Abstract
In this paper, the thickness-stretch vibration of an infinite piezoelectric plate is studied, with consideration of the flexoelectric effect. The theoretical model developed herein is based on a one-dimensional formulation, with the assumption that the displacement and electric potential vary through the thickness. The Gibbs energy density function and variational principle are adopted to derive the constitutive equation with flexoelectricity, governing equations, and boundary conditions. For the effect of flexoelectricity, the coupling between the strain gradient through the thickness and the electric field is considered. Two electric boundary conditions are used in this work and the corresponding frequency shift due to the flexoelectricity is calculated. The present results demonstrate that the flexoelectric effect decreases the fundamental frequency of the thickness-stretch vibration and has a significant effect on the vibrational frequencies of the thickness-stretch mode of a thin piezoelectric plate. The results also show that the flexoelectric effect has a significant size dependency, and should be taken into consideration for the design and development of next-generation high-precision and high-frequency piezoelectric transducers and resonators in the future.
Highlights
Piezoelectric materials are widely used in various functional devices due to their electromechanical coupling capabilities
The frequency shift of the thickness-stretch vibration with flexoelectricity was calculated in this work
It was observed that the frequency shift for the open circuit boundary condition was slightly more significant than for the short circuit boundary condition
Summary
Piezoelectric materials are widely used in various functional devices due to their electromechanical coupling capabilities. Liu [17] investigated the thickness-stretch vibration of a crystal plate carrying a micro-rod array fixed on the top surface, with rods modeled by the one-dimensional structural theory for extensional vibration In addition to these works, there are many studies regarding nonlinear thickness-stretch vibrations [18], the thickness-stretch vibration of a magnetoelectric plate with electrodes [19], a plate under biasing field [20], the electroelastic effect [21], spurious mode analysis [22], and so on. The results reveal that the direct effect of flexoelectricity affects the thicknessstretch vibration by decreasing the fundamental frequency, and has a significant size-dependent phenomenon This model can aid in the understanding of the micro/nano mechanical behaviors of thickness-stretch vibrations, and can be used as guidance for the design of next-generation high-precision piezoelectric resonators. The governing equations are reduced to the following equations by ignoring the body force and volume charge density: ρui (7a)
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