Three-dimensional equations recapitulation
carrier concentration perturbation, 114
piezoelectric constitutive relations, 113
uniform doping, 114
Three-dimensional material constants, 148
Three-dimensional phenomenological theory, 1
Time-harmonic
boundary conditions, 99
differential equations, 99
linear homogeneous algebraic equations,
100
n-type semiconductor, 98
polynomial equations, 100
Time-harmonic bending
carrier concentration perturbation, 101, 102
linear algebraic equations, 100
linear theory, 100
resonances, 100, 101
static bending analysis, 100
ZnO beam, 98, 99
Total charge density, 192
Transient bending
approximation, 105
boundary and initial conditions, 103
electron concentration perturbation, 107,
108
electron distribution, 106
extensional waves, 106
free vibration modes, 104
horizontal reference state, 106
initial-boundary-value problem, 105
linear combination, 105
piezoelectric coupling, 104
shear deformation, 102
shear force boundary condition, 104
standard mathematical problem, 105, 106
theoretical analysis, 104
variable separation, 104
ZnO beam, 102, 103
Transient vibration
end force, 69
hyperbolic wave equation, 71
initial and boundary conditions, 68, 69
initial-boundary-value problem, 71
integration, 71
Laplace transform, 71
one-dimensional governing equations, 67
piezoelectrically stiffened elastic constant,
69
piezoelectric semiconductor rod, 67, 68
piezoelectricity subproblem, 68
propagation, 70
time instants, 70–72
variables separation method, 69
Transverse shear force, 92, 155
Two-dimensional equations/model, hierarchy
electromechanical loads, 116
index convention, 116
integration, 115
plate constitutive equations, 116
plate thickness, 116
power series, 114
uniform thickness, 114
Two-dimensional gradient operator, 142
Two-dimensional Laplacian, 8, 142
Two-dimensional problem, 13
U
Undetermined constants, 143, 167
Uniform doping, 13, 46, 149, 157
V
Variables separation method, 69
Vibration modes, 65
Voigt’s anisotropic plate elastic constants, 121
Z
Zero- and first-order equations
carrier concentration
gradients, 117
perturbations, 117
displacements, 117
motion, 118
plate constitutive relations, 118
plate extension/bending problems analysis,
117
shear forces, 119
surface loads, 119
Zero-order equations, 143
Zinc oxide (ZnO), 220
ZnO piezoelectric semiconductor rod, 181
230
Index
carrier concentration perturbation, 114
piezoelectric constitutive relations, 113
uniform doping, 114
Three-dimensional material constants, 148
Three-dimensional phenomenological theory, 1
Time-harmonic
boundary conditions, 99
differential equations, 99
linear homogeneous algebraic equations,
100
n-type semiconductor, 98
polynomial equations, 100
Time-harmonic bending
carrier concentration perturbation, 101, 102
linear algebraic equations, 100
linear theory, 100
resonances, 100, 101
static bending analysis, 100
ZnO beam, 98, 99
Total charge density, 192
Transient bending
approximation, 105
boundary and initial conditions, 103
electron concentration perturbation, 107,
108
electron distribution, 106
extensional waves, 106
free vibration modes, 104
horizontal reference state, 106
initial-boundary-value problem, 105
linear combination, 105
piezoelectric coupling, 104
shear deformation, 102
shear force boundary condition, 104
standard mathematical problem, 105, 106
theoretical analysis, 104
variable separation, 104
ZnO beam, 102, 103
Transient vibration
end force, 69
hyperbolic wave equation, 71
initial and boundary conditions, 68, 69
initial-boundary-value problem, 71
integration, 71
Laplace transform, 71
one-dimensional governing equations, 67
piezoelectrically stiffened elastic constant,
69
piezoelectric semiconductor rod, 67, 68
piezoelectricity subproblem, 68
propagation, 70
time instants, 70–72
variables separation method, 69
Transverse shear force, 92, 155
Two-dimensional equations/model, hierarchy
electromechanical loads, 116
index convention, 116
integration, 115
plate constitutive equations, 116
plate thickness, 116
power series, 114
uniform thickness, 114
Two-dimensional gradient operator, 142
Two-dimensional Laplacian, 8, 142
Two-dimensional problem, 13
U
Undetermined constants, 143, 167
Uniform doping, 13, 46, 149, 157
V
Variables separation method, 69
Vibration modes, 65
Voigt’s anisotropic plate elastic constants, 121
Z
Zero- and first-order equations
carrier concentration
gradients, 117
perturbations, 117
displacements, 117
motion, 118
plate constitutive relations, 118
plate extension/bending problems analysis,
117
shear forces, 119
surface loads, 119
Zero-order equations, 143
Zinc oxide (ZnO), 220
ZnO piezoelectric semiconductor rod, 181
230
Index
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