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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...
Thickness-extensional vibration of a rectangular piezoelectric thin film filter symmetrically covered with two driving electrodes was studied in this paper. The Tiersten and Stevens scalar equation was employed. The Ritz method based on the variational formulation constructed in our previous work was used with trigonometric series as basis functions. Free vibration modes and corresponding resonant...
This paper analyses free vibration frequencies and modes for thickness-shear and thickness-twist vibrations of centrally partially electroded circular AT-cut quartz plate by using 3-D finite element models of commercial package ANSYS. The analysis has been done with the 3-D Finite Element Analysis (FEA) for displacements and vibration frequency at the thickness-shear mode, which is important in the...
In this paper, the piezoelectric film, electrodes and the silicon substrate of FBARs are modeled as a layered sandwich structure for studying the wave propagation in it. The harmonic solutions should satisfy the governing equations of each layer. Then, the dispersion relations can be obtained by the continuity conditions and boundary conditions. The dispersion curves are compared with the results...
We present a discussion on propagation properties of thickness-twist (TT) waves in a Y-cut quartz plate with an elastic or a functionally graded (FGM) top layer. Through a detailed deduction for the disperse relation, we studied the effects of various physical parameters on dispersion curves and cutoff frequencies. The study can provide a theoretical and numerical reference for the design and calibration...
This paper analyses free vibration frequencies and modes for thickness-shear and thickness-twist vibrations of centrally partially electroded circular AT-cut quartz plate. The elliptical coordinate is introduced for both un electroded and electrode part. Exact solutions of Mathieu equations which are transferred from the two-dimensional scalar differential equation derived by Tiersten and Smythe are...
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...
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