Dynamic anti-plane interaction between an impermeable crack and a circular cavity in an infinite piezoelectric medium

Abstract

Wave propagation in an infinite elastic piezoelectric medium with a circular cavity and an impermeable crack subjected to steady-state anti-plane shearing was studied based on Green’s function and the crack-division technique. Theoretical solutions were derived for the whole elastic displacement and electric potential field in the interaction between the circular cavity and the impermeable crack. Expressions were obtained on the dynamic stress concentration factor (DSCF) at the cavity’s edge, the dynamic stress intensity factor (DSIF) and the dynamic electric displacement intensity factor (DEDIF) at the crack tip. Numerical solutions were performed and plotted with different incident wave numbers, parameters of piezoelectric materials and geometries of the structure. Finally, some of the calculation results were compared with the case of dynamic anti-plane interaction of a permeable crack and a circular cavity in an infinite piezoelectric medium. This paper can provide a valuable reference for the design of piezoelectric actuators and sensors widely used in marine structures.

Keywords

piezoelectric medium / impermeable crack / dynamic stress intensity factor / dynamic stress concentration factor / dynamic electric displacement intensity factor / Green’s function