Jia Lou

Buckling and Post-Buckling of Symmetric Functionally Graded Microplate Lying on Nonlinear Elastic Foundation Based on Modified Couple Stress Theory

This paper is concerned with the buckling and post-buckling behaviors of a simply supported symmetric functionally graded (FG) microplate lying on a nonlinear elastic foundation. The modified couple stress theory is used to capture the size effects of the FG microplate, and the Mindlin plate theory with von Karman’s geometric nonlinearity taken into account is adopted to describe its deflection behavior. Based on these assumptions and the principle of minimum potential energy, the equilibrium equations of the FG microplate and associated boundary conditions are derived. By applying the Galerkin method to the equilibrium equations, closed-form solutions for the critical buckling load and the load–displacement relation in the post-buckling stage are obtained. Furthermore, the effects of the power law index, the material length scale parameter to thickness ratio, the stiffness of the elastic foundation, and in-plane boundary conditions on the buckling and post-buckling behaviors of the FG microplate are disc...

On the coupling effects of piezoelectricity and flexoelectricity in piezoelectric nanostructures

Flexoelectricity is a novel kind of electromechanical coupling phenomenon that is prevalent in all solid dielectrics and usually of vital importance in nanostructures and soft materials. Although the fundamental theory of flexoelectric solids and related beam or plate theories were extensively studied in recent years, the coupling effect of flexoelectricity and piezoelectricity in piezoelectric nanostructures has not been completely clarified yet. In the present work, a geometrically nonlinear piezoelectric plate model is established with a focus on the coupling effect. The constitutive equations for piezoelectric plates are derived under both the electrically short-circuit and open-circuit conditions. It is found that due to the coupling between flexoelectricity and piezoelectricity, stretching-bending coupling stiffness arises in the homogeneous plate and its specific value relies on the applied electrical boundary conditions. The effects of the flexoelectric-piezoelectric coupling on the effective mech...

Thickness shear vibration of ZnO thin film with dissipation

Thickness shear vibration of ZnO thin film with consideration of viscosity effects is investigated. The Kelvin mode is used to describe the viscosity of the materials. Based on the three-dimensional piezoelectric theory, the governing equations of ZnO thin film are obtained. The calculation results are presented and discussed in detail.

A Comsol analysis of vibrations of quartz crystal plates with Mindlin plate equations

In the design and optimization of quartz crystal resonators, the finite element method has been adopted for the analysis of quartz crystal plates with complications for the vibration frequency and mode shapes. Further extension of such analysis can be made by using complex solutions to extract the electrical parameters of quartz crystal resonators because it is a typical electronic component in circuit applications. With Comsol which is widely used in industry and academic research, the Mindlin plate equations for the analysis of quartz crystal plates at thickness-shear mode are implemented for demonstration and validation purposes. To demonstrate the usefulness of Comsol in the vibration analysis of quartz crystal plates with coupled equations, we choose to utilize the first-order Mindlin plate equations and establish the analytical model with the input of differential equations in standard form as specified by Comsol. Then we found the equations can be processed and solved with the built-in solver of Comsol and results are reasonable and accurate. With the procedure and results presented in this study, it is clear that high frequency vibrations of quartz crystal resonators can be analyzed by the Mindlin plate equations and Comsol for accurate solutions needed in the optimization and design. The results are compared with analytical solutions and other FEM tools for accuracy. It is clear that the Mindlin plate can be conveniently used for the analysis, and results can be obtained quickly by taking advantage of Comsol.

Effects of a viscous and conductive liquid on thickness shear vibration of ZnO films with tilted c-axis orientation

The thickness-shear vibration of c-axis tilted 430 ZnO thin film, one side of it is contacted with a layer of viscous conductive liquids is analyzed. The frequency equation has been derived from the three-dimensional linear piezoelectricity theory. The effects of conductivity on the shift in the resonant frequency has been analyzed and discussed in detail. By setting the density, the viscous coefficient and the thickness of the liquid as specified values, the relation of the shift in the resonant frequency and the conductivity is obtained. The present results demonstrate that the shift in the resonant frequency decreases with the conductivity in a special range. Analysis method and calculation results can provide important reference to the resonators design.

Vibration of magnetoelectric laminate composite PMN-PT under bias magnetic fields

It has been discovered that laminate composites of longitudinally magnetized magnetostrictive and transversely poled piezoelectric layers have a giant magneto-electric effect under a low bias magnetic field. The maximum induced magnetoelectric coupling coefficient at resonance is 3.66 V/(cm×Oe), which is over 11 times higher than magnetoelectric coupling coefficient at sub-resonance frequency. The results reveal that laminated of PMN-PT and Terfenol-D have a high sensitivity of less than 10-6T to a DC magnetic field.

Experimental study on extensional vibration of a piezoelectric/piezomagnetic laminated plate

In this paper, the electromagnetic energy harvesting scheme by using a Terfenol-D/PZT/Terfenol-D composite magnetoelectric (ME) transducer and a circuit is presented. In the experiments, the electrodes on the piezoelectric layer are connected by a circuit whose impedance is denoted by Z, which is the load impedance. we have analyzed and observed the load dependence of the ME coefficient and the basic behaviors of the power density. A giant sharp ME coefficient αE a of 24.5 mv/Oe appears at 3.72×105 rad/s under the load impedance Z of 2000Ω.

Analyzing thickness shear vibration of ZnO thin film with a viscoelastic layer

According to the linear piezoelectric theory, the frequency equation of thickness shear vibration is obtained for investigating the ZnO thin film with a layer of viscoelastic media. Fortunately, some useful results are harvested. From these results, we find that the relative resonant frequency significantly increases when the viscous coefficient is in the range of 0-2Ns/m2. The relation between the relative resonant frequency and the density and thickness of the viscoelastic media also has been discussed. These need to be considered in the design of resonators.