马铁菊头蝠声道声学特性的数值分析

采用有限元数值计算得到了马铁菊头蝠声道内部的声场分布,给出了马铁菊头蝠声道内几种特殊的腔体结构在蝙蝠发声过程中的作用。通过微型CT扫描并经过三维重构得到了马铁菊头蝠声道的三维立体模型用于有限元数值计算,通过在声门处放置单位声源计算得到了整个声道内部以及鼻孔周围的声压分布。结果表明,马铁菊头蝠声道包含了鼻腔结构后声波在声门上方的声压幅度明显大于不含鼻腔结构的情况,从传输曲线来看,声门上方鼻腔的存在使得系统对声波传输在二次谐波频率处呈现低阻抗效果,同时鼻腔的改变还可影响二次谐波的位置。而声门下方的气管空腔主要影响声波的背向转播,声门下方的气管空腔的存在可明显降低蝙蝠发声时声场在声道声门下方的声压幅度,同时抑制声音背向传播时二次谐波成分的强度。     

一维非线性声波传播特性

针对一维非线性声波的传播问题进行了有限元仿真和实验研究. 首先推导了一维非线性声波方程的有限元形式, 含有高阶矩阵的非线性项导致声波具有波形畸变、谐波滋生、基频信号能量向高次谐波传递等非线性特性. 编制有限元程序对一维非线性声波进行了计算并对仿真得到的畸变非线性声波信号进行处理, 分析其传播性质和物理意义. 为验证有限元计算结果, 开展了水中的非线性声波传播的实验研究, 得到了不同输入信号幅度激励下和不同传播距离的畸变非线性声波信号. 然后对基波和二次谐波的传播性质进行详细讨论, 分析了二次谐波幅度与传播距离和输入信号幅度的变化关系及其意义, 拟合出二次谐波幅度随传播距离变化的方程并阐述了拟合方程的物理意义. 结果表明, 数值仿真信号及其频谱均与实验结果有较好的一致性, 证实计算方法和结果的正确性, 并提出了具有一定物理意义的二次谐波随传播距离变化的简单数学关系. 最后还对固体中的非线性声波传播性质进行了初步探讨. 本研究工作可为流体介质中的非线性声传播问题提供理论和实验依据.     

含气泡水的强非线性声学特性

本文提出一种描述含气泡水的非线性声场的物理模型。在声波驱动下,气泡壁作受迫振动,遵循Rayleigh-Plesset方程,当共振时振幅很大,产生强烈的非线性振动。这非线性力学振动成为二次谐波声压的源,从而声场表现为强非线性。理论计算与WU和Zhu的实验结果进行了比较,诸如强二次谐波声压等重要声学特性符合得比较满意。     

二维矩形波导管中的非线性声传播

本文采用部分波和二阶微扰理论对二维矩形波导管内声波的非线性传播问题进行了研究。由二次谐波的边界条件和初始条件,可得到物理图象清晰、便于计算的二次谐波声场解析式。结果表明,不同基波传播模式间的相互作用不存在二阶非线性,管内任意振幅分布的稳态激发源产生的二次谐波为各个模式二次谐波之和,且二次谐波声场分布具有对称性。     

基于Fourier-Bessel级数的Bessel型超声场二次谐波近场特性研究

将Fourier-Bessel级数引入KZK方程的求解，用于计算黏滞媒质中零阶Bessel型超声场的二次谐波声场，得到其级数形式的解析解，并由此得出二次谐波声场在近场分布的一个新结论.设声源表面声压分布为J₀(α₀r)，则二次谐波声压在近场的径向分布服从J²₀(α₀r)函数规律.这一结论合理解释了相关的实验结果，表明二次谐波声场在近场和远场有不同的径向分布，从而解决了非线性Bessel型超声场二次谐波的近场分布问题.研究还发现二次谐波声场具有类似基波声场的有限衍射特性.给出了一个数值计算和仿真实例.     

