PSI - Issue 70

Arpit Singh et al. / Procedia Structural Integrity 70 (2025) 580–587

582

Nomenclature S k

Second-order strain tensor

d jk E j T m

Mechanical strain per unit electric field

c

Constant electric field

Mechanical stress G Conductance of the beam B Susceptance of the beam ͞ ⅈ Electric permittivity of sensor at constant stress d im , d jk Strain coefficients (or constants) of PZT S͞͞͞͞͞ km E Structure's effective mechanical impedance

Complex elastic compliance at the constant electric field

Z s,eff Z a,eff

Mechanical impedance of the PZT patch

v

Poisson’s coefficient

G i0

Conductance recorded by the PZT sensor before to structural damage

G i

Corresponding conductance at the i

th measurement points following damage

Y Admittance

2. Electro-mechanical Impedance (EMI) techniques Electro-mechanical Impedance (EMI) is a non-destructive method applied in Structural Health Monitoring (SHM) to evaluate structures and materials. Initial research had depended on static models to analyze piezoelectric (PZT) sensor-structure interactions. Liang et al. (1993) had initiated EMI with a dynamic model, though it was effective for 1D structures alone, neglecting multidimensional factors. Zhou et al. had later generalized it to 2D systems. To bridge gaps between 1D and 2D models, Bhalla and Soh (2004a) proposed the concept of "effective impedance," validated in the frequency range 200 – 400 kHz. EMI takes advantage of the coupling between a structure's mechanical response and the electrical response of PZT sensors through their two-way energy conversion and allows one to monitor in real time. The sensors utilized in EMI are piezoelectric, meaning that they are capable of either producing an electrical signal or detecting mechanical vibration. PZT sensors can be used to cover varied infrastructure, including bridges or skyscrapers, to measure structural response under dynamic loading states. They are incorporated into SHM systems to identify defects at an early stage of damage by examining changes in vibration signatures before noticeable macroscopic signs of damage. PZT sensors allow engineers to continuously monitor critical factors such as altered vibration modes, natural frequencies, and impedance variations by being embedded into or surface-bonded to structural parts. All of the above changes in admittance signatures are symptoms of a damaged state that can be caused by the effects of fatigue, environment, or material degradation, and PZT sensors record these. These sensor data from PZTs are processed by a variety of algorithms and techniques, such as data fusion, machine learning, and statistical analysis, that create an overall health monitoring for the structure. Advanced signal processing methods improve monitoring system sensitivity to allow accurate damage localization and severity quantification. Lead zirconate titanate (PZT) sensors, though fragile by nature, have merits like miniaturization and low weight, making it easy to deploy them in newer infrastructure development and retrofitting projects. Their energy-efficient operation enables sustained deployment in challenging environments, including remote or hard-to-access locations. The PZT (Pb(Zr 1 x Ti x )O 3 ), non-centrosymmetric crystals show the conserve effects. Piezoelectric materials generate mechanical strain when subjected to external electric fields. Under low-intensity fields, their linear constitutive behavior is mathematically represented by the following equations (Ikeda, 1990; Eq.-1): = + (1) Such variations can thus be caught and studied based on the electrical signals induced by piezoelectric sensors. Force transfer between the parent structure and the PZT sensor is uniform over the entire interface perimeter, with plane stress conditions being approximated within the sensor. The patch is considered to be negligibly small relative