ELECTRICALLY FORCED THICKNESS-SHEAR VIBRATIONS OF QUARTZ PLATE WITH NONLINEAR COUPLING TO EXTENSION |
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Authors: | Rongxing Wu Jiashi Yang Jianke Du Ji Wang |
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Institution: | [1]Piezoelectric Device Laboratory, School of Engineering, Ningbo University, Ningbo 315211, China [2]Department of Engineering Mechanics, University of Nebraska, Lincoln, NE 68588-0526, USA |
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Abstract: | We study electrically forced nonlinear thickness-shear vibrations of a quartz plate resonator with relatively large amplitude. It is shown that thickness-shear is nonlinearly coupled to extension due to the well-known Poynting effect in nonlinear elasticity. This coupling is relatively strong when the resonant frequency of the extensional mode is about twice the resonant frequency of the thickness-shear mode. This happens when the plate length/thickness ratio assumes certain values. With this nonlinear coupling, the thickness-shear motion is no longer sinusoidal. Coupling to extension also affects energy trapping which is related to device mounting. When damping is 0.01, nonlinear coupling causes a frequency shift of the order of 10-e which is not insignificant,and an amplitude change of the order of 10-8. The effects are expected to be stronger under real damping of 10-5 or larger. To avoid nonlinear coupling to extension, certain values of the aspect ratio of the plate should be avoided. |
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Keywords: | piezoelectricity resonator vibration quartz plate |
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