Numerical Simulation Of Piezoelectric Actuator Generated Lamb Wave Propagation In Plates

At present, it is getting mature to use spectral element method (SEM) in simulation ofdamage detection based on Lamb wave techniques. The efficiency of the SEM is widelyrecognized. But most of these simulations have not considered the electro-mechanical couplingeffect of piezoelectric actuators and sensors and their influences on the simulations. On the otherhand, it is common to simulate piezoelectric effect by using the ordinary finite element method(FEM) and is rare by using the SEM. This paper combines constitutive equations of piezoelectricmaterial and the SEM frequently used in Lamb wave simulation, from simple to complex, todevelop a rod spectral element with piezoelectric actuator/sensor, a beam spectral element withpiezoelectric actuator/sensor, a piezoelectric plane strain spectral element and a plate spectralelement with piezoelectric actuator/sensor, and then apply these elements in the numericalsimulations of actuation, propagation and receiving of Lamb wave in rods, beams and plates.Comparisons to existing results reported in literatures and with the results re-calculated by usingcommercial software ANSYS verify the correctness of the developed elements. Together with theelliptical position technology, a single damage in an aluminum plate is identified. The researchshows that, through inverse piezoelectric effect, piezoelectric actuators transfer electric load toforce load acting on the substrate, mainly concentrated along the edges connected withpiezoelectric patches. Even if simulate without considering piezoelectric actuators, it cannotsimply apply the force load at a point as done by former scholars. Correspondingly, there existsstress concentration along the edges of piezoelectric actuator stuck to the substrate, and themaximum von-Mises stress increases rapidly with the decrease of the thickness ratio of theactuator to substrate. On the other hand, the sensor can combine the complex displacementcomponents in terms of several degrees of freedom into a simple electric signal throughpiezoelectric effect. The signal is easily measured and analyzed in practice. The amplitude of thesensing signal decreases with the increase of the thickness ratio of the actuator to substrate, andincreases at first then decreases with the increase of the thickness ratio of the sensor to substrate.The reported results may provide some useful information for practical applications.