A planar stress-free boundary is known to destructively alter the nonlinear wave generation process including the second harmonic component. This is the reason why the harmonic generation measurements in the study of nonlinear fluids and solids have been limited to the through-transmission setup. Recently, we have found through acoustic modeling and simulation that a dual element transducer composed of the annular ring emitter and the inner disk receiver improves the second harmonic generation in the pulse-echo mode with the stress-free boundary. This paper utilizes a dual element transducer for nonlinearity parameter (β) measurements of solid specimens in the pulse-echo testing configuration. The theoretical derivation provides the received beam fields and the formula for β determination with all necessary corrections incorporating diffraction, attenuation and boundary reflection. The dual element transducer is applied to pulse-echo β measurements of aluminum alloy samples, and the results are found to be in good agreement with the through-transmission method.

中文翻译：

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双元素换能器用于二次谐波产生和固体材料非线性的脉冲回波测量

已知平面无应力边界会破坏性地改变包括二次谐波分量的非线性波的生成过程。这就是为什么在非线性流体和固体研究中将谐波生成测量限制在直通传输设置中的原因。最近，我们通过声学建模和仿真发现，由环形发射器和内部磁盘接收器组成的双元件换能器可以在无应力边界的脉冲回波模式下改善二次谐波的产生。本文利用双元件换能器在脉冲回波测试配置中测量固体样品的非线性参数（β）。理论推导提供了接收到的光束场和β的公式确定所有必要的校正，包括衍射，衰减和边界反射。将双元件换能器应用于铝合金样品的脉冲回波β测量，结果与透射法非常吻合。