Active control of axisymmetric shells with piezoelectric layers: a mixed laminated theory with a high order displacement field

This paper presents the development of a semi-analytical axisymmetric shell finite element model with embedded and/or surface bonded piezoelectric ring actuators and/or sensors for active damping vibration control of the structure. A mixed finite element approach is used, which combines the equivalent single-layer higher order shear deformation theory, to represent the mechanical behavior with a layerwise discretization in the thickness direction to represent the distribution of the electric potential of each piezoelectric layer of the frusta conical finite element. To achieve a mechanism of active control of the dynamic response of the structure a feedback control algorithm is used coupling the sensor and active piezoelectric layers. Two illustrative examples are presented and discussed.