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17.1 从超声波谐波测量中确定三阶弹性常数 Determination of Third-Order Elastic Constants from Ultrasonic Harmonic Generation Measurements
M. A. Breazeale and Jacob Philip (田纳西大学物理系 Department of Physics, The University of Tennessee, Knoxville, Tennessee)

1. Introduction 2

2. 立方晶体中的纵波谐波生成 Harmonic Generation of Longitudinal Waves in Cubic Crystals 5

   1. 介质中传播的平面波运动方程 The Equations of Motion for Plane Elastic Waves Propagating through a Medium 5
   2. 立方晶体中沿纯模式方向传播的波 Wave Propagation along Pure Mode Directions in a Cubic Crystal 9
   3. 超声非线性参数 The Ultrasonic Nonlineanty Parameter 11

3. 电容接收器用于绝对幅值测量 The Capacitive Receiver as a Tool for Absolute-Amplitude Measurements 12

   1. 室温下测量的电容接收器 The Capacitive Receiver for Room-Temperature Measurements 13
   2. 电容接收器的校准 Calibration of the Capacitive Receiver 15
   3. 可变间距的电容接收器 The Variable-Gap Capacitive Receiver 17

4. 测量技术 The Measurement Technique 18

   1. 试件准备 Sample Preparation 18
   2. 室温下的测量 Room-Temperature Measurements 18
   3. 声速测量 Velocity Measurements 21
   4. 低温测量 Cryogenic Measurements 22

5. 一些固体的结论 Results for Some Solids 27

   1. 金属（铜） Metals (Copper) 29
   2. 半导体锗和硅 Semiconductors Germanium and Silicon 32
   3. 离子化合物NaCl和KCl Ionic Solids NaCl and KCl 37
   4. 钙钛矿家族 Perovskite Family 40
   5. 熔融石英 Fused Silica 46

6. 硅和锗的三阶弹性常数随温度的变化 Temperature Variation of the Third-Order Elastic Constants of Silicon and Germanium 50

   1. 方法 The Method 51
   2. 结果 Results 53
   3. 计算得到的硅和锗的 Gruneisen 参数和热膨胀的温度函数 The Gruneisen Parameter and Thermal Expansion of Silicon and Germanium Calculated as a Function of Temperature 54

7. Conclusions 56
   References 57

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17.2 声弹性和残余应力的超声测量 Acoustoelasticity and Ultrasonic Measurements of Residual Stresses
YIH-HSING РАО（鲍亦兴） and WOLFGANG SACHSE (康奈尔大学理论和应用机械系, Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, New York)
HIDEKAZU FUKUOKA (大阪大学工学部, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, Japan)

1. Introduction 62

2. 预应力体中的波运动 Wave Motion in a Prestressed Body 64

   1. 位移、应变和应力 Displacements, Strains, and Stresses 66
   2. 预应力体的运动方程 Equations of Motion for a Prestressed Body 68
   3. 声弹性方程 Equations of Acoustoelasticity 69

3. 声弹性双折射理论 Theory of Acoustoelastic Birefringence 71

   1. 均匀预变形 Homogeneous Predeformation 71
   2. 正交各向异性介质中的平面波 Plane Waves in Orthotropic Media 73
   3. 声弹性双折射 Acoustoelastic Birefringence 77
   4. 近似公式 Approximate Formulas 80
   5. 外加应力和残余应力 Applied and Residual Stresses 82

4. 预应力半空间中的表面波 Surface Waves in a Prestressed Half-Space 84

   1. 表面波方程 Equations of Surface Waves 84
   2. 表面层的初始应力 Initial Stresses in a Surface Layer 88

5. 残余应力和非弹性的影响 Residual Stresses and Inelastic Effects 89

   1. 残余应力 Residual Stresses 89
   2. 热应力的影响 Thermoelastic Effects 93
   3. 塑性变形的影响 Effects of Plastic Deformation 96
   4. 不均匀的影响 Effects of Inhomogeneity 99
   5. 残余应力的声弹性理论的建立 Toward an Acoustoelastic Theory for Residual Stresses 100

6. 声弹性实验技术 Experimental Techniques for Acoustoelasticity 101

   1. 声弹性测量的竞争效应 Competing Effects on Acoustoelastic Measurements 102
   2. 超声技术 Ultrasonic Techniques 104

7. 外加应力的超声测量 Ultrasonic Measurements of Applied Stresses 109

   1. 声弹性双折射 Acoustoelastic Birefringences 109
   2. 二维应力场 Two-Dimensional Stress Fields 115
   3. 表面波和三维应力场 Surface Waves and Three-Dimensional Stress Fields 118
   4. 谐波的测量 Measurements of Wave Harmonics 120

