固体中二维纵波非线性方程的摄动解  

Perturbation solution of two-dimensional longitudinal wave nonlinear equation in solid

作　　者：钱昕彤 韩庆邦 苏娜娜 钱佳文 柏乐 单鸣雷 QIAN Xintong;HAN Qingbang;SU Nana;QIAN Jiawen;BAI Le;SHAN Minglei(College of Internet of Things,Hohai University,Changzhou 213022,Jiangsu,China)

机构地区：[1]河海大学物联网工程学院,江苏常州213022

出　　处：《声学技术》2022年第1期57-63,共7页Technical Acoustics

基　　金：国家自然科学基金(11874140、11574072);声场声信息国家重点实验室开放课题研究基金(SKLA201913)资助项目。

摘　　要：针对二维纵波非线性方程的求解问题进行了研究。从二维纵波非线性方程出发,围绕声马赫数对该方程的解进行二阶摄动展开,求解出二维非线性纵波方程的二阶摄动解。根据计算结果定义二次谐波沿x轴的传播分量和沿y轴的传播分量与入射基波的振幅比为非线性系数,并对基波和二次谐波的传播特性进行详细讨论,探究了二维纵波在固体中传播时其入射波振幅、入射波频率、入射角以及声传播距离对非线性系数的影响。该非线性系数可以描述二维非线性纵波的基波和二次谐波的传播规律,可用于固体材料的非线性定性分析,为后续探究二维纵波斜入射在固体中的传播规律提供理论依据。The main work in this paper is to solve the two-dimensional nonlinear longitudinal wave equation.The perturbation method is used to expand the solution of this equation to the second order with acoustic Mach coefficient.According to the calculation results,the amplitude ratio of the second harmonic propagation components along the x-axis and y-axis to the incident fundamental wave is defined as nonlinear coefficients,and the propagation characteristics of the fundamental wave and the second harmonic are discussed in detail.When the two-dimensional longitudinal wave propagates in a solid,the effects of incident wave frequency,incident angle and sound propagation distance on the nonlinear coefficient are explored.This nonlinear coefficient can describe the propagation regularities of the fundamental wave and the second harmonic of the two-dimensional nonlinear longitudinal wave,and can be used to qualitatively analyze the nonlinearity of solid materials,which provides a theoretical basis for the subsequent exploration of the propagation regularity of oblique incident longitudinal wave in solid.

关 键 词：非线性纵波方程 二次谐波 摄动解 

分 类 号：O422.7[理学—声学]