scholarly journals Flexoelectric effect on thickness-shear vibration of a rectangular piezoelectric crystal plate

2021 ◽  
Author(s):  
Yang Zheng ◽  
Bin Huang ◽  
Ji Wang
Keyword(s):  
Boundary Conditions ◽  
Displacement Function ◽  
Crystal Plate ◽  
Symmetric Mode ◽  
Piezoelectric Crystal ◽  
Flexoelectric Effect ◽  
Shear Vibration ◽  
Shear Modes ◽  
Piezoelectric Crystal Plate ◽  
Thickness Shear

Abstract Thickness-shear (TSh) vibration of a rectangular piezoelectric crystal plate is studied with the consideration of flexoelectric effect in this paper. The developed theoretical model is based on the assumed displacement function which includes the anti-symmetric mode through thickness and symmetric mode in length. The constitutive equation with flexoelectricity, governing equations and boundary conditions are derived from the Gibbs energy density function and variational principle. For the effect of flexoelectricity, we only consider the shear strain gradient in the thickness direction so as to simply the mathematical model. Thus, two flexoelectric coefficients are used in the present model. The electric potential functions are also obtained for different electric boundary conditions. The present results clearly show that the flexoelectric effect has significant effect on vibration frequencies of thickness-shear modes of thin piezoelectric crystal plate. It is also found that the flexoelectric coefficients and length to thickness ratio have influence on the thickness-shear modes. The results tell that flexoelectricity cannot be neglected for design of small size piezoelectric resonators.

Response of Three Oscillators Coupled by a Weak Nonlinearity

1977 ◽  
Vol 44 (1) ◽  
pp. 141-146 ◽  
Author(s):  
N. Yen ◽  
R. E. Kronauer
Keyword(s):  
Perturbation Expansion ◽  
Phase Variation ◽  
Transient Behavior ◽  
Conservative System ◽  
Crystal Plate ◽  
High Frequency Oscillation ◽  
Piezoelectric Crystal ◽  
Weak Nonlinearity ◽  
Resonance Modes ◽  
Piezoelectric Crystal Plate

As a simplified model of the exchange processes occurring among resonance modes in physical systems, such as a piezoelectric crystal plate or an acoustic interferometer, a study is made of the response of three oscillators that are coupled by a weak nonlinearity and whose frequencies satisfy the condition ω1 + ω2 ≅ ω3. The transient behavior is obtained by a perturbation expansion. There exist three integral constraints on the amplitude and phase variation of the oscillations for a conservative system, and the solution of the response can be reduced to quadrature. The phase diagram describing the motion indicates that the high frequency oscillation is unstable; the energy associated with it, under certain conditions, can be diverted to lower frequency oscillations. For nonconservative systems, the effects of dissipation and detuning are examined for their role in limiting the energy exchange among the oscillations and in determining the steady-state response to forcing. Predictions from this analysis are compared with results of a reported experiment in which a piezoelectric crystal plate is forced to oscillate at amplitudes sufficient to generate coupled subharmonics.

scholarly journals Higher-Order Overtone Thickness-Shear Vibrations of Multilayered Thin-Film Acoustic Wave Resonators and Angular Rate Sensing

2019 ◽  
Vol 24 (No 1) ◽  
Author(s):  
Hui Chen ◽  
Ji Wang ◽  
Jianke Du ◽  
Jiashi Yang
Keyword(s):  
Coriolis Force ◽  
Angular Rate ◽  
Higher Order ◽  
Shear Mode ◽  
Thickness Shear Mode ◽  
Shear Vibration ◽  
Shear Modes ◽  
Acoustic Wave Resonators ◽  
Multilayered Thin Films ◽  
Thickness Shear

We propose a new structure for piezoelectric gyroscopes. It is made from multilayered thin films of AlN or ZnO with alternating c-axes along the film thickness. It is shown theoretically that when such a film is electrically driven into higher-order overtone thickness-shear vibration in one of the two in-plane directions of the film and is rotating about the film normal, the Coriolis force due to the rotation causes a higher-order overtone thicknessshear vibration in a perpendicular direction with an electrical output that can be used to measure the angular rate of the rotation. Different from existing thickness-shear mode piezoelectric gyroscopes which are based on the fundamental or the second overtone thickness-shear mode, the proposed gyroscope operates with higher-order overtone thickness-shear modes with higher frequencies and hence potentially higher sensitivity. Because of the overtone modes, the Coriolis force acting on the gyroscope forms a self-equilibrated system and does not transmit a net force or torque to the mounting structure. This implies higher device quality factor and better performance.

The nonlinear analysis of elastic wave of piezoelectric crystal plate with perturbation method

Wave Motion ◽  
2014 ◽  
Vol 51 (5) ◽  
pp. 798-803 ◽  
Author(s):  
Yanping Fan ◽  
Xiaojun Ji ◽  
Xianping Liu ◽  
Ping Cai
Keyword(s):  
Elastic Wave ◽  
Perturbation Method ◽  
Nonlinear Analysis ◽  
Crystal Plate ◽  
Piezoelectric Crystal ◽  
Piezoelectric Crystal Plate

Thickness-shear vibration of a Z-strip AT-cut quartz crystal plate with nonuniform electrode pairs

2017 ◽  
Vol 506 (1) ◽  
pp. 48-62 ◽  
Author(s):  
Zinan Zhao ◽  
Zhenghua Qian ◽  
Bin Wang
Keyword(s):  
Quartz Crystal ◽  
Crystal Plate ◽  
Shear Vibration ◽  
Thickness Shear

Thickness-shear vibration of circular crystal plate in cylindrical shell as pressure sensor

2006 ◽  
Vol 27 (6) ◽  
pp. 749-755 ◽  
Author(s):  
Yuan-tai Hu ◽  
Zhi-jian Cui ◽  
Shu-nong Jiang ◽  
Jia-shi Yang
Keyword(s):  
Cylindrical Shell ◽  
Pressure Sensor ◽  
Crystal Plate ◽  
Shear Vibration ◽  
Thickness Shear

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

Free Vibration of Orthotropic Skew Plates

1999 ◽  
Vol 122 (3) ◽  
pp. 313-317 ◽  
Author(s):  
A. M. Farag ◽  
A. S. Ashour
Keyword(s):  
Boundary Conditions ◽  
Transition Matrix ◽  
Longitudinal Direction ◽  
Displacement Function ◽  
Characteristic Matrix ◽  
Skew Angle ◽  
Kantorovich Method ◽  
Vibration Effect ◽  
Finite Strip Method ◽  
Semianalytical Method

The main purpose of this paper is to develop a fast converging semianalytical method for assessing the vibration effect on thin orthotropic skew (or parallelogram/oblique) plates. Since the geometry of the skew plate is not helpful in the mathematical treatments, the analysis is often performed by more complicated and laborious methods. A successive conjunction of the Kantorovich method and the transition matrix is exploited herein to develop a new modification of the finite strip method to reduce the complexity of the problem. The displacement function is expressed as the product of a basic trigonometric series function in the longitudinal direction and an unknown function that has to be determined in the other direction. Using the new transition matrix, after necessary simplification and the satisfaction of the boundary conditions, yields a set of simultaneous equations that leads to the characteristic matrix of vibration. The influence of the skew angle, the aspect ratio, the properties of orthotropy, and the prescribed boundary conditions are investigated. Convergence of the solution is investigated and the accuracy of the results is compared with that available from other numerical methods. The numerical results show that the convergence is rapidly deduced and the comparisons agree very well with known results. [S0739-3717(00)00202-6]

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