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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...
This paper mainly analyzes the fundamental thickness shear modes of z-strip quartz crystal filter with the scalar equations derived by Tiersten and Smythe. Effects of the mass ratio and the distance between the electrodes on the operation modes and the resonant frequencies are also studied. Exact modes can be obtained and the results show that the operation modes without nodal lines on the electroded...
In this paper, we studied the nonlinear effects arising from large thickness-shear deformation on transient process in an AT-cut quartz crystal plate resonator operating in thickness-shear modes. Based on the Mindlin's plate theory, a system of first-order nonlinear equations of the vibration amplitude evolution was obtained when the evolution amplitude is much slower compared to the high-frequency...
We study thickness-twist vibrations of a rotated Y-cut quartz plate with two pairs of electrodes. One is a known driving voltage. The other is connected to an output circuit. The structure can operate as a filter. Both free and electrically forced vibrations are studied. Resonant frequencies, mode shapes and the related energy trapping, output voltage, input admittance, and input and output powers...
We perform a theoretical analysis on electrically forced, coupled thickness-shear and flexural vibrations of rectangular piezoelectric plates of monoclinic crystals. Mindlin's first-order theory for piezoelectric plates is used. Two types of boundary conditions are considered. Trigonometric series solutions are obtained. The motional capacitance of the plates and its frequency dependence under a time-harmonic...
We present our recent modeling results on power transmission through an elastic wall by piezoelectric transducers and acoustic waves. This includes the case of finite piezoelectric transducers on plates, power transmission through circular cylindrical shells, and mechanical nonlinearity due to large deformations near resonance.
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