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We analyze thickness-shear vibration of an axially poled circular cylindrical tube with unattached electrodes and air gaps. Both free and electrically forced vibrations are studied. Exact solutions are obtained from the equations of linear piezoelectricity. Resonant frequencies and the impedance of the transducer are calculated from the solution. Results show that the resonant frequencies are sensitive to the dimensions of the air gaps when the gaps are thin. The impedance depends strongly on the air gaps.
We analyze thickness-shear vibration of an axially poled circular cylindrical tube with unattached electrodes and air gaps. Both free and electrically forced vibrations are studied. Exact solutions are obtained from the equations of linear piezoelectricity. Resonant frequencies and the impedance of the transducers are. Results from that solution. Results show that that vital frequencies are sensitive to the dimensions of the air gaps when the gaps are thin. The impedance depends strongly on the air gaps.