中文摘要：

基于准线性近似理论研究有限幅值波的反射基波和二次谐波声场特性,采用多元高斯声束将其表征为平面波解、衍射项和衰减项组合的形式,推导出超声反射法测量固体纵波非线性系数的计算模型。对经垂直入射自由界面的反射二次谐波进行模拟分析,结果显示,尽管入射二次谐波的反射波与新产生的二次谐波相位相反导致总的反射二次谐波减弱,但当试块厚度大于1/2倍瑞利距离时,探头接受到的反射二次谐波可用于固体材料纵波非线性系数的有效测量。设计并开展了6061铝的纵波非线性系数测量试验,结果表明当考虑反射、衍射修正和衰减补偿后,反射法测得的纵波非线性系数值与透射法的测量结果相近,但相比透射法,反射法具有试验要求低、限制条件少等优势,为固体材料纵波非线性系数测量的实际应用提供了一种有效方法。

英文摘要：

The reflected fundamental and second harmonic sound fields of finite amplitude are studied based on the quasilinear theory, and they are presented as the combinations of pure plane wave solutions, attenuation corrections and diffraction corrections with multi-Gaussian beams model. A modified equation for calculating nonlinear parameter using pulse-echo method is derived. These second harmonic components reflected from a stress-free interface at normal incidence are simulated, and the results show that the total second harmonic components will be reduced as the reflected component and the new generated one have inverse phases. However, it is found that when the thickness of the sample is larger than 1/2 of the Rayleigh distance, the pulse-echo method can be used to determine the nonlinear parameter as the transducer can receive effective total second harmonic components. The nonlinear parameter of Al-6061 sample is measured experimentally using pulse-echo method, and the measured value with consideration of diffractions and attenuations is close to that from pitch-catch method, which verifies the proposed method. Compared with pitch-catch method, the pulse-echo method is less limited by the experiment setup and it provides a useful tool to determine the nonlinear parameters of solids.