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水介质中声波非线性相互作用的研究
摘要
本文根据声波的非线性传播机理，推导了声波非线性相互作用的幅值解，仿真研究了声波非线性作用后的能量转移现象，实验验证了相关理论。根据海洋介质的物理特征和声波传播特性，初步构建了海洋介质中声波非线性相互作用的动力学模型，利用非线性动力学理论中的混沌判断方法，仿真分析了声波经动力学模型后声能量变化的动态演化过程，并基于仿真结果，提出利用声波之间非线性相互作用降低低频声波能量的技术方案，随后的实验结论验证了提出的方案。
本文主要做了以下几方面工作： 1.本文阐述了非线性声学的发展进程，包括水介质中混沌现象的研究和非线性声学与非线性动力学交叉领域的研究。上世纪中期以来，声学工作者取得了一系列研究进展，特别是从声波之间非线性相互作用的研究得知，声学非线性是一个值得人们花费大气力进行研究和探索的领域。声学中的非线性直接或间接地推动着人们在声学科学方面的进步，对未来非线性声学的发展奠定了一定的基础。 2.本文分析了线性系统与非线性系统输出的动力学特性，说明了非线性系统对本文研究的重要性。利用拉普拉斯变换求解了二阶变参量微分方程的解析解。以单自由度Duffing系统为例，利用非线性动力学理论的混沌判断方法，仿真分析了系统参数或外部激励参数对系统输出动力学特性的影响，确定了系统处于不同运动状态的参数阈值，进而引出水介质中声波非线性变参量相互作用的数学机理。 3.本文根据非线性声学的声波传播理论，利用非线性波动方程求解了单频大振幅声波非线性传播后声波幅值的表现形式，数值分析了单频大振幅声波生成多阶谐波的过程中基频波与各阶谐波之间的能量转移过程。从Burgers方程出发，利用谱分解法对低频声波与高频声波(大振幅波)非线性相互作用过程进行了理论推导，给出了相互作用后低频声波的幅值解，仿真分析了两波不同初始相位差、频率比及声源级对低频声波能量变化的影响。实验研究了两波非线性相互作用后声能量的转移问题，在误差允许范围内，两波相互作用后低频声波能量变化的实验结果与仿真结果存在一定吻合。当三列声波频率满足谐振条件时，理论推导了声波非线性相互作用后三列声波的幅值表现形式，数值计算了有、无耗散时声波能量随传播距离，高频声波幅值、频率，介质非线性参数的变化曲线。实验研究了三列声波非线性相互作用后低频声波的能量降低和放大效果，表明高频声波的声源级在一定范围内，可获得实验结果与仿真结果较为一致的低频声波放大或降低效应。 4.本文建立了海洋介质中声波非线性相互作用的经验模型，分析了系统中非线性模块、放大模块、延迟模块及模块中各参数对声波输出能量的影响。研究了开环控制与闭环控制的特点。用混沌动力学理论分析了声波经开环控制与闭环控制系统后输出的时域图、功率谱图、相图及最大Lyapunov指数，表明开环控制系统可以改变声波的频谱结构，但不能使输出声波呈现混沌状态。研究了低频声波在外界高频扰动作用下，经非线性反馈控制系统后输出的时域图、功率谱图、相图及最大Lyapunov指数，表明高频外激励扰动下的反馈控制系统可以使低频声波输出的频谱结构改变，并在合适参数的控制作用下，系统输出可呈现混沌状态、输入的低频声波频带展宽，能量变化。最终，选取不同的外部激励参数作用于非线性控制系统干扰低频声波，表明外部小幅值的高频扰动有利于使低频声波经非线性控制系统后输出呈现混沌状态，能量降低。由此，初步建立海洋介质中声波非线性相互作用后声能量转换的系统模型。 5.上述各方面的研究工作，均是在导师的创新思想指导下，在自制水池中进行了相关实验研究，这些实验支持了论文中的部分理论研究成果。实验中也发现了一些新的特殊现象，这些工作为后续进一步开展研究工作提供参考。 According to the acoustical nonlinear propagation theory, the amplitude solution ofnonlinear sounds mutual impact is proposed in the paper. The phenomena of energytransmitting with the nonlinear sounds mutual impact are also modeled, and someexperiments are carried out to verify the conclusions. According to the physical characteristicsof ocean medium and the feature of sound propagation, preliminarily develop a sounds mutualimpact dynamical model; then, model and analyze the energy dynamic evolution after soundpassing the model by using the chaos judgment method, which is from nonlinear dynamicstheory. finally, based on the simulation results, propose a technical solution to decreaselow-frequency parts energy of sounds by using the nonlinear mutual impact of the sounds.The verification results support the technical proposal. This paper mainly conduct the following researchs: 1. This paper describes the development of nonlinear acoustics, including the researcheson chaotic phenomenon of the water medium, the cross areas of nonlinear acoustics anddynamics. A lot of achievements are obtained on this area since1950s. From the researches onthe nonlinear effect of acoustic waves, the research on nonlinear acoustics is a field need tobe investigated more manpower. The nonlinear acoustics brought many improvements onacoustical techniques directly or indirectly, and formed a good basis for future research. 2. This paper analysised kinetics characteristics of the output in the linear system andnonlinear system, explained the the importance of the nonlinear system. Solved the analyticalsolution of the second order variable parametethe differential equation by using Laplacetransform. Taking single freedom Duffing system for example. By using nonlinear dynamicstheory of chaos judge method, this paper analysised the effect of the system parameters orexternal incentive system to the kinetics characteristics of the system output, confirmed theparameters threshold of the system in different motion state Then draw out mathematicalmechanism, which the interaction of the nonlinear variable parameter acoustic wave in thewater medium. 