An improved analytic model for designing the polymer-composite stepped-plate transducer using the modified Mindlin plate theory

A stepped-plate transducer (SPT) uses an extensive radiating plate to produce highly-directional ultrasound beams. In this paper, we present an improved analytical model for designing the polymer-composite stepped -plate transducer (PCSPT). The polymer-composite features the lightweight and flexible properties, and there can be little change in the resonant frequency and mode shape when the steps are attached. With the outstanding merit, it is feasible to construct SPTs with polymer-composite steps without taking the steps into consideration. The modified Mindlin plate theory (MMPT) is applied to improve the accuracy in the equivalent circuit model (ECM) that is used to predict the high-frequency vibratory responses. Our analytical model can be used to design well-tuned SPTs to achieve the desired dynamic responses such as resonant frequencies, mode shape and bandwidth for various high-power ultrasonic applications. We use several numerical design examples to illustrate that the design of the transducer can be accomplished without analyzing the sophisticated stepped-plate's behavior. We also perform a series of experiments to verify that the PCSPT is capable of functioning as a high-power ultrasonic transducer.