Mechanically induced electric potential and charge redistribution in laminated composite piezoelectric semiconductor circular cylindrical thin shells

Abstract

We study electromechanical effects and piezotronic behaviors in a Kirchhoff–Love laminated composite piezoelectric semiconductor circular cylindrical thin shell, which is composed of a non-piezoelectric semiconductor core and two piezoelectric dielectric layers. A second-order assumption for electric potentials and carrier concentration perturbations is utilized to capture accurate descriptions of the electric field and charge distributions within the composite shell, where the zeroth-order, first-order, and second-order forms represent constant, antisymmetric, and symmetric distributions along the thickness, respectively. The field equations and boundary conditions are simultaneously derived through a principle of virtual work and the fundamental lemma of the calculus of variation. The new governing equations derived show a new coupling relation between mechanical deformation and charge behavior in the composite shell, where all mechanical deformations (extension, bending of the shell) and all distribution forms of electric potential (zeroth-, first-, second-order electric potentials) are coupled, which is different from piezoelectric semiconductor beams and plates. Then, the numerical results of electromechanical effects and piezotronic behaviors in static bending and forced vibration problems of the shell are conducted with the derived theoretical model. Numerical studies of static bending graphically show some fundamental coupling relations between mechanical forces and charge distributions in deformed piezoelectric semiconductor shells. The new results from the forced vibration analysis given by the current model show that the deflection amplitude and the electric potential distribution in the thin shell are frequency-dependent and can be adjusted by controlling the excitation frequency. In addition, the semiconducting properties (dependence of mechanical behavior on doping level) are studied in both static and dynamic problems. The mechanically controlled charge distribution suggests that shell-shaped piezoelectric semiconductor shells could serve as an effective means of sensing or energy harvesting by converting mechanical energy into electricity.