Resonant and equivalent circuit characteristics of piezoelectric ceramics disk with different (diameter-to-thickness) ratio

In this paper, the resonant spectrum of the piezoelectric ceramic thin disk with different diameter-to-thickness ratio in the frequency range from 50 kHz to 1 MHz was studied by the impedance analysis method. If the diameter-to-thickness ratio was higher than 15, the vibration mode of the piezoelectric ceramic thin disk was pure radial mode, besides the fundamental radial mode, there are some radial overtone modes with inharmonic frequency separation in the entire frequency range from 50 kHz to 1 MHz. The number of radial overtone modes depended on the diameter; the ceramic disk with larger diameter had more overtone modes than that of ceramic disk with smaller diameter. With the same diameter, the resonant frequency ratio of fundamental mode to that of overtone mode was decreased with the increasing of thickness. With the same thickness, the resonant frequency ratio of fundamental mode to that of overtone mode was decreased with the decreasing of diameter. But when the diameter-to-thickness ratio was less than 15, some other vibration modes were existed in the frequency range higher than 600 kHz. From experiment, it is found that the effective electromechanical coupling factor k_eff was decreased with the increasing of overtone mode order. The decrease of effective electromechanical coupling factor k_eff was due to the less electrical energy transfer to mechanical energy with the increasing of overtone mode order. In the equivalent circuit, the motional resistance R₁ and the motional inductance L₁ were increased, but the motional capacitance C₁ and the capacitance C_o were decreased with the increasing of overtone mode order.