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弹性微管内气泡的非线性受迫振动*
Nonlinear forced oscillations of gaseous bubbles in elastic microtubules*
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摘要: 将弹性管壁视为膜弹性结构,探索在外部声场作用下弹性微管内液柱-气泡-管壁构成耦合振动系统的非线性特征.利用逐级近似法对系统非线性共振频率、基频和三倍频振动幅值响应、分频激励共振机理等进行了理论分析.基频和三倍频振动的幅-频响应数值结果表明:气泡的轴向共振和管壁共振不能同时出现;两垂直方向的振动均表现出幅值响应多值性,进而可能引起系统的不稳定声响应;三倍频振动在低频区的声响应强于高频区.Abstract: The wall of elastic microtubules can be described as a membrane-type elastic structure. An oscillating system driven by ultrasound consists of liquid columns, a bubble and elastic wall of the tube. The nonlinear properties of this system are explored. Based on the successive approximation method, the nonlinear resonance frequencies, the amplitude response of fundamental and third oscillations to driving acoustic wave, and the mechanism of resonance response related to the driving wave whose frequency is lower than the resonant frequency are analyzed theoretically. The nonlinear system is oscillating in two directions: the axial and radial directions of the bubble in the microtubule. Numerical results show that the resonance responses cannot be present simultaneously. It has been found that the amplitudes of the fundamental and third harmonic oscillation are multivalued, which may lead to instable response. The third harmonic oscillation is stronger in the region of lower frequencies.
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