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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.
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 certain certain value. Here the 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 avoid ed.