Dynamic response of a cracked thermopiezoelectric strip under thermoelectric loading using fractional heat conduction

Abstract

This study is concerned with the dynamic behavior of a piezoelectric material strip with a parallel crack under thermal shock and transient electric loading. The governing thermal and electromechanical equations are exactly reduced to a system of Cauchy-type singular integral equations by applying Laplace and Fourier transforms and the dislocation density functions. Numerical examples are discussed in detail to show the effects of the applied heat conduction model, cracked strip configuration, and electrical load variables on the dynamic thermal results and the stress-electric displacement intensity factors. The results reveal that the overshooting phenomenon would be more evident with the longer relaxation time and higher fractional order, while the wave behavior becomes weaker and stronger, respectively. There are apparent inflection points on the dynamic stress intensity factors (DSIFs) and the dynamic electric displacement intensity factor (DEDF) curves for different configurations of the strip and the coefficients of the heat conduction model. In addition, the stress intensity factors are insensitive to the electric load which has a dominant influence on the electric displacement intensity factor.