a	Half-length of PZT patch
c	Depth of crack
d 31	Piezoelectric constant
f	Frequency
hp, ha, hs	Thickness of piezoelectric patch, bonding layer, and host beam, respectively
i	$\sqrt{-1}$
l	Length of host beam
lp,	Length of PZT wafer
t	Time variable
u	Axial displacement due to axial force in host beam
up	Axial displacement of PZT patch
us	Axial displacement on the surface of the host beam
w	Transverse deflection
wp	Width of PZT patch
x, y, z	Cartesian coordinates
A	Cross-sectional area
D 3	Electric displacement
E 3	Electric potential
Ep, Es	Young’s modulus of PZT patch and host beam, respectively
η	Mechanical loss factors
${\overline{E}}_p$	Complex Young’s modulus of PZT patch, ${\overline{E}}_p=E_p(1+\eta \mathrm{i})$
Ga, G	Shear rigidity of bonding layer and host beam, respectively
I	Moment of area
Ii	Electric current flowing through i-th PZT sensor
M, N, Q	Bending moment, axial force, and shear force, respectively
T 1	Longitudinal stress in PZT patch
V	Electric voltage
Y	Electric admittance of PZT patch
δ	Dielectric loss factors
${\epsilon }_{33}^T$, ${\overline{\epsilon }}_{33}^T$	Dielectric constant and complex dielectric constant, respectively, and ${\overline{\epsilon }}_{33}^T={\epsilon }_{33}^T(1-\delta \mathrm{i})$
εp	Axial strain of PZT patch
φ	Shear rotation
κ	Shear correction factor (π2/12)
μ	Poisson’s ratio of host structural member
ρp, ρs	Mass density of PZT patch and host beam, respectively
τ(x)	Transferred shear stress between PZT patch and the host beam
ω	Circular frequency
ψ	Stiffness ratio, ψ = Eshs/(Ephp)
Γ	Shear lag parameter $\mathrm{\Gamma }=\sqrt{(\overline{G}{\theta }_a/{\overline{h}}_a^2)(\psi +\alpha )/\psi }$, where $\overline{G}=G_a/E_p$, θa = ha/hp, ${\overline{h}}_a=h_a/a$, α = 1.