二维多流体域耦合声场的光滑有限元解法

针对声学有限元分析中四节点等参单元计算精度低,对网格质量敏感的问题,将光滑有限元法引入到多流体域耦合声场的数值分析中,提出了二维多流体域耦合声场的光滑有限元解法。该方法在Helmholtz控制方程与多流体域耦合界面的声压/质点法向速度连续条件的基础上,得到二维多流体耦合声场的离散控制方程,并采用光滑有限元的分区光滑技术将声学梯度矩阵形函数导数的域内积分转换形函数的域边界积分,避免了雅克比矩阵的计算。以管道二维多流体域耦合内声场为数值分析算例,研究结果表明,与标准有限元相比,对单元尺寸较大或扭曲严重的四边形网格模型,光滑有限元的计算精度更高。因此光滑有限元能很好地应用于大尺寸单元或扭曲严重的网格模型下二维多流体域耦合声场的预测,具有良好的工程应用前景。     

材料非线性衰减系数的二次谐波测量方法研究

采用有限幅值法测量材料在基波和非线性引起的二次谐波作用下的衰减系数:利用准线性下的KZK方程推导基波和二次谐波的声压分布,并提取波束修正系数;采用短纯音信号进行非线性实验,对检测得到的基波和二次谐波声压进行衍射修正处理,有效抑制衍射对衰减系数测量的不利影响,继而通过线性拟合的方法计算得到更精确的基波和二次谐波的衰减系数。以水为例进行实验,研究了实验测量所得衰减系数的频率依赖关系,结果表明在非线性条件下水的衰减系数与频率间存在较强的线性关系,而线性条件下衰减系数随频率呈现二次方增长的特性则不适用于非线性条件。该研究提出了准确测量非线性声波衰减系数的方法,为更有效地应用非线性超声检测提供理论依据。     

概率盒框架下混合认知不确定声场的响应预测

针对含概率盒-证据混合认知不确定参数声场的响应预测问题,提出了一种概率盒框架下的改进区间蒙特卡洛方法。该方法首先将混合认知不确定参数转换为纯概率盒形式,然后结合有限元方法推导出混合认知不确定声场的盖根鲍尔多项式代理模型,再采用蒙特卡洛方法求解代理模型得到声压响应。以含概率盒-证据混合认知不确定参数的二维管道声场模型和卡车乘客舱声腔模型为例,计算结果表明混合认知不确定参数影响下的声压响应为概率盒形式,其包括声压响应极值和相应的概率信息,并且所提方法较常规混合离散方法效率更优,较基于一阶摄动法的区间蒙特卡洛方法准确性更高。研究结果表明:所提方法可以有效预测混合认知不确定声场的声压响应,并可进行声学性能的风险和保守估计。     

超声在液体中的非线性传播及反常衰减

本文从广义的Navier-Stokes流体方程出发,考虑到流体介质的黏滞性和存在的热传导,导出了更接近实际流体的三维非线性声波动方程.鉴于声传播所涉及的空间和时间尺度的复杂性和多样性,文中针对一维情形下的非线性波动方程进行了求解和分析.由方程的二级近似解可以看出,声压振幅的衰减遵循几何级数规律,而且驱动声波的频率越高声压的衰减就越快.在满足条件ωb《ρ0c_0~2时,基波的衰减系数与驱动频率的平方及耗散系数的乘积成正比;二次谐波的衰减规律更加复杂,与频率的更高次幂相关.对声衰减系数及声压的分布进行数值计算发现,声压的分布还与初始的声压幅值及频率有关,初始的声压与频率越高衰减得越快.另外,当声压高于液体的空化阈值时,液体中就会出现大量的空化泡,文中模拟了单个空化泡的运动,发现随着声压的增大空化泡的振动越剧烈、空化泡所受的黏滞力变大,随着声波作用时间的增大黏滞力的幅值迅速增大并与驱动声压值同阶,因而空化泡的非线性径向运动引起的声衰减不容忽视.结果表明,驱动声压越高在空化区域附近引起的声衰减越快、输出的声压越低.     

