A SELF-SENSING PIEZOLAMINATED ACTUATOR MODEL FOR SHELLS USING A FIRST-ORDER SHEAR DEFORMATION-THEORY

A composite piezolaminated shallow thin shell theory has been develope d in which the individual laminae are capable of electromechanical tra nsduction. Utilizing a first order shear deformation approximation and assuming that an electrical field may be applied only across the thic kness of a given lamina, the resulting shell theory shows that piezola minae are capable of exciting and sensing bending, torsion, inplane sh earing, and inplane stretching. Piezolaminae are shown to be incapable of exciting and sensing transverse shear unless a three-dimensional e lectrical field is applied. Inplane shearing and torsion transduction only becomes possible when the dominant rolling axis of a given piezol amina is skewed such as not to coincide with a principal geometric axi s. Constitutive relationships are derived which describe how each piez olamina may function simultaneously as both a sensor and an actuator. Two-dimensional piezoelectric field functions are introduced which des cribe 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 transvers e shear deformation is neglected according to Love's first approximati on.