| 非线性声波方程二次谐波高阶近似解及实验验证 |
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| 引用本文： | 张世功,张克声,丁凯,吴先梅.非线性声波方程二次谐波高阶近似解及实验验证[J].声学学报,2021,46(4):633-640. |
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| 作者姓名： | 张世功 张克声 丁凯 吴先梅 |
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| 作者单位： | 1. 贵州理工学院 贵阳 550003; |
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| 基金项目： | 贵州理工学院高层次人才引进项目(XJGC20190670)贵州省科学技术基金项目(黔科合基础-ZK[2021]一般318)资助贵州理工学院科技专项项目(KJZX17-005)近地面探测技术重点实验室基金项目(TCGZ2018A003)国家自然科学基金项目(11764007) |
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| 摘 要： | 非线性声波方程的传统二次谐波二阶近似解不够精确,对测量材料的非线性系数造成较大误差。利用摄动法展开非线性声波方程得到一系列非齐次偏微分方程,根据低阶解的性质拟定高阶特解的形式,通过符号计算求出高次谐波特解,对所有二次谐波成分求和最终获得二次谐波的高阶近似解。在水中开展非线性声学实验验证高阶近似解,结果表明:二次谐波相对幅度随传播距离和输入信号均呈现先增加后减小的趋势,高阶近似解即使在传播距离不太短和输入信号不太弱的宽泛条件下也能更好地吻合实验结果。得到的高阶近似解不仅弥补了现有二次谐波幅度理论公式的不足,进行非线性声学实验时还可扩展测量范围,充分利用实验数据也能提高非线性系数的测量精度。
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| 关 键 词： | 非线性声波 二次谐波 高阶近似解 摄动法 |
| 收稿时间： | 2020-04-01 |
High order approximate solution of nonlinear acoustic equation:development and validation |
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| Affiliation: | 1. Guizhou Institute of Technology, Guiyang, 550003;2. Science and Technology on Near-Surface Detection Laboratory, Wuxi, 214035;3. Guizhou Research Center for Multidisciplinary Conjunction of Medicine and Engineering, Guiyang, 550003;4. Institute of Acoustics, Chinese Academy of Sciences, Beijing, 100190 |
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| Abstract: | For the nonlinear acoustic wave equation,the commonly used second harmonic solution is not accurate enough,which causes a big error in measuring the material nonlinearity.Using perturbation method,nonlinear acoustic wave equation can be expanded into a series of inhomogeneous partial differential equations.The special solution forms of the high harmonics are formulated according to the properties of the low harmonic solutions.Then the high-order harmonic solutions are obtained with symbol calculation tool.Thus the high order approximate solution of the second harmonic can be achieved by summing up all of the second harmonic solutions.To verify the high order approximate solution,nonlinear acoustic experiments are carried out in water.The results show that the relative amplitude of the second harmonic increases firstly and then decreases with the propagation distance and the excited primary amplitude.The high order approximate solution can make up for the theory deficiency of the second harmonic perturbation solution,can broaden experimental range in measuring the material nonlinearity and can improve the accuracy of the measured nonlinearity by making full use of the experimental data. |
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