【作者】 董雷；

【导师】 杨德森；

【作者基本信息】 哈尔滨工程大学 ， 水声工程， 2011， 博士

【摘要】 随着科学技术的不断发展进步,非线性声学理论被越来越多的应用到工程实践当中,在国防、医疗、工业等领域都有对大功率声源的广泛应用,这也迫使对非线性声学理论的研究更加深入。非线性声学作为一门物理学领域中的非线性理论,其中的许多问题具有非线性科学问题的普遍特性,混沌理论为非线性问题的研究提供了有效手段,可以通过混沌理论方法对其进行研究。本文首先研究了非线性时间序列的分析方法,以非线性时间序列为基础对非线性系统特性进行研究,利用非线性系统的混沌吸引子特征对不同非线性系统特性进行了判断,通过相空间重构方法对非线性时间序列进行了重构,并对相空间重构中延迟时间和嵌入维数的选取方法进行了研究,研究了非线性时间序列的Lyapunov (?)旨数计算方法,通过Lyapunov指数对非线性时间序列的特征进行了分析。本文从非线性动力学系统振动特性出发,对非线性系统振动特性及其研究方法进行了探讨,通过系统相图、Poincare截面、功率谱、Lyapunov指数等研究方法,对不同状态的非线性系统特性进行了分析,讨论了外激励参数对非线性系统振动状态的影响,并重点研究了不同状态条件下系统的输出功率谱特性,得到系统在进入混沌状态后输出的激励频点功率明显下降的结论。为了对非线性系统振动状态进行有效控制,文中针对非线性系统参数对系统特性的影响进行了研究,讨论了非线性系数和阻尼系数改变时系统特性的变化规律,总结了外激励条件下非线性系统进入混沌状态的规律,以及系统进入混沌状态后对激励参数的敏感性,同时,讨论了系统非线性系数和阻尼系数对非线性系统输出功率的影响。研究了多频激励条件下非线性系统的振动状态,通过多尺度分析方法对多频激励条件下的非线性系统幅频响应特性进行了分析,对比研究了单频激励和多频激励条件下非线性系统的振动状态,对加入多频激励参数对系统振动状态的影响进行了总结。针对非线性声学理论中的大振幅波传播问题进行了研究,通过非线性波动方程研究了单频和多频大振幅波的非线性传播问题,对单频大振幅平面波、柱面波和球面波的传播规律进行了对比研究,分析了在单频大振幅波传播过程中基频波能量和高阶谐波能量的变化情况,利用谱分解法对大振幅波的非线性相互作用问题进行了研究,讨论了两波非线性相互作用条件下,不同初始相位、频率及能量对低频波能量的影响,并将谱分解法的计算结果与Fenlon理论计算结果进行了比较。对时域有限差分计算方法进行了研究,并利用时域有限差分方法通过对非线性波动方程的数值计算研究了大振幅波的非线性传播问题,通过计算结果对单频和多频大振幅波的传播进行了时域和频域分析。对频散介质中的大振幅波非线性传播问题进行了研究,通过行波变换方法对非线性波动方程进行了变换,得到了非线性波动方程的等效非线性系统模型,通过相平面分析方法和Melnikov方法对该系统进行了研究,得到了系统进入混沌状态的理论阈值。通过试验研究了大振幅波非线性相互作用问题,得到了两波相互作用使低频波能量产生下降的试验结果,对两波非线性相互作用产生的和、差频波能量进行了理论计算和实验测量,得到两波能量较大条件下理论计算与实际结果较为符合的结论。采用锥形弹簧为非线性元件构建了非线性振动模型,对非线性波动方程行波变换得到的等效非线性系统进行了试验研究,通过调整外激励频率和幅度研究了非线性系统的振动状态,利用重构相空间、Lyapunov指数和功率谱方法对系统的周期、倍周期和混沌状态进行了分析。对外激励条件下气泡的非线性振动特性进行了研究,讨论了不同外激励参数条件对气泡非线性振动的影响,并对不同状态条件下的气泡振动特性进行了分析,通过等效介质方法对含气泡水介质的非线性特性进行了研究,利用对不同含气泡水介质的等效非线性参数(B/A)n的计算研究了介质的非线性特性,得到含气泡水介质具有较强非线性特性的结论,通过水池试验对含气泡水介质的非线性系数进行了测量和计算,为实际问题中确定非线性系统参数,建立等效非线性系统模型提供了有效方法。更多还原

