Analysis of Piezoelectric Devices

Appendix 1: Notation

? ij , ? KL

Kronecker delta

? iK , ? Ki

Shifter

? ijk , ? IJK

Permutation tensor

X K

Reference position of a material point

y i

Present position of a material point

u K

Mechanical displacement vector

J

Jacobian

C KL

Deformation tensor

S KL

Finite strain tensor

S kl

Linear strain tensor

v i

Velocity vector

d ij

Deformation rate tensor

? ij

Spin tensor

D/Dt

Material time derivative

? 0

Reference mass density (scalar)

?

Present mass density

? e

Free charge density per unit present volume (scalar)

? E

Free charge density per unit reference volume (scalar)

? e

Surface free charge per unit present area (scalar)

? E

Surface free charge per unit reference area (scalar)

Q e

Free charge (scalar)

Q

Quality factor

I

Current

V

Voltage

Z

Impedance

? 0

Permittivity of free space (scalar)

Electrostatic potential

E i

Electric field

P i

Electric polarization per unit present volume

? i

Electric polarization per unit mass

D i

Electric displacement vector

Reference electric field vector

Reference electric polarization vector

Reference electric displacement vector

f j

Mechanical body force per unit mass

? ij

Cauchy stress tensor

Electrostatic stress tensor

Symmetric stress tensor in spatial, two-point, and material form

Symmetric Maxwell stress...

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