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We derived a system of two-dimensional equations for thickness-extensional vibrations of a four-layered plate consisting of a piezoelectric thin film on an elastic substrate with driving and ground electrodes. It takes into consideration the couplings among the thickness-extensional mode to extensional, flexural, fundamental and second-order thickness-shear modes. Mindlin's approach of using a power...
A theoretical analysis on a rectangular energy-trapped piezoelectric thin zinc oxide film resonator operating with thickness-extensional modes is performed in this paper. The two-dimensional scalar differential equations derived by Tiersten and Stevens are used which can describe the in-plane mode distribution. Based on the scalar equations, we construct a variational formulation which provides a...
We study free vibrations of a circular AT-cut quartz resonator using the two-dimensional scalar differential equation by Tiersten and Smythe in conjunction with COMSOL. Resonant frequencies and mode shapes are obtained and compared with available experimental results as well as available analytical solutions of the scalar equation. The accuracy of various analytical solutions is examined.
This paper mainly analyzes the fundamental and third order thickness shear modes of z-strip quartz resonator with the scalar equations derived by Tiersten and Smythe. Effects of the mass ratio and the length of the electrode on the operation modes and resonant frequencies are also studied. Exact modes can be obtained and the results show that the operation modes without nodal lines on the electroded...
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