Using the Relaxation Oscillations Principle for Simple Phonation Modeling

Well-known multimass models of vocal folds are useful to describe main behavior observed in human voicing but their principle of functioning, based on harmonic oscillation, may appear complex. This work is designed to show that a simple one-mass model ruled by laws of relaxation oscillation can also depict main behavior of glottis dynamic. Theory of relaxation oscillation is detailed. A relaxation oscillation model is assessed through a numerical simulation using conventional values for tissue characteristics and subglottal pressure. As expected, raising the mass decreases the fundamental frequency and increases the amplitude of vocal fold vibration: for a mass ranging from 0.01 to 0.4 g, F0 decreased from 297.5 to 42.5 Hz and vibrational amplitude increased from 1.26 to 3.25 mm (for stiffness k=10Nm(-1), damping r=0.015 N s m(-1), and subglottal pressure=1 kPa). Stiffness value has the opposite effect. The subglottal pressure controls the fundamental frequency with a rate ranging from 20 to 50 Hz/kPa. The vibrational amplitude is also controlled linearly by subglottal pressure from 0.22 to 0.26 mm/kPa. The range of phonation threshold pressure (PTP) is close to the values currently proposed, that is, 0.1 to 1 kPa and varies with the fundamental frequency. The relaxation oscillator is a simple and useful tool for modeling vocal fold vibration.     

Measures of spectral slope using an excised larynx model

Spectral measures of the glottal source were investigated using an excised canine larynx (CL) model for various aerodynamic and phonatory conditions. These measures included spectral harmonic difference H1-H2 and spectral slope that are highly correlated with voice quality but not reported in a systematic manner using an excised larynx model. It was hypothesized that the acoustic spectra of the glottal source were significantly influenced by the subglottal pressure, glottal adduction, and vocal fold elongation, as well as the resulting vibration pattern. CLs were prepared, mounted on the bench with and without false vocal folds, and made to oscillate with a flow of heated and humidified air. Major control parameters were subglottal pressure, adduction, and elongation. Electroglottograph, subglottal pressure, flow rate, and audio signals were analyzed using custom software. Results suggest that an increase in subglottal pressure and glottal adduction may change the energy balance between harmonics by increasing the spectral energy of the first few harmonics in an unpredictable manner. It is suggested that changes in the dynamics of vocal fold motion may be responsible for different spectral patterns. The finding that the spectral harmonics do not conform to previous findings was demonstrated through various cases. Results of this study may shed light on phonatory spectral control when the larynx is part of a complete vocal tract system.     

Nonlinear source-filter coupling in phonation: theory

A theory of interaction between the source of sound in phonation and the vocal tract filter is developed. The degree of interaction is controlled by the cross-sectional area of the laryngeal vestibule (epilarynx tube), which raises the inertive reactance of the supraglottal vocal tract. Both subglottal and supraglottal reactances can enhance the driving pressures of the vocal folds and the glottal flow, thereby increasing the energy level at the source. The theory predicts that instabilities in vibration modes may occur when harmonics pass through formants during pitch or vowel changes. Unlike in most musical instruments (e.g., woodwinds and brasses), a stable harmonic source spectrum is not obtained by tuning harmonics to vocal tract resonances, but rather by placing harmonics into favorable reactance regions. This allows for positive reinforcement of the harmonics by supraglottal inertive reactance (and to a lesser degree by subglottal compliant reactance) without the risk of instability. The traditional linear source-filter theory is encumbered with possible inconsistencies in the glottal flow spectrum, which is shown to be influenced by interaction. In addition, the linear theory does not predict bifurcations in the dynamical behavior of vocal fold vibration due to acoustic loading by the vocal tract.     

Measurement of formant frequencies and bandwidths in singing

That singers under certain circumstances adjust the articulation of the vocal tract (formant tuning) to enhance acoustic output is both apparent from measurements and understood in theory. The precise effect of a formant on an approaching (retreating) harmonic as the latter varies in frequency during actual singing, however, is difficult to isolate. In this study variations in amplitude of radiated sound components as well as supraglottal and subglottal (esophageal) pressures accompanying the vibrato-related sweep of voice harmonics were used as a basis for estimating the effective center frequencies and bandwidths of the first and second formants.     

