To achieve a high magnification of amplitude by using an ultrasonic resonant transformer, one may choose from several different tapering rods. The basic transformers include conical, hyperbolic (catenoidal), exponential, multi-step cylindrical, and Fourier, etc. The Fourier transformers are better in the characteristics of higher bending stiffness and lower maximum strain over other single section transformers. The higher order Fourier transformers presented in this paper give more flexibility in optimization for desired mechanical characteristics.

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