Theoretical modeling of resonant modes of composite ultrasonictransducers

摘要

Although a great deal of effort has been devoted to the modelingnof composite piezoelectric materials, most of the earlier works arenbased on the assumption that the structure of the composite relative tonthe wavelength is very fine. Such approximation cannot address thencomplete dynamic behavior of composites. In order to understand thenoverall characteristics of composite ultrasonic transducers, a dynamicnmodel was developed, in which the acoustic waves propagating in 2-2ncomposites along the thickness direction were analyzed by solving thencoupled elastic equations of the constituent phases. By neglecting thenboundary conditions of the free surfaces and simply taking the resonatornthickness as half a wavelength, the resonant modes of the compositentransducers as functions of aspect ratio of the ceramic plate elementsnand volume fraction of ceramic phase can be calculated from this model.nThe theoretical dispersion curves for the thickness mode and the lateralnperiodical mode agree with the experimental results. The vibrationndistribution in the ceramic and polymer phases at the resonant frequencynas a function of the composite thickness as well as the volume fractionnof the ceramic phase are obtained, and through the discussion of thenvibration field the variation rule of the resonant frequency is wellnexplained. For the resonant frequency the results of the isostrainnmodel, the stopband resonance model, and the T-matrix model arenconsistent with the predictions made by this model under the specialncondition of very fine structure