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Simulation of the multi-morph bender transducer

The finite element method (FEM) is used to simulate a multi-morph bender bar, which comprises an inert substrate having two pairs of piezoelectric elements attached to its two sides. The simulation shows that the multi-morph bender bar has a lower fundamental frequency than the trilaminar bender bar. The effects of geometry on its fundamental frequency and conductance are investigated, demonstrating that the two pairs of piezoelectric elements affect differently. Simultaneously, a gap is proposed to carve in this multi-morph bar structure. By choosing adequate structure sizes, the proper working frequency and highly efficient radiation performance can be obtained. Numerical simulation results provide a good guidance on the optimization design for the multi-morph bender transducers.