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We study coupled extensional and flexural cylindrical vibrations of a corrugated cylindrical shell piezoelectric transducer consisting of multiple pieces of circular cylindrical surfaces smoothly connected along their generatrices. Using the classical shell theory, a theoretical solution is obtained. Based on the solution, basic vibration characteristics of resonant frequencies, mode shapes, and internal forces are calculated and examined for the corrugated transducers, consisting of a few circular pieces each about 50 mum thick, with radius of 5 mm and span angle of 120deg. For these transducers the first resonance is of the order of 10-100 Hz.