This paper presents the development of a semianalytical 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. The electric potential function is represented through a layerwise discretization in the thickness direction and the influence of the interpolation functions is discussed. The displacement field and the electric potential are expanded in Fourier series in the circumferential direction, considering symmetric and anti-symmetric terms. Static and dynamic analyses are performed and several examples are presented and discussed to illustrate the accuracy and capabilities of the model.

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