“…First, the resonance occurring at the lowest frequency is a radial vibration mode, and at this time, the resonance and anti-resonance frequencies and resonance resistance values affect the electromechanical coupling coefficient and mechanical quality coefficient [28][29][30]. Second, the thickness vibration mode of piezoelectric ceramics occurring at high frequencies is the most important vibration mode for transmitting and receiving ultrasonic waves, and the center frequency of the vibrator strongly depends on the thickness of the piezoelectric ceramics [31]. Therefore, to analyze the resonance mode according to the change in thickness, the diameter (D) of the ceramic was fixed to 16 mm, which is the diameter after sintering, and the models were designed with four thicknesses (T), namely 0.8, 1.2, 1.6, and 2.0 mm.…”