缩写词与符号
材料性能
| \( E \) | 弹性模量（杨氏模量） | Pa |
| \( G \) | 剪切模量（刚性模量） | Pa |
| \( \nu \) [nu] | 泊松比 | ——— |
| \( \rho \) [rho] | 密度 | kg/m3 |
| \( \alpha \) [alpha] | 热膨胀系数 | 1/°C |
| \( HRC \), \( R_c \) | 洛氏硬度（C 标尺） | ——— |
| \( HV \) | 维氏硬度 | ——— |
| \( c_{tw} \) | 细杆波速 | m/sec |
| \( c_d \) | 膨胀波速 | m/sec |
| \( c_s \) | 剪切波速 | m/sec |
| \( c_{tp} \) | 薄板波速 | m/sec |
| \( Q_{material} \) | 指定材料在指定频率和应变下的Q | ——— |
电学
| \( L \) | 电感 | H |
| \( C \) | 电容 | F |
| \( R \) | 电阻 | ohm |
| \( Y \) | 导纳 | ohm |
| \( Z \) | 阻抗 | ohm |
| \( v \), \( V \) | 电压 | volt |
| \( i \), \( I \) | 电流 | ampere 或 amp |
| \( q \) | 电荷 | coulomb |
| \( E \) | 电场强度 | volt/m |
| \( \varepsilon \) [epsilon] | 介电常数（绝对介电常数） | F/m |
| \( \varepsilon_o \) | 真空介电常数 | F/m |
| \( K \) | 介电常数（相对） | ——— |
应力与应变
| \( \sigma \) [sigma] | 拉伸或压缩应力 | Pa |
| \( \epsilon \) [epsilon] | 拉伸或压缩应变 | ——— |
| \( \tau \) [tau] | 剪切应力 | Pa |
| \( \gamma \) [gamma] | 剪切应变 | ——— |
| \( \sigma_{ij} \) [sigma] | 作用于 i 平面沿 j 方向的应力（见注） | Pa |
| \( \epsilon_{ij} \) [epsilon] | 作用于 i 平面沿 j 方向的应变（见注） | ——— |
| \( \sigma_v \) [sigma] | von Mises 应力 | Pa |
| \( k_t \) | 应力集中系数 | ——— |
压电陶瓷与换能器
| \( T_c \) | 居里温度 | °C |
| \( d \) | 电荷常数或应变常数 | m/volt |
| \( g \) | 电压常数 | m2/coulomb |
| \( \kappa \) [kappa] | 机电耦合系数 | ——— |
| \( \kappa_{eff} \) [kappa] | 机电耦合系数（有效值） | ——— |
| \( C_o \) | 压电夹持（截止）电容 | F |
| \( tan\delta \) [tan delta] | 介电损耗角正切 | ——— |
| \( T \) | 应力（仅用于压电分析） | Pa |
| \( S \) | 应变（仅用于压电分析） | ——— |
| \( E \) | 电场强度 | volt/m |
| \( D \) | 电位移 | coulomb |
| \( Y \) | 杨氏模量（仅用于压电分析） | Pa |
| \( s \) | 柔度（仅用于压电分析） | 1/Pa |
| \( f_s \) | 串联谐振频率 | Hz, kHz |
| \( f_p \) | 并联谐振频率 | Hz, kHz |
| \( f_{sc} \) | 短路谐振频率 | Hz, kHz |
| \( f_{oc} \) | 开路谐振频率 | Hz, kHz |
| \( f_m \) | 阻抗（绝对值）最小的频率 | Hz, kHz |
| \( f_n \) | 阻抗（绝对值）最大的频率 | Hz, kHz |
性能
| \( f \) | 频率 | Hz, kHz |
| \( f_r \) | 谐振频率（泛指） | Hz, kHz |
| \( u \), \( U \) | 振幅（位移） | µ [peak], m |
| \( \overline{U} \) [u bar] | 平均振幅 | µ [peak], m |
| \( \dot{u} \), \( \dot{U} \) [u dot] | 速度 | m/sec |
| \( \ddot{u} \), \( \ddot{U} \) [u double-dot] | 加速度 | m/sec2 |
| \( \widehat{U} \) [U hat] | 振幅均匀性 | ——— |
| \( \widehat{A} \) [A hat] | 振幅不对称度 | ——— |
| \( G \) | 增益 | ——— |
| \( p \), \( P \) | 功率 | W or kW |
| \( I \) | 声功率强度 | W/m2 |
| \( \overline{I} \) [I bar] | 平均声功率强度 | W/m2 |
| \( \varphi \) | 调谐率 | Hz/mm |
| \( Q_{stack} \) | 叠堆的Q | ——— |
| \( \delta \) | 对数衰减率 | ——— |
波
| \( \lambda \) [lambda] | 波长 | m |
| \( \Gamma \) [gamma] | 半波长 | m |
| \( \Gamma_{tw} \) [gamma] | 细杆半波长 | m |
| \( k_w \) | 波数 | 1/m |
| \( c_{eff} \) | 波速（有效值） | m/sec |
疲劳
| \( N \) | 失效循环次数 | 次循环 |
| \( S \) | 应力 | Pa |
| \( R \) | 应力比 | Pa |
| \( S_n \) | 持久极限（疲劳极限） | Pa |
| \( {S'}_n \) | R.R. Moore 低频旋转弯曲试验的持久极限 | Pa |
| \( K_f \) | 疲劳缺口系数 | ——— |
数学
| ≈ | 约等于 |
| α | 正比于 |
| Δ [delta] | 小增量或变化量 |
| ∑ [sigma] | 求和 |
| ∫ | 积分 |
| \( \ln \) | 自然对数 |
| \( e \)（自然对数底） | 2.71828183... |
| \( \overline{Z} \) [character overlined] | 1. 平均值 2. 复数的模 |
| \( Z' \) [character prime] | 复数的实部 |