【Abstract】 With the continuous development and progress of science and technology, nonlinear acoustic theory is more applications to engineering practice, in national defence, medical treatment, industrial and other fields have a wide range of high-power source applications, which also forced nonlinear acoustic theory more in depth research. Nonlinear acoustics as a nonlinear theory in physics, in which many of the problems have the common characteristics of the problem of nonlinear science, chaos theory provides an effective means for study nonlinear problems, we can be to study nonlinear acoustic theory through chaos theory approach.This paper studies the nonlinear time series analysis method, based on nonlinear time series to study the characteristics of nonlinear systems, the different characteristics of nonlinear systems were judged through nonlinear systems chaotic attractor, by phase space reconstruction reconstructed phase space of nonlinear time series, and the selection methods of delay time and embedding dimension were studied, sdudied the method of Lyapunov exponent computation of nonlinear time series, by Lyapunov exponent characteristic of nonlinear time series were judged.In this paper, the vibration characteristics of the nonlinear system and its research methods are discussed, through the system phase diagram, Poincare section, power spectrum, Lyapunov exponent methods analyzed the characteristics of the non-linear system different states, discussed influence of the external excitation parameters on the vibration state of nonlinear systems, and focus on the output power spectrum characteristics of the system states under the different conditions, get the conclusions that the output excitation frequency power of system decreased when system into chaos. To the state of the nonlinear vibration control, in this paper the influence of the nonlinear system parameters on the system characteristics were studied, discussed the influence of the nonlinear coefficient and damping change on characteristics of the system, summarized the law that nonlinear system into chaos under conditions of external excitation and the parameters sensitivity that the system enters chaotic state under the excitation, also discussed the influence of the nonlinear coefficient and damping coefficient on the output power of nonlinear systems. Sdudied the vibration state of nonlinear systems under multi-frequency excitation, amplitude frequency response characteristics of nonlinear systems under multi-frequency excitation were analyzed through multi-scale analysis, compare the vibration state nonlinear system of single-frequency excitation condition with multi-frequency excitation, summarized the influence of joining multi-frequency excitation parameters on the vibration state of the system.The problem of large amplitude acoustic wave propagation in nonlinear acoustic theory was studied, studied the nonlinear propagation of single frequency and multi-frequency large amplitude wave through a nonlinear wave equation, compared propagation law of single frequency plane wave, cylindrical wave and spherical wave, analysed the energy changes of the basis frequency and high frequency wave in the single-frequency large amplitude wave propagation, by the spectral decomposition method studied the nonlinear interaction of large amplitude waves, discussed the influence of different initial phase, frequency and energy on the low-frequency wave energy under two waves nonlinear interaction conditions, and the calculated results of spectral decomposition and Fenlon theoretical results are compared. Studied Finite difference time domain method, and by numerical calculation of nonlinear wave equation studied the problem of large amplitude wave nonlinear propagation, studied the propagations of single-frequency and multi-frequency large amplitude wave through the time domain and frequency domain analysis.Nonlinear propagation problem of large amplitude wave is studied in the dispersion medium, by traveling wave transformation of nonlinear wave equation obtained the equivalent nonlinear system model, through the phase plane analysis method and Melnikov method studied this system, and get the theoretical threshold of the system into chaotic state. By experiment studied the large amplitude wave nonlinear interaction, get the experiment results that low frequency wave energy generated drop in two waves interaction, the sum and difference frequency wave energy were calculated and experimental measured under nonlinear interaction of two waves, obtained the conclusions that the calculation with actual results are more accordant under two waves interaction of large energy. Using the conical spring constructed nonlinear vibration model, through experiment studied the equivalent nonlinear system of nonlinear wave equation using traveling wave transformation, by adjusting the excitation frequency and amplitude studied the vibration state of the nonlinear system, using phase space, Lyapunov exponent and power spectrum methods studied the periodic, doubling period and chaos states.Under the conditions of external excitation the nonlinear vibration characteristics of bubbles were studied, discussed the influence of difference external excitation parameters on the nonlinear vibration of the bubble, and analyzed the vibration characteristics of the bubbles under different states, through the effective medium method nonlinear characteristics of water medium containing the bubbles were studied, using equivalent nonlinear parameter (B/A)n of different water media containing bubbles studied the nonlinear characteristics of the media, get the conclusions that the water medium with bubbles has strong nonlinear characteristics, through experiment the nonlinear coefficients of water medium containing the bubble were measured and calculatedto determine nonlinear system parameters of the actual problem, constructed the equivalent nonlinear system model provides effective way.更多还原