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Electrically forced thickness-shear vibrations of quartz plate with nonlinear coupling to extension

Electrically forced thickness-shear vibrations of quartz plate with nonlinear coupling to extension 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 10−6 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Acta Mechanica Solida Sinica" Springer Journals

Electrically forced thickness-shear vibrations of quartz plate with nonlinear coupling to extension

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Publisher
Springer Journals
Copyright
2008 The Chinese Society of Theoretical and Applied Mechanics and Technology
ISSN
0894-9166
eISSN
1860-2134
DOI
10.1007/s10338-008-0867-5
Publisher site
See Article on Publisher Site

Abstract

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 10−6 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.

Journal

"Acta Mechanica Solida Sinica"Springer Journals

Published: Dec 1, 2008

Keywords: Theoretical and Applied Mechanics; Surfaces and Interfaces, Thin Films; Classical Mechanics

References