| \( Z'' \) [character doubleprime] | 复数的虚部 |
统计
| \( s \) | 标准差 |
| \( R^2 \) | 决定系数 |
几何
| \( r \), \( R \) | 半径 | mm |
| \( d \), \( D \) | 直径 | mm |
| Ø | 直径 | mm |
| ØOD, O.D. | 外径 | mm |
| ØID, I.D. | 内径 | mm |
| \( h \) | 高度（厚度） | m, mm |
| \( \tilde {A} \) [A tilde] | 面积 | m2 |
| \( \tilde {V} \) [V tilde] | 体积 | m3 |
机械加工
| Ra | 粗糙度，平均值 |
| TIR | 总指示器读数 |
其他
| \( m \) | 质量 | kg |
| \( k \) | 刚度 | N/m |
| Ṕ [P accent] | 压力 | Pa |
| \( W \) | 能量 | N m = joule |
| \( \widehat{W} \) [W hat] | 能量密度 | N m/m2 = joule/m2 |
| \( KE \) | 动能 | N m = joule |
| \( PE \) | 势能 | N m = joule |
单位
| Hz | 赫兹 |
| kHz | 千赫兹 |
| µ [mu] | 微米 |
| °C | 摄氏度 |
| N | 牛顿 |
| Pa | 帕斯卡 |
| MPa | 兆帕（=106 Pa） |
| GPa | 吉帕（=109 Pa） |
| Ω | 欧姆 |
| C | 库仑 |
| F | 法拉 [coulomb/volt] |
| H | 亨利 [volt-second/ampere] |
首字母缩写词
| ASTM | 美国试验与材料协会（American Society for Testing and Materials） |
| AISI | 美国钢铁协会（American Iron and Steel Institute） |
| CARD | 计算机辅助谐振器设计（Computer Aided Resonator Design） |
| FEA | 有限元分析 |
| FEM | 有限元方法 |
| PZT | 锆钛酸铅压电陶瓷 |
| RMS | 均方根 |
注 —
- 这些缩写词和符号总体上与文献中的用法一致。但为了清晰起见，或为了避免与其他缩写词和符号冲突，其中一些已作更改。
- 在某些情况下，缩写词或符号的选取取决于主题。例如，力学讨论中用 \( \sigma \) 表示应力，而压电讨论中用 \( S \) 表示应力。在疲劳讨论中，\( \sigma \) 和 \( S \) 都有使用。这些冲突源于既定的惯例。
- 在某些情况下，同一缩写词或符号可能因上下文不同而具有不同的含义。例如，\( E \) 既用于"弹性模量"，也用于"电场强度"。
- 单位总体上遵循 MKS 单位制，尤其是在公式中使用时。但也可方便地使用其他单位（例如图纸中使用 mm）。
- 当同时给出小写和大写字符时，小写字符表示瞬时值，而大写字符表示幅值（例如 RMS、峰值、峰‑峰值）。例如，\( u \) 是瞬时振幅（位移），而 \( U \) 是峰值振幅。
- 当应力或应变符号后带双下标时，第一个下标表示相关平面（该平面由垂直于该平面的轴来指示），第二个下标表示应力或应变的方向。例如，\( \sigma_{XY} \) 表示作用于 X 平面沿 Y 方向的应力。（参见 Juvinall，第 21 页。）
Abbreviations and symbols
Contents
Material properties
| \( E \) | Modulus of elasticity (Young's modulus) | Pa |
| \( G \) | Shear modulus (modulus of rigidity) | Pa |
| \( \nu \) [nu] | Poisson's ratio | ——— |
| \( \rho \) [rho] | Density | kg/m3 |
| \( \alpha \) [alpha] | Coefficient of thermal expansion | 1/°C |
| \( HRC \), \( R_c \) | Rockwell hardness (C scale) | ——— |
| \( HV \) | Vickers hardness | ——— |
| \( c_{tw} \) | Thin wire wave speed | m/sec |
| \( c_d \) | Dilatational wave speed | m/sec |
| \( c_s \) | Shear wave speed | m/sec |
| \( c_{tp} \) | Thin-plate wave speed | m/sec |
| \( Q_{material} \) | Q of the specified material at a specified frequency and strain | ——— |
Electrical
| \( L \) | Inductance | H |
| \( C \) | Capacitance | F |
| \( R \) | Resistance | ohm |
| \( Y \) | Admittance | ohm |
| \( Z \) | Impedance | ohm |
| \( v \), \( V \) | Voltage | volt |
| \( i \), \( I \) | Current | ampere or amp |
| \( q \) | Charge | coulomb |
| \( E \) | Electric field strength | volt/m |
| \( \varepsilon \) [epsilon] | Permittivity | F/m |
| \( \varepsilon_o \) | Permittivity of free space | F/m |
| \( K \) | Dielectric constant | ——— |
Stress & strain
| \( \sigma \) [sigma] | Tensile or compressive stress | Pa |
| \( \epsilon \) [epsilon] | Tensile or compressive strain | ——— |
| \( \tau \) [tau] | Shear stress | Pa |
| \( \gamma \) [gamma] | Shear strain | ——— |
| \( \sigma_{ij} \) [sigma] | Stress on i plane acting in j direction (see note) | Pa |
