Latin Letters
$\mathbf{B}$	Body force per unit mass (gravitational force)
$b$	Width of the beam
$C_{LN}$	Green deformation tensor
${\dot{C}}_{LN}$	Deformation (strain) rate tensor in material coordinates
$\mathbf{D}$	Electric displacement vector
$d_{31}$	Piezoelectric strain coefficient
$d_{ij}$	Deformation (strain) rate tensor
$dS$	Surface area element
$dV$	Volume element
$\mathbf{E}$	Electric field vector
$E_{LN}$	Green–Lagrange strain tensor (finite deformation)
${\dot{E}}_{LN}$	Green–Lagrange strain rate tensor
${\tilde{E}}_{IJ}$	Strain tensor in the linearized theory
${\tilde{e}}_{ij}$	Infinitesimal strain tensor in spatial coordinates
${\mathbf{F}}_P$	Distributed force due to polarization and electric field
$F_{mM}$	Deformation gradient of the forward motion
$F_{Ii}^{-1}$	Deformation gradient of the inverse motion
$G_M$	Temperature gradient in material coordinate
$h$	Heat energy source per unit mass
$h^E$	Electrostatic energy source
$I$	Second moment of area of the cross-section
$J$	Jacobian
$K_0$	Curvature
$L$	Beam length
${\mathbf{m}}_P$	Distributed couple due to polarization and electric field
$M$	Bending moment
$\mathbf{n}$	Outward unit normal vector of the discontinuity surface
$\mathbf{P}$	Polarization vector
$\mathbf{q}$	Heat flux vector
$Q_I$	Heat vector in material coordinates
$r\left(h\right)$	Successive difference ratio (convergence criterion)
$S\left(t\right)$	Surface of the body
$t$	Time
$t_c$	Thickness of the aluminum core
$t_p$	Thickness of the PZT patch
$\mathbf{u}$	Displacement vector
$u_i$	Components of the displacement vector
$U$	Relative displacement velocity of the discontinuity surface with respect to the medium
$V$	Applied electric potential
$V\left(t\right)$	Volume
$\mathbf{v}$	Velocity vector
${\mathbf{v}}_{i,j}$	Velocity gradient tensor
$w\left(L\right)$	Free-tip displacement
$w_f$	Free surface charge distribution
${\mathbf{w}}_{ij}$	Spin (whirl) tensor
$\mathbf{X}$	Position vector in the undeformed configuration
$X_{M,m}$	Deformation gradient of inverse motion
$\mathbf{y}$	Position vector in the deformed configuration
$y_{m,M}$	Deformation gradient
$Y$	Young’s modulus
$YI$	Bending stiffness per unit width
$z_t,z_b$	Thickness coordinate for the upper and lower patches
Greek Letters
${\mathsf{\Sigma }}_{ijkl}$	Elasticity tensor components in spatial coordinates
${\mu }_{ijl}$	Piezoelectric coupling tensor components in spatial coordinates
${\beta }_{il}$	Electric permittivity tensor components in spatial coordinates
${ϵ}_{ij}$	Infinitesimal strain tensor components
${\xi }_0$	Permittivity of free space
$\eta$	Entropy density per unit volume
$\epsilon$	Internal energy per unit volume
$\theta$	Temperature
ΠI	Polarization vector per unit mass
$\rho$	Mass density in the deformed configuration
${\rho }_0$	Mass density in the reference configuration
$\mathsf{\Sigma }$	Thermodynamic stress potential
${\sigma }_{ij}$	Asymmetric stress tensor components
${\overline{\sigma }}_{ij}$	Symmetric stress tensor components
${\sigma }_y$	Peel stress
${\tau }_{xy}$	Interface shear stress
$\phi$	Electric potential
$\psi$	Helmholtz free energy density/thermodynamic potential
$\Gamma$	Discontinuity surface
${\omega }_k$	Angular velocity components
Special Notation
${\delta }_{ij}$	Kronecker delta
${\epsilon }_{ijk}$	Permutation tensor
$\nabla$	Gradient operator
${(\cdot )}_i$	Derivative with respect to variable $i$
$⟦\cdot ⟧$	Jump across the discontinuity surface
PATH1	Longitudinal interface path (clamped end → free end)
PATH2	Transverse interface path (along patch width)
Abbreviations
FEM	Finite Element Method
PZT	Lead–Zirconate–Titanate
DOF	Degree of Freedom
APDL	ANSYS Parametric Design Language
2D/3D	Two-Dimensional/Three-Dimensional