3. Based on the theory of wave propagation in nonlinear acoustics, amplituderepresentation of the single frequency large-amplitude sound wave after nonlinearpropagation is solved through the nonlinear wave equation. The energy transfer between thefundamental frequency wave and higher order harmonic waves generated in propagation issimulated. From the Burgers equation, the spectral decomposition method is applied to analyze the nonlinear interactions between the low-frequency weak signal wave and pumpwave (large amplitude wave). The effects of various initial phase differences, frequency ratiosand source levels between the two waves on change of the low-frequency signal energy aresimulated and the amplitude solution of the low-frequency weak signal is given. The energytransfer between the two waves in interaction is studied and result of energy changes of thelow-frequency wave in experiment conform to that in the simulation. The amplituderepresentations of three resonant waves after interaction are derived. The variation curves ofwave energy with and without dissipation are given respectively through numericalcalculation under the conditions of various propagating distances, medium nonlinearparameters and amplitude and frequency of pump waves. The effects of energy reduction andamplification of the low-frequency weak wave after interaction are studied by experiments,which show that values of the reduction and amplification obtained in experiments areconsistent with those of the simulation when source level of the pump wave is within certainlimits. 4. In this paper, the empirical model of sound wave nonlinear interaction in marinemedium is built, which is used to analyze the influence of nonlinear module, amplificationmodule, delayed module and various parameters of the system on the output sound energy.Automatic control theory is applied to study the features of open-loop control and closed-loopcontrol. The system output dynamic characters are analyzed by chaos dynamic theory with thegraphs of time-domain, power spectrum, phase diagram and maximum Lyapunov exponentunder the open-loop control and closed-loop control. The research show that open-loopcontrol system can change the sound spectrum, but unable to turn the output wave spectruminto chaos status. The low-frequency wave of the feedback system under the externalhigh-frequency excitation is studied with the graphs mentioned above and the results indicatethat the feedback control system can change the frequency spectrum of the output signalunder the excitation. System output signal energy will present the chaos status and frequencyband of the low-frequency wave will appear widening when the control parameters arewell-chosen. Finally, various parameters of external excitation are chosen to act on thenonlinear control system to interfere the low-frequency wave, which demonstrate that smallextent of external high-frequency disturbance is conductive to lead the low-frequency wave toachieve the chaos status and show energy decrease through nonlinear control system. Theenergy transfer model of sound wave nonlinear interactions in marine medium is establishedpreliminarily. 5. Each aspect of research above has been done in the innovative guidance of tutor. The related experiments in the tank and the small flume support the results of theoretical studies inthe thesis. Some new special phenomenon has been found in the experiments, which providereference for subsequent research.
引文
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