| \( \epsilon_{ij} \) [epsilon] | Strain on i plane acting in j direction (see note) | ——— |
| \( \sigma_v \) [sigma] | von Mises stress | Pa |
| \( k_t \) | Stress concentration factor | ——— |
Piezoelectric ceramics & transducer
| \( T_c \) | Curie temperature | °C |
| \( d \) | Charge constant or strain constant | m/volt |
| \( g \) | Voltage constant | m2/coulomb |
| \( \kappa \) [kappa] | Electromechanical coupling coefficient | ——— |
| \( \kappa_{eff} \) [kappa] | Electromechanical coupling coefficient (effective) | ——— |
| \( C_o \) | Piezoelectric clamped (blocked) capacitance | F |
| \( tan\delta \) [tan delta] | Dielectric loss tangent | ——— |
| \( T \) | Stress (piezoelectric analysis only) | Pa |
| \( S \) | Strain (piezoelectric analysis only) | ——— |
| \( E \) | Electric field strength | volt/m |
| \( D \) | Dielectric displacement | coulomb |
| \( Y \) | Young's modulus (piezoelectric analysis only) | Pa |
| \( s \) | Compliance (piezoelectric analysis only) | 1/Pa |
| \( f_s \) | Series resonance frequency | Hz, kHz |
| \( f_p \) | Parallel resonance frequency | Hz, kHz |
| \( f_{sc} \) | Short circuit resonance frequency | Hz, kHz |
| \( f_{oc} \) | Open circuit resonance frequency | Hz, kHz |
| \( f_m \) | Frequency of minimum (absolute value) impedance | Hz, kHz |
| \( f_n \) | Frequency of maximum (absolute value) impedance | Hz, kHz |
Performance
| \( f \) | Frequency | Hz, kHz |
| \( f_r \) | Resonant frequency (generic) | Hz, kHz |
| \( u \), \( U \) | Amplitude (displacement) | µ [peak], m |
| \( \overline{U} \) [u bar] | Average amplitude | µ [peak], m |
| \( \dot{u} \), \( \dot{U} \) [u dot] | Velocity | m/sec |
| \( \ddot{u} \), \( \ddot{U} \) [u double-dot] | Acceleration | m/sec2 |
| \( \widehat{U} \) [U hat] | Uniformity of amplitude | ——— |
| \( \widehat{A} \) [A hat] | Asymmetry of amplitude | ——— |
| \( G \) | Gain | ——— |
| \( p \), \( P \) | Power | W or kW |
| \( I \) | Acoustic power intensity | W/m2 |
| \( \overline{I} \) [I bar] | Average acoustic power intensity | W/m2 |
| \( \varphi \) | tuning rate | Hz/mm |
| \( Q_{stack} \) | Q of the stack | ——— |
| \( \delta \) | Log decrement | ——— |
Waves
| \( \lambda \) [lambda] | Wavelength | m |
| \( \Gamma \) [gamma] | Half wavelength | m |
| \( \Gamma_{tw} \) [gamma] | Thin-wire half-wavelength | m |
| \( k_w \) | Wave number | 1/m |
| \( c_{eff} \) | Wave speed (effective) | m/sec |
Fatigue
| \( N \) | Number of cycles to failure | Cycles |
| \( S \) | Stress | Pa |
| \( R \) | Stress ratio | Pa |
| \( S_n \) | Endurance limit (fatigue limit) | Pa |
| \( {S'}_n \) | Endurance limit for R.R. Moore low frequency rotating bending tests | Pa |
| \( K_f \) | Fatigue notch factor | ——— |
Math
| ≈ | Approximately equal |
| α | Proportional to |
| Δ [delta] | Small increment or change |
| ∑ [sigma] | Summation |
| ∫ | Integral |
| \( \ln \) | Natural logarithm |
| \( e \) (Napierian base) | 2.71828183... |
| \( \overline{Z} \) [character overlined] | 1. Average 2. Magnitude of a complex number |
