Electromechanical response of laterally clamped piezoelectric wafers: Absence of in-plane mechanical resonances in the electromechanical impedance spectrum

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We discuss the electromechanical response characteristics of laterally clamped piezoelectric wafers. The impedance spectra (both magnitude and phase) obtained from finite element simulations of uniformly polarized free and clamped circular and square wafers are first presented. It is observed that the magnitude and phase of the impedance spectrum for free piezoelectric wafers shows all the in-plane extensional modes as electromechanical resonances, while that for a clamped wafer does not show any of them. However, it is also shown that the spectrum corresponding to the out-of-plane displacement on the surface of the wafer actually shows the in-plane resonances for both free and clamped wafers. In other words, it is found that the clamped wafer shows in-plane mechanical resonances but these do not appear in the electromechanical impedance spectrum. This observation is then generalized and explained using an analytical model for thin piezoelectric wafers of arbitrary shape. In particular, it is shown that the impedance spectrum of laterally clamped piezoelectric wafers of any arbitrary shape do not show in-plane extensional modes as electromechanical resonances. Moreover, the impedance spectrum of a laterally clamped wafer is shown to depend only on its area and thickness but not its shape. The above findings are relevant to measurement techniques that rely explicitly on the characteristics of the impedance spectrum observed for a piezoelectric wafer. In addition, the absence of resonances resulting from lateral clamping allows for broadband operation of piezoelectric wafers as sensors and actuators for applications such as ultrasonic range finding, underwater acoustics and acoustic imaging.