A Linear Theory Of Piezoelastic Shell Vibrations

Abstract In recent years, the strong demand for high performance structures has driven a new development of "smart" materials and structures. Piezoelectric smart structures composed of passive elastic materials and active piezoelectric materials have been recently developed, which seem to be very promising in a variety of engineering applications. To broaden the theoretical fundamentals, a linear piezoelastic thin-shell vibration theory is proposed in this paper. Generic piezoelastic system equations of piezoelectric shell continua are formulated using Hamilton's principle and linear piezoelectricity theory. General electric and mechanical boundary conditions are also derived. The proposed piezoelectric shell theory is very generic, and can be simplified to account for many other commonly occurring geometries, such as spheres, cylinders, plates, cones, etc., based on four system parameters, two Lame parameters and two radii of curvature. Simplifications of the generic theory to two plate cases are demonstrated in case studies.