for compressible liquids of infinite extent. While the correct resonance frequency and loss factor are not recovered from this model in the linear approximation, it provides reasonable agreement with observations of inertial motion.
考虑了三种模型来描述脉动圆柱气泡的动力学。推导了无限可压缩液体中圆柱气泡的线性解。该解考虑了由于粘性、热传导和声波辐射引起的损失。结果表明，辐射是主要的损失机制，比相同半径的球形气泡大 22 倍。预测的共振频率为其他模型的限制形式提供了比较基础。考虑的第二种模型是常用的瑞利-普莱塞特形式的方程，要求不可压缩液体在有限范围内才能发生气泡脉动。液体的径向范围成为一个拟合参数，结果发现，对于模拟惯性运动与声振动，需要使用非常不同的参数值。第三种模型是由 V. K. Kedrinskii 以无限可压缩液体的吉尔莫方程的形式发展起来的[爆炸动力学（Springer，纽约，2005 年），第 23-26 页]。在这个模型中，在线性近似下，无法从该模型中恢复出正确的共振频率和损耗因子，但它与惯性运动的观测结果吻合较好。
