Torsional wave propagation in a circumferentially poled piezoelectric cylindrical transducer with unattached electrodes

The present study is devoted to the propagation of torsional waves in a circumferentially poled piezoelectric hollow cylinder with air gaps between the cylinder surfaces and two electrodes. The state space method is employed to obtain a transfer relation between the state variables at the inner and outer surfaces of the hollow cylinder. The air gaps are treated as the free space. The characteristic equations are derived by taking into account the boundary and continuity conditions. Numerical examples clearly show the effect of gaps on the wave propagation in the piezoelectric hollow cylinder.