New definitions of the nonlinear equivalent circuits of a broad plate for thickness-extensional vibration and a thin bar for length-extensional vibration are presented. These are obtained by extending Mason's linear equivalent circuits to the nonlinear region and are applied to the analysis of the second harmonic generation at the resonance point in the broad plate of Z-cut LiNb03 and to the determination of the fourth-order compliance constant of X-cut longitudinal mode quartz crystal resonator by evaluating the resonance frequency difference as a function of current amplitude. The successful result of simulation of the generation of acoustic phase conjugate wave in a lead zirconate titanate (PZT) ceramic thin bar is also presented.
Mason's equivalent circuit is well known as a linear equivalent circuit for acoustic devices. By combining Mason's equivalent circuit with Smith's equivalent circuit of surface acoustic wave devices, it becomes a very effective tool for the physical interpretation of acoustic devices. If such equivalent circuit analysis can also be performed for the nonlinear problem, then comparatively simpler and accurate analysis can be obtained for almost all types of nonlinear problems. In this paper, equations are formulated to analyze the equivalent circuit of nonlinear‐type acoustic devices. At first, Mason's equivalent circuit is extended to the nonlinear region for the basic circuits of a thin bar of length‐extensional vibration and a broad plate of thickness‐extensional vibrations. Next, this equivalent circuit is used to analyze the thickness‐extensional vibration of Z‐cut LiNbO3 and second harmonic generation at the resonance point is clarified. Finally, these nonlinear equivalent circuits of length‐extensional vibration are applied to determine the nonlinear constants of PZT ceramics and the nonlinear constants of the equivalent circuit are clarified.
The generation of acoustic phase conjugate waves is demonstrated using our previously reported nonlinear equivalent circuit of thin bar with length-extensional vibration. Next, a new nonlinear equivalent circuit for propagating nonlinear surface acoustic wave (SAW) is proposed. Using this new circuit, it is shown that the metallic grating wave guide of SAW is equivalent to the nonlinear lattice in which the SAW soliton propagates. Finally, the experimental study about this waveguide is successfully performed.
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