| \( Z' \) [character prime] | Real part of a complex number |
| \( Z'' \) [character doubleprime] | Imaginary part of a complex number |
Statistics
| \( s \) | Standard deviation |
| \( R^2 \) | Coefficient of determination |
Geometry
| \( r \), \( R \) | Radius | mm |
| \( d \), \( D \) | Diameter | mm |
| Ø | Diameter | mm |
| ØOD, O.D. | Outside diameter | mm |
| ØID, I.D. | Inside diameter | mm |
| \( h \) | Height (thickness) | m, mm |
| \( \tilde {A} \) [A tilde] | Area | m2 |
| \( \tilde {V} \) [V tilde] | Volume | m3 |
Machining
| Ra | Roughness, average |
| TIR | Total indicator reading |
Other
| \( m \) | Mass | kg |
| \( k \) | Stiffness | N/m |
| Ṕ [P accent] | Pressure | Pa |
| \( W \) | Energy | N m = joule |
| \( \widehat{W} \) [W hat] | Energy density | N m/m2 = joule/m2 |
| \( KE \) | Kinetic energy | N m = joule |
| \( PE \) | Potential energy | N m = joule |
Units
| Hz | Hertz |
| kHz | kiloHertz |
| µ [mu] | Micron |
| °C | Degrees Celcius (centigrade) |
| N | newton |
| Pa | pascal |
| MPa | Mega-pascal (=106 Pa) |
| GPa | Giga-pascal (=109 Pa) |
| Ω | ohm |
| C | coulomb |
| F | farad [coulomb/volt] |
| H | henry [volt-second/ampere] |
Acronyms
| ASTM | American Society for Testing and Materials |
| AISI | American Iron and Steel Institute |
| CARD | Computer Aided Resonator Design |
| FEA | Finite Element Analysis |
| FEM | Finite Element Method |
| PZT | Lead Zirconate Titinate peizoelectric ceramic |
| RMS | Root mean squared |
Notes —
- These abbreviations and symbols generally conform to those in the literature. However, some have been changed for clarity or because of conflicts with other abbreviations and symbols.
- In some cases the choice of abbreviation or symbol will depend on the topic. For example, discussions of mechanics use \( \sigma \) for stress whereas discussions of piezoelectrics use \( S \) for stress. In fatigue both \( \sigma \) and \( S \) are used. These conflicts occur because of established conventions.
- In some cases the same abbreviation or symbol may have different meanings depending on the context. For example, \( E \) is used for both "modulus of elasticity" and "electric field strength".
- Units generally conform to the MKS system, particularly when used in equations. However, other units may conveniently be used (e.g., mm in drawings).
- When both lowercase and uppercase characters are shown, the lowercase character indicates an instantaneous value whereas the uppercase character indicates a magnitude (e.g., RMS, peak, peak‑to‑peak). For example, \( u \) is the instantaneous amplitude (displacement) whereas \( U \) is the peak amplitude.
- When a stress or strain symbol is followed by double subscripts, the first subscript indicates the associated plane (where the plane is indicated by the axis that is perpendicular to the plane). The second subscript indicates the direction of stress or strain. For example, \( \sigma_{XY} \) indicates a stress acting on the X plane in the Y direction. (See Juvinall, p. 21.)