Theoretical modeling of resonant modes of composite ultrasonic transducers

摘要

Although a great deal of effort has been devoted to the modeling of composite piezoelectric materials, most of the earlier works are based on the assumption that the structure of the composite relative to the wavelength is very fine. Such approximation cannot address the complete dynamic behavior of composites. In order to understand the overall characteristics of composite ultrasonic transducers, a dynamic model was developed, in which the acoustic waves propagating in 2-2 composites along the thickness direction were analyzed by solving the coupled elastic equations of the constituent phases. By neglecting the boundary conditions of the free surfaces and simply taking the resonator thickness as half a wavelength, the resonant modes of the composite transducers as functions of aspect ratio of the ceramic plate elements and volume fraction of ceramic phase can be calculated from this model. The theoretical dispersion curves for the thickness mode and the lateral periodical mode agree with the experimental results. The vibration distribution in the ceramic and polymer phases at the resonant frequency as a function of the composite thickness as well as the volume fraction of the ceramic phase are obtained, and through the discussion of the vibration field the variation rule of the resonant frequency is well explained. For the resonant frequency the results of the isostrain model, the stopband resonance model, and the T-matrix model are consistent with the predictions made by this model under the special condition of very fine structure.