Circular piezoelectric transducers with axial polarization are proposed as low frequency acoustic sensors for dark matter bubble\nchamber detectors.The axial vibration behaviour of the transducer is studied by three different methods: analytical models, FEM\nsimulation, and experimental setup. To optimize disk geometry for this application, the dependence of the vibrational modes\nin function of the diameter-to-thickness ratio from 0.5 (a tall cylinder) to 20.0 (a thin disk) has been studied. Resonant and\nantiresonant frequencies for each of the lowest modes are determined and electromechanical coupling coefficients are calculated.\nFrom this analysis, due to the requirements of radiopurity and little volume, optimal diameter-to-thickness ratios for good\ntransducer performance are discussed
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