8. 残余应力的超声测量 Ultrasonic Measurements of Residual Stresses 121

   1. 塑性变形介质中的波 Waves in Plastically Deformed Media 121
   2. 残余应力的测量 Measurements of Residual Stresses 126
   3. 织构和应力引起的双折射 Texture and Stress Induced Birefringence 133

9. Conclusion 137
   References 140

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17.3 空气对声音的吸收 Absorption of Sound by the Atmosphere
H E BASS (密西西比大学物理声学研究组, Physical Acoustics Research Group, The University of Mississippi, University, Mississippi)
L С SUTHERLAND (Wyle Laboratories, El Segundo, California)
JOE PIERCY (加拿大国家研究委员会物理部, Division of Physics, National Research Council, Ottawa, Ontario, Canada)
LANDON EVANS (波音飞机公司, Boeing Aircraft Company, Wichita, Kansas)

1. Introduction 145

2. 空气吸声理论 Theory of Atmospheric Absorption of Sound 147

   1. 经典吸收 Classical Absorption 151
   2. 旋转松弛吸收 Rotational Relaxation Absorption 153
   3. 振动松弛吸收 Vibrational Relaxation Absorption 157
   4. 总吸收 Total Absorption 171

3. 预测的和实验的空气吸收损失对比 A Comparison of Predicted Atmospheric Absorption Loss with Experimental Data 174

   1. 松弛系数的实验室测量 Laboratory Measurements of Relaxation Parameters 174
   2. 与实验吸收数据的对比 Comparison with Experimental Absorption Data 189
   3. 与替代预测模型相关的初步结论 Preliminary Conclusions Relative to the Alternative Prediction Models 220
   4. 提出的空气吸收预测模型与其他方法的比较 Comparison of Proposed Air-Absorption Prediction Model with Other Methods 220

4. Appendix Symbols, Definitions, and Units 224

   References 228

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17.4 随机声场的统计特性 Statistical Properties of Random Wave Fields
KARL JOACHIM EBELING (德国第三物理研究所, Dnttes Physikahsches Institut, Unwersitat Gottingen Gottingen, Federal Republic of Germany)

1. Introduction 234

2. 简单声场变量的统计特性 Statistical Properties of Simple Sound Field Variables 236

   1. 单频声场的表征 Characterization of Pure-Tone Sound Fields 236
   2. 随机声场的基本统计性质 Basic Statistical Properties of Random Wave Fields 237
   3. 统计声场中的空间相关性 Spatial Correlation in Statistical Wave Fields 241
   4. 振幅和能量密度基上的平均 Averaging on Amplitude and Energy Density Basis 244

3. 含导数量的概率密度 Probability Densities of Quantities Containing Derivatives 246

   1. 解析信号及其空间导数的联合统计 Joint Statistics of the Analytic Signal and Its Spatial Derivative 246
   2. 能量通量密度的单分量分布 Distribution for One Component of the Energy Flux Density 248
   3. 势能密度和过水平点的空间导数 Spatial Derivative of the Potential Energy Density and Level Crossings 251
   4. 拉普拉斯分布变量的平均 Averaging of Laplacian Distributed Variables 252

4. 二维和三维梯度的统计 Statistics of Two- and Three-Dimensional Gradients 254

   1. 二维能量通量矢量的分布 Distribution of the Two-Dimensional Energy Flux Vector 254
   2. 二维能量通量密度的方向依赖性 Directional Dependence of the Two-Dimensional Energy Flux Density 259
   3. 二维能量密度梯度的行为 Behavior of Two-Dimensional Energy Density Gradients 262
   4. 三维能量通量密度 Three-Dimensional Energy Flux Densities 263

5. 随机波场的空间频谱 The Spatial Frequency Spectrum of Random Wave Fields 265

   1. 局部平稳过程的空间功率谱 Spatial Power Spectra of Locally Stationary Processes 265
   2. 角功率谱 The Angular Power Spectrum 267
   3. 空间扩散率一个度量 A Measure for Spatial Diffusivity 274
   4. 角功率谱的测量 Measurement of Angular Power Spectra 277
   5. 与辐射的联系 Connection with the Radiance 283

6. 粗糙表面的散射 Scattering at Rough Surfaces 287

   1. 基本关系 Basic Relations 287
   2. 二阶高度分布 Second-Order Height Distributions 289
   3. 二维空间频谱的传播 Propagation of the Two-Dimensional Spatial Frequency Spectrum 295
   4. 最大长度序列漫射体的散射 Scattering at Maximum-Length Sequence Diffusors 298
   5. 远场与高度分布的联系 Connection between Far Field and Height Distribution 301

7. 讨论与结论 Discussion and Conclusion 303

   1. 关于一些场变量的统计 On the Statistics of Some Field Variables 303
   2. 关于平面波在随机场中的方向分布 On the Directional Distribution of Plane Waves in Random Fields 305
   3. 关于粗糙表面的散射 On the Scattering at Rough Surfaces 306

8. Appendix Important Symbols 307
   References 309

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