Excitation efficiency and mode selection of ultrasonic Lamb wave mixing
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摘要:
研究了超声Lamb波混频的激励效率与模式选择。在非零能量流和相匹配条件的基础上, 结合Lamb波在结构中的状态分布, 提出了以激励效率参量作为超声Lamb波混频模式选择的依据。根据混频条件筛选混频模式对, 计算相应的激励效率参量, 并通过超声Lamb波混频的仿真模拟与实验测量进行验证。通过对比仿真与实验中得到的非线性参量与激励效率参量的关系, 证明了激励效率参量作为模式选择依据的有效性。研究表明, 激励效率参量可以有效地表征超声Lamb波混频的激发效率, 从而筛选非线性效应明显的模式对, 更好地实现损伤的检测与表征。
Abstract:The excitation efficiency and mode selection of ultrasonic Lamb wave mixing were studied. Based on the non-zero energy flow and matching conditions, combined with the distribution of Lamb wave in the structure, the excitation efficiency parameter was proposed as the basis for ultrasonic Lamb wave mixing mode selection. Based on the wave mixing conditions, the mode pairs were selected and excitation efficiency parameters were calculated. The effectiveness of the excitation efficiency parameter was verified through simulation and experimental measurements of ultrasonic Lamb wave mixing. Comparing the relationship between nonlinear parameters and excitation efficiency parameters obtained from simulation and experiments, the effectiveness of excitation efficiency parameters as a basis for mode selection has been demonstrated. Therefore, the excitation efficiency parameter can effectively characterize the excitation efficiency of ultrasonic Lamb wave mixing, thereby achieving the screening of mode pairs with obvious nonlinear effects for better detection and characterization of damage.
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Key words:
- Nonlinear ultrasonic /
- Lamb wave mixing /
- Excitation efficiency /
- Mode selection
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表 1 混频模式对筛选结果
模式对 $ {\boldsymbol{f}}_{\boldsymbol{a}} $ (MHz) $ {\boldsymbol{k}}_{\boldsymbol{a}} $ $ {\boldsymbol{f}}_{\boldsymbol{b}} $ (MHz) $ {\boldsymbol{k}}_{\boldsymbol{b}} $ $ {\boldsymbol{f}}_{\boldsymbol{n}} $ (MHz) $ {\boldsymbol{k}}_{\boldsymbol{n}} $ $ {\boldsymbol{k}}_{\boldsymbol{n}} $ Mode 1 0.713 0.139 0.933 0.189 1.646 0.052 与$ {k}_{b} $同向 S0S0S2 2 0.784 0.153 1.358 0.382 2.142 0.232 与$ {k}_{b} $同向 S0S0S2 3 2.044 0.679 0.971 0.198 3.015 0.485 与$ {k}_{a} $同向 S0S0S2 4 1.079 0.237 1.947 0.328 3.026 0.085 与$ {k}_{b} $同向 S0S1S3 5 2.002 0.698 2.319 0.803 4.321 0.112 与$ {k}_{b} $同向 A0A0S4 
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表 2 混频模式对激励效率参量
模式对 基频波1 基频波2 混频波 激励效率参量 标准化激励效率参量 1 0.713 MHz S0 0.933 MHz S0 1.646 MHz S2 1.277 × 10-15 1.000 2 0.784 MHz S0 1.358 MHz S0 2.142 MHz S2 1.558 × 10-15 1.220 3 2.044 MHz S0 0.971 MHz S0 3.015 MHz S2 0.614 × 10-15 0.481 4 1.079 MHz S0 1.947 MHz S1 3.026 MHz S3 3.1047 × 10-15 2.431 5 2.002 MHz A0 2.319 MHz A0 4.321 MHz S4 3.0521 × 10-15 2.390
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表 3 316L参数表
材料 杨氏模量 (MPa) 泊松比 密度 (t/mm3) 三阶弹性常数 (MPa) A B C 316L 2.02 × 105 0.28 7.89 × 10−9 −1.035 × 10−6 −8.25 × 10−5 −3.96 × 10−5
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表 4 三组模式对的标准化参量值
模式对 基频波1 基频波2 标准化激励效率参量 标准化非线性参量仿真值 标准化非线性参量测量值 1 0.713 MHz S0 0.933 MHz S0 1.000 1.000 1.000 2 0.784 MHz S0 1.358 MHz S0 1.220 1.363 1.370 3 2.044 MHz S0 0.971 MHz S0 0.481 0.553 0.558
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表 5 三组模式对的标准化参量值
模式对 基频波1 基频波2 混频波 标准化激励效率参量 非线性参量测量值 1 0.713 MHz S0 0.933 MHz S0 1.646 MHz S2 1.000 1.433 2 0.784 MHz S0 1.358 MHz S0 2.142 MHz S2 1.220 1.963 3 2.044 MHz S0 0.971 MHz S0 3.015 MHz S2 0.481 0.800 4 1.079 MHz S0 1.947 MHz S1 3.026 MHz S3 2.431 3.122 5 2.002 MHz A0 2.319 MHz A0 4.321 MHz S4 2.390 2.754
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