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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...
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...
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...
In this paper, we consider the sandwich structure composed of silicon substrate, piezoelectric layer and electrode layers in the typical structure of FBAR. We assume a special solution in the form of harmonic wave in the piezoelectric layer, and substitute it into the simplified stress equations of motion and the charge equation of electrostatic. A correction to the solution assumed is obtained in...
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...
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...
The existence and propagation of Bleustein-Gulyaev (B-G) waves in a functionally graded piezoelectric substrate with exponential variation is studied by analytical technique. The dispersion equations for the existence of the B-G waves with respect to phase velocity are obtained for both electrically open and short conditions. A detailed investigation of the effect of the gradient coefficient on dispersion...
This paper addresses control problems of flexible robot arms by using direct strain feedback method. The purpose is to make clear why direct strain feedback can damp out the vibration of the flexible arms satisfactorily. New findings involved in this paper are that the direct strain feedback introduces a class of differential operators which we call A-dependent operators, and that the closed loop...
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