Bending (cont.)
time harmonic, 98
transient bending, 102
Bending equations
compact matrix notation, 122
energy density function, 123
extensional displacements, 124
first-order constitutive relations, 123
first-order strains, 121
higher-order plate displacements, 121
mechanical, 121
relaxed material constants, 122
shear deformation, 121
thickness expansion/contraction, 122
thickness-shear deformation, 122
thickness-shear vibration, 123
transverse shear forces, 122
zero-order constitutive relations, 121
zero-order plate shear strains, 122
Bending moment M, 205
Bending without shear deformation,
reduction, 124
Biasing fields
definition, 85
dynamic incremental fields, 86, 87
one-dimensional equations, 85
piezoelectric semiconductor rod, 85, 86
Bleustein-Gulyaev wave, 146
Boltzmann constant, 2, 215
Boltzmann distribution, 35
Boundary-value problem, 105, 151
Buckling
across nodal points, 111
axial force, 108
carrier concentration perturbation, 110
electromechanical coupling, 109
linear homogeneous equations, 109
load, 109
modes, 109, 110
piezoelectric dielectric beam, 110
piezoelectric semiconductor beam, 111
shear deformation, 108
zero deflection and bending moment, 109
ZnO beam, 108
Built-in electric field, 18, 23
Built-in potential, 18
C
Cadium selenide (SdSe), 216
Cantilever static bending
arbitrary constants, 97
boundary conditions, 96
carrier concentration perturbation, 96
electron concentration perturbation, 97
end force, 97, 98
geometric parameters, 97
linear algebraic equations, 97
linearized theory, 97
n-type semiconductor, 95
ZnO beam, 95
Carrier concentration perturbation, 101
Classical theory, 73
Clausius-Duhem inequality, 10
Composite rod extensions
average extensional stress, 152
axial force, 149
boundary-value problem, 151
constitutive relations, 148
differential element, 150, 154
electric displacement, 150
electron concentration perturbation,
152–154
electrostatics charge equations, 150
global charge neutrality conditions, 151
hyperbolic functions, 153
initial carrier concentration, 153
mechanical displacement, 151
n-type semiconductor, 152
piezoelectric dielectric layers, 147, 148
piezoelectric layers, 155
polarization charge density, 151
semiconductor, 149
static, 150
strain-displacement relation, 148
three-dimensional material constants, 148
COMSOL commercial software, 53
COMSOL numerical solution, 106
Continuity equation, 1
Crystals of class equation
constitutive relations, 126
electrostatics, 126, 127
extension, 125, 127
flexure, 127
material matrices, 125
semiconduction, 127, 128
shear, 125
stress relaxation, 126
thickness-shear correction, 126
ZnO, 125
Current-voltage relation/I-V curve, 57, 83,
186, 195
Curvilinear coordinate system, 132
224
Index
time harmonic, 98
transient bending, 102
Bending equations
compact matrix notation, 122
energy density function, 123
extensional displacements, 124
first-order constitutive relations, 123
first-order strains, 121
higher-order plate displacements, 121
mechanical, 121
relaxed material constants, 122
shear deformation, 121
thickness expansion/contraction, 122
thickness-shear deformation, 122
thickness-shear vibration, 123
transverse shear forces, 122
zero-order constitutive relations, 121
zero-order plate shear strains, 122
Bending moment M, 205
Bending without shear deformation,
reduction, 124
Biasing fields
definition, 85
dynamic incremental fields, 86, 87
one-dimensional equations, 85
piezoelectric semiconductor rod, 85, 86
Bleustein-Gulyaev wave, 146
Boltzmann constant, 2, 215
Boltzmann distribution, 35
Boundary-value problem, 105, 151
Buckling
across nodal points, 111
axial force, 108
carrier concentration perturbation, 110
electromechanical coupling, 109
linear homogeneous equations, 109
load, 109
modes, 109, 110
piezoelectric dielectric beam, 110
piezoelectric semiconductor beam, 111
shear deformation, 108
zero deflection and bending moment, 109
ZnO beam, 108
Built-in electric field, 18, 23
Built-in potential, 18
C
Cadium selenide (SdSe), 216
Cantilever static bending
arbitrary constants, 97
boundary conditions, 96
carrier concentration perturbation, 96
electron concentration perturbation, 97
end force, 97, 98
geometric parameters, 97
linear algebraic equations, 97
linearized theory, 97
n-type semiconductor, 95
ZnO beam, 95
Carrier concentration perturbation, 101
Classical theory, 73
Clausius-Duhem inequality, 10
Composite rod extensions
average extensional stress, 152
axial force, 149
boundary-value problem, 151
constitutive relations, 148
differential element, 150, 154
electric displacement, 150
electron concentration perturbation,
152–154
electrostatics charge equations, 150
global charge neutrality conditions, 151
hyperbolic functions, 153
initial carrier concentration, 153
mechanical displacement, 151
n-type semiconductor, 152
piezoelectric dielectric layers, 147, 148
piezoelectric layers, 155
polarization charge density, 151
semiconductor, 149
static, 150
strain-displacement relation, 148
three-dimensional material constants, 148
COMSOL commercial software, 53
COMSOL numerical solution, 106
Continuity equation, 1
Crystals of class equation
constitutive relations, 126
electrostatics, 126, 127
extension, 125, 127
flexure, 127
material matrices, 125
semiconduction, 127, 128
shear, 125
stress relaxation, 126
thickness-shear correction, 126
ZnO, 125
Current-voltage relation/I-V curve, 57, 83,
186, 195
Curvilinear coordinate system, 132
224
Index