In spacecraft, severe vibrations induced by the launch vehicle may cause damage to the precision payload. Therefore active adapters with vibration suspending characteristics are needed. This paper presents theoretical studies of the active vibration control characteristics of conical shells with laminated piezoelectric actuators. A diagonal piezoelectric actuator is proposed to control the axial, lateral and transverse vibrations of the conical shell. Modal functions are designed to represent the free vibrations of the conical shell with clamped-free boundary conditions. General formulae of the modal control force and corresponding components are derived based on the converse piezoelectric effects and then specified for the diagonal actuators. By using an open-loop control method, the modal control characteristics of diagonal actuator segments at different locations are investigated and compared, and the axial, lateral and transverse vibrations of two conical shell models are evaluated. The optimal locations of actuator segments for the control of different natural modes are also investigated.

This paper presents shear piezoelectric sensors for conical shell sensing. The piezoelectric patch is polarized in the longitudinal direction of conical shell structure. The electrodes are fixed at the sides parallel to the directions of polarization. Sensors in this arrangement are only sensitive to the in-plane shear strains. Both sensing equations and modal signals are derived based on the thin-shell assumption and piezoelectric effect. Numerical results are presented for free torsional vibrations of frustum shell of revolution with clamped-free boundary, and the effects of sensor length on the output are evaluated. The amplitudes of the output signal of the sensors are lower than that of modal ones, but they are all share the same trends. The amplitudes depend on the deformation of the shell and the length of the sensor. The results indicate the optimal locations of the piezoelectric sensor for sensing the torsional vibration of clamped-free shell. The output signals of the sensor can be used as the control input for later active vibration control. The sensing equations are applicable to sense shear strains and torsion of other type shells by replacing the strain equation.

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