Dynamic Analysis of a Piezoelectric Material with an Impermeable Penny-Shaped Crack under Pure Torsional Wave
A torsional transient wave was assumed acting at infinity on the piezoelectric body with an embedded penny-shaped crack. Appropriate governing equations and boundary conditions have been built within the three-dimensional electroelasticity. The total displacement field was simply considered as the combination of two parts, one related to incident waves inducing an oscillating motion, and another with the scattered waves. An electric impermeable crack was assumed to simplify the mathematical analysis. The problem was formulated in terms of integral transforms techniques. Hankel transform were applied to obtain the dual integral equations, which were then expressed to Fredholm integral equations of the second kind.
S.W. Nam, Y.W. Chang, S.B. Lee and N.J. Kim
Z. T. Chen, "Dynamic Analysis of a Piezoelectric Material with an Impermeable Penny-Shaped Crack under Pure Torsional Wave ", Key Engineering Materials, Vols. 345-346, pp. 433-436, 2007