# Studies on a Piezoelectric Cylindrical Transducer for Borehole Dipole Acoustic Measurements
## 3 Comparison with Traditional Transducer  
The conventional transducer is hard to generate large displacement in the frequency range below 1 kHz. This is because, for the piezoelectric material itself, the strain is so limited that it is hard to generate large displacement in the low frequency range [20]. Moreover, the radiation surface of the conventional transducer is so limited that it is hard to improve the radiation performance in low frequency.  
To better understand the vibration mechanism differences between the proposed and the conventional transducers, the finite element model for the conventional transducer was established, and is shown in Figure 10. The transducer uses four long and four short piezoelectric bender bars to vibrate generating dipole signal in \(x\)-\(x\) and \(y\)-\(y\) directions. When the conventional transducer is working in one direction, i.e., the \(x\)-\(x\) direction, four bender bars which include two long bender bars facing each other and two short bender bars facing each other are excited by applying a voltage at the same time. The bender bars in our proposed transducer and conventional transducer are of same size and same materials.  
Through numerical simulation, the transmitting voltage response curves of the proposed transducer and the traditional transducer (XMAC tool) are shown as the black solid line and the red solid line, respectively, in Figure 11. In the numerical simulation results, the transmitting voltage response amplitudes at the resonance frequencies of 497 Hz, 980 Hz, 3698 Hz, 4118 Hz, 4692 Hz and 5000 Hz were 99 dB, 121 dB, 123 dB, 114 dB, 116 dB and 127 dB, respectively. The resonant peaks of 497 Hz and 3698 Hz corresponded to effects of the first and third order of bending vibration modes of the long bender bars, and the resonant peaks of 980 Hz and 5000 Hz corresponded to effects of the first order and third order bending vibration modes of the two short bender bars. Vibration modes at 4118 Hz and 4692 Hz, respectively, were the transition modes of the third order bending vibration mode in the length direction of the long bender bar to the third order bending vibration mode in the length direction of the two short bars. For the traditional transducer, the numerical simulated transmitting voltage response amplitudes at the resonance frequencies of 440 Hz, 920 Hz, 1120 Hz and 2720 Hz and 4260 Hz and 4890 Hz were 93 dB, 107 dB, 99 dB, 122 dB, 114 dB and 117 dB, respectively, and the resonant peaks of 440 Hz and 2720 Hz corresponded to the first and third order of bending modes of long benders in the length direction, respectively. The resonant peaks of 920 Hz and 1120 Hz mainly corresponded to the first order bending modes of the short benders in length direction. At 1120 Hz, the second order bending mode of the long benders appeared. The resonant peaks of 4260 Hz and 4890 Hz corresponded to the third order bending modes of short benders in the length  
Figure 10: The \(xz\) plane sectional view of finite element model of the conventional bender-type transducer with its frame.  
direction. At 4260 Hz, the long benders and short benders were in the same phase, while at 4890 Hz, the long benders and short benders were in opposite phases.  
The numerical analyses show that the transmitting voltage response of the newly designed transducer is 6 dB, 14 dB and 10 dB more than that of the traditional transducer at about 450 Hz, 900 Hz and 5000 Hz, respectively. From the comparison, it is concluded that the radiation performance of the proposed transducer is improved mainly because radiation surface is increased largely by using the cylindrical shell.