Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 11674206, 11874253)
Received Date:09 December 2020
Accepted Date:28 December 2020
Available Online:29 May 2021
Published Online:05 June 2021
Abstract:The formula for the nonlinear propagation of harmonics is obtained by using the generalized Navier-Stokes equations and the modified equations of state, considering the presence of heat transfer and fluid viscidity. The quantitative relationship among the harmonic pressure, initial sound pressure amplitude, frequency and the media property is obtained by approximately solving the single-frequency acoustic equation. In this paper, the hamonics’ distributions and propagations in the radiation field of single- and double-frequency sound source with different driving pressures and frequencies are discussed. It is found that new harmonics constantly appear in the sound field, and each-order harmonic of excitation gradually increases and then weakens with the increase of distance. The amplitude of harmonic pressure increases with the increase of the driving acoustic pressure near the sound source, but decreases with the increase of the frequency. Compared with the single-frequency field, the dual-frequency field has a large propagation distance, a very uniform acoustic energy distribution, and a large harmonic content in the far-field when the input total sound energy is constant. The physical mechanism is that the higher driving frequency causes a faster acoustic loss, a slower harmonic accumulation, and a smaller sound propagation distance. The higher driving pressure causes the much fundamental sound energy to be transferred, the more harmonics to be generated, the fundamental wave to be attenuated faster, and the negative effect of sound pressure on far-field sound energy to be increased. Through the analysis, it is found that the multi-frequency sound source can increase the propagation distance of sound, and improve the uniformity of sound energy distribution. Keywords:nonlinear effect/ wave equations/ acoustic parametrics
从图1可以看到, 在声源附近的声场中以基波为主, 谐波的含量较少; 随着传播距离的增大, 基波的声压逐渐减小, 谐波的声压逐渐增大. 这表明声场的能量由基波向高次谐波发生了转移且在临界距离处达到了最大; 阶数越高的谐波声压越小转移的能量也越少. 图1中谐波声能约占基频能量的13%, 其中有9%的声能转换成了二次谐波. 为了简化问题, 以下仅讨论二次谐波的产生与传播规律. 在不同驱动声压、不同频率下产生的二次谐波曲线如图2所示. 从图2(a)中可以看出, 当声波频率为1.5 MHz时, 驱动声压越大, 产生的二次谐波的声压越大; 随着距离的增大, 二次谐波的声压值先增大后减小; 二次谐波的幅值越大, 衰减的也越快. 从图2(b)中可以看出, 驱动声压幅值为4.8 × 105 Pa时, 驱动频率越大, 二次谐波的声压幅值越小; 随着距离的增大, 二次谐波的声压幅值先增大后减小; 声压幅值越小的二次谐波衰减得越快. 图1和图2表明, 谐波的强度与声源的驱动声压、频率以及和声源的间距有关, 驱动声压较高、频率较低的声场中更容易滋生谐波. 图 2 二次谐波曲线 (a)不同声压下的二次谐波; (b)不同频率下的二次谐波 Figure2. The distribution of second harmonic: (a) Different acoustic pressure; (b) different acoustic frequency.
驱动声压不同时, 产生的谐波的声能与声场总能量之比的分布曲线如图3所示. 当频率为1.5 MHz时, 随着驱动声压的增大, 声场中谐波能量的含量比也随之增大, 这说明在声的非线性传播过程中, 驱动声压越大基波向谐波转移的声能量越多; 随着距离的增大, 谐波的含量逐渐积累增大而后减小, 驱动声压越强谐波含量比的变化越快. 图 3 谐波声能与总能量比分布 Figure3. Distributions of the ratio of the hamonic and total energies.
图 5 差频波声压分布曲线 Figure5. The acoustic pressure curves of difference frequency.
从图4和图5可以看出, 在频率比n一定时, 和差频波的声压幅值都随着m的增大而增大; 声压比m一定时, 随着n的增大而减小; 差频波的声压比和频波的大且衰减得慢; 驱动声压极值和频率值较小时激发的谐频波较强, 如n = 2, m = 1/1时, 激发的和差频波最强, 且差频波声压约为和频波的3倍. 由图6可以看到, 在频率比n一定时, 谐波的声能含量随着m的增大而增大; 声压比m一定时, 随着n的增大而减小; 随着传播距离的增大, 谐波的含量先增大后减小. 当n = 2, m = 1∶1时, 谐波含量达到最大约占声场总声能的50%, 说明声场中的能量转移不仅与输入的声功率有关, 还与入射声的组成成分有关. 图 6 谐波声能与总能量比分布 Figure6. The ratio of the hamonic and total energies.
23.3.声参量效应对声场分布的影响 -->
3.3.声参量效应对声场分布的影响
声波在非线性传播中产生的谐波与声场的驱动声压幅值、频率及介质的性质密切相关, 同时原声场也会因谐波的存在而发生改变. 在输入总声能相同的情况下, 单、双列声波传播中的声能变化及场中声能的分布如图7和图8所示. 图 7 基频声能量的分布 Figure7. The distribution of fundamental energy.
图 8 基频声能量与总声能量比分布 Figure8. The ratio of the fundamental and total energies.