On subglottal formant analysis

When subglottal pressure signals which are recorded during normal speech production are spectrally analyzed, the frequency of the first spectral maximum appears to deviate appreciably from the first resonance frequency which has been reported in the literature and which stems from measurements of the acoustic impedance of the subglottal system. It is postulated that this is caused by the spectrum of the excitation function. This hypothesis is corroborated by a modeling study. Using an extended version of the well-known two-mass model of the vocal folds that can account for a glottal leak, it is shown that under realistic physiological assumptions glottal flow waveforms are generated whose spectral properties cause a downward shift of the location of the first spectral maximum in the subglottal pressure signals. The order of magnitude of this effect is investigated for different glottal settings and with a subglottal system that is modeled according to the impedance measurements reported in the literature. The outcomes of this modeling study show that the location of the first spectral maximum of the subglottal pressure may deviate appreciably from the natural frequency of the subglottal system. As a consequence, however, the comfortable assumption that in normal speech the glottal excitation function is constant and zero during the "closed glottis interval" has to be called into question.     

An anatomically based, time-domain acoustic model of the subglottal system for speech production

A time-domain model of sound wave propagation in the branching airways of the subglottal system is presented. The model is formulated as an extension to an acoustic transmission-line modeling scheme originally developed for simulating the supraglottal system in the time-domain during speech production [Maeda (1982). Speech Commun. 1, 199-229; Mokhtari et al. (2008). Speech Commun. 50, 179-190]. The approach allows for predictions of time-varying acoustic pressure and volume velocity at any point along the various generations of subglottal airways from trachea to alveoli. In addition, the model can be configured so that its overall structure simulates different geometric forms, including airways that branch in a symmetric or asymmetric pattern. Three subglottal configurations, two symmetric and one asymmetric, were represented based on reported anatomical dimensions of the subglottal airways. Estimates of the acoustic input impedances of these subglottal configurations revealed resonant characteristics similar to those found in the previous studies. Simulations of voiced sound propagation into the subglottal airways, achieved by coupling the subglottal model to a two-mass vocal fold model and a supraglottal tract configured for different vowels, yielded predictions of time-domain sound pressure waveforms below the vocal folds that compare favorably to previous measurements in human subjects.     

An aeroacoustic approach to phonation

A fluid mechanical, or aeroacoustic, point of view is followed to study possible sources of sound during phonation. Concentration is on two features of the vocal tract during phonation: abrupt area change from the glottis to the vocal tract and the finite length of the vocal tract. With these features, a source of sound distinct from the volume velocity source can be identified and a preliminary account of its effect on the acoustic field given. This source of sound is an oscillating force resulting from an interaction of rotational fluid motion with itself. Because of the schematic nature of the geometry of the model used here, this source may be considerably modified in actual phonation. It is concluded that specification of volume velocity is not enough to specify the source during phonation, even neglecting source-tract interaction.     

Effects on the glottal voice source of vocal loudness variation in untrained female and male voices

Subglottal pressure is one of the main voice control factors, controlling vocal loudness. In this investigation the effects of subglottal pressure variation on the voice source in untrained female and male voices phonating at a low, a middle, and a high fundamental frequency are analyzed. The subjects produced a series of /pae/ syllables at varied degrees of vocal loudness, attempting to keep pitch constant. Subglottal pressure was estimated from the oral pressure during the /p/ occlusion. Ten subglottal pressure values, approximately equidistantly spaced within the pressure range used, were identified, and the voice source of the vowels following these pressure values was analyzed by inverse filtering the airflow signal as captured by a Rothenberg mask. The maximum flow declination rate (MFDR) was found to increase linearly with subglottal pressure, but a given subglottal pressure produced lower values for female than for male voices. The closed quotient increased quickly with subglottal pressure at low pressures and slowly at high pressures, such that the relationship can be approximated by a power function. For a given subglottal pressure value, female voices reached lower values of closed quotient than male voices.     

Voice source characteristics in six premier country singers

Voice source characteristics as derived from inverse filtering were analyzed in 6 country singers' speech and singing. Results showed that the closed quotient varied systematically with vocal loudness, and that glottal compliance (the ratio between transglottal AC volume displacement and subglottal pressure) decreased with increases in fundamental frequency but remained unaffected by vocal loudness. No striking differences were found in source characteristics between speech and singing within subjects. The degree of phonatory press, as judged by a panel of 19 expert listeners, appeared related to the range in which the singer was singing and to the sound pressure level gain from a doubling of subglottal pressure.