柱状扰动体引起圆柱谐振腔共振频率偏移的数值模拟

Resonance frequency shift in a cylindrical cavity with an inner small coaxial cylinder

基于微扰理论,研究了内部存在一个同轴圆柱扰动体时圆柱谐振腔共振频率的偏移问题.其中,圆柱谐振腔的边侧面是刚性的,上下底面应力自由.经过推导,得出了圆柱扰动体存在时谐振腔的声势与共振频率的表达式.在此基础上,分析了谐振腔与圆柱扰动体各种参数对谐振腔共振频率的影响.数值模拟结果表明,谐振腔的共振频率受扰动体在谐振腔中的位置影响较大.圆柱谐振腔的共振频率在圆柱扰动体居中时是最大值,并且其共振频率对扰动体的声速敏感;当扰动体在谐振腔两端时,谐振腔共振频率是最小值,并且其对扰动体的密度敏感.最后,通过数值模拟结果和实验测量结果之间的对比,发现两者的基本变化趋势是吻合的.

Based on the perturbation theory, the resonance acoustic spectroscopy for a resonance cylindrical cavity with an inner small coaxial cylinder is investigated. Analytical expressions, in a cylindrical cavity with rigid walls and traction-free ends, are derived for the acoustic resonance frequency shifts caused by the inclusion of a coaxially small cylindrical sample. The effects of various parameters on resonant frequencies of the resonant cylinder are studied in detail. The simulation results show that the lowest mode resonant frequency is more sensitive to the position of sample. When the sample is located in the middle of the cylinder cavity, the resonant frequency gets its maximum and is more sensitive to the sample velocity. When the sample is located at two ends, the resonant frequency gets its minimum and is more sensitive to sample density. At last, through the comparison of the experimental and theoretical values, their changing tendency is in agreement qualitatively.