微管内气泡的受迫振动

Forced oscillations of gaseous bubbles in microtubules

在气泡-液柱一维耦合振动模型的基础上对刚性微管两侧声压不相等时管内柱状气泡的轴向一维受迫振动进行了理论探索.声压不均匀分布不影响气泡线性振动时的共振频率,但振动幅度受到有效声压幅值的影响.利用逐级近似法分析了管内非线性振动气泡的基频、三倍频和三分之一分频振动的幅-频响应关系,结果表明当驱动声压超过0.1 MPa时,气泡振动处于非线性状态.非线性声响应特征主要表现为:基频和分频振动幅值响应的多值性;三倍频振动在低频区响应强于高频区;三分频振动在大于共振频率的频域内出现的概率更大.

Based on the model for the one-dimensional coupled oscillation of bubble-liquid column in tube, a theoretical investigation of the forced oscillation of a cylindrical gaseous bubble in a microtubule is presented. For the case that the two acoustic pressures of mierotubule ends are not homogenous, the linear natural frequency is not affected, but its oscillating amplitude is influenced by the effective acoustic pressure amplitude. The relations between the amplitudes of fundamental, third and one third harmonic oscillations and the acoustic frequency are analyzed using the succession-level approximation method. Numerical results show that the bubble oscillates nonlinearly if the effective value of acoustic pressure exceeds 0.1MPa. It is found that the amplituds of fundamental, third and one third harmonic oscillations are multivalued, and the response of third harmonic oscillation is stronger in the region of lower frequencies. Furthermore, the third harmonic oscillation may be probably induced in the region of ω/ω0≥ 1.