声波幅度对有限振幅声波传播畸变的影响

摘要

To confirm the characteristic of nonlinear propagation,the propagation distortion of single-frequency and double-frequency acoustic wave was investigated by theories and experiments.According to the propagation equation of single acoustic wave by Riemann Earnshaw and Bessel-Fubini,the simulation harmonic curves were got in the process of nonlinear propagation,and the threshold relationship between nonlinear effect and amplitude of single-frequency acoustic wave was observed based on experiments. Based on the mathematical analytic formula of nonlinear cumulative velocity of acoustic wave and gradient of acoustic waves at discontinuity point after nonlinear interaction of two acoustic waves by Burgers equation,the relation curve of nonlinear cumulative velocity of acoustic wave,transitive gradient and amplitude ratio of acoustic wave were simulated.The results show that when acoustic wave propagates with nonlinear effect in medium,the characteristic of nonlinear propagation has cumulative effect.When the initial phase difference is 0 or π,the nonlinear interaction is gradually decreased or increased among nonlinear cumulative velocity of acoustic wave,transitive gradient and amplitude ratio of acoustic wave. When the amplitude ratio is increased to a certain value,the nonlinear cumulative velocity of acoustic wave and the transitive gradient both tend to a constant value.%为确定声波的非线性传播特性，采用理论与试验相结合的方式对单列声波与两列声波传播的畸变现象进行研究。依据黎曼厄恩肖与 Bessel-Fubini 解理论给出了单列声波的传播方程，仿真研究了非线性传播过程中产生的各阶谐波曲线，试验观测了单列声波非线性效应与声波幅值的阈值关系；采用 Burgers 方程给出了两列声波发生非线性相互作用后声波非线性累积速度与间断点处声波梯度的数学解析式，仿真分析了声波传播过程中非线性累积速度、跃变梯度与声波幅值比的关系曲线。结果表明，当声波在介质中以非线性效应传播时，非线性传播特性具有累积效应；初始相位差为0或π的两列声波发生非线性相互作用时，非线性累积速度、间断点处声波跃变梯度与声波幅值比存在逐渐减小或逐渐增大的趋势；当幅值比增大到某一个固定值时，随幅值比的继续增大，声波的非线性累积速度与跃变梯度均趋于恒定值。