A Self-Sensing Piezolaminated Actuator Model for Shells Using a First Order Shear Deformation Theory

Abstract

A composite piezolaminated shallow thin shell theory has been developed in which the individual laminae are capable of electromechanical transduction. Utilizing a first order shear deformation approximation and assuming that an electrical field may be applied only across the thickness of a given lamina, the resulting shell theory shows that piezolaminae are capable of exciting and sensing bending, torsion, inplane shearing, and inplane stretching. Piezolaminae are shown to be incapable of exciting and sensing transverse shear unless a three-dimensional electrical field is applied. Inplane shearing and torsion transduction only becomes possible when the dominant rolling axis of a given piezolamina is skewed such as not to coincide with a principal geometric axis. Constitutive relationships are derived which describe how each piezolamina may function simultaneously as both a sensor and an actuator. Two-dimensional piezoelectric field functions are introduced which describe how nonuniformly distributed electromechanical transduction will affect the nature of the applied excitation and acquired measurement. The equations of motion are also given for a shell in which transverse shear deformation is neglected according to Love's first approximation.