考虑表面效应纳米压电双晶中波的频散分析

Dispersion Analysis of Waves in Nanoscale Piezoelectric Double Crystals Considering Surface Effects

基于非局部应变梯度理论探究了考虑表面弹性和表面残余应力的纳米压电双晶中波的频散特性,压电双晶的上下压电层暴露在电场之中并且整体沉积在粘弹性基底之上。利用哈密顿原理和正弦剪切理论推导了控制方程,利用含非局部参数和长度尺度参数的尺度依赖本构关系得到了运动方程,带入谐波解求解相应的特征方程。数值揭示了表面弹性和表面残余应力、尺度参数和波数以及粘弹性基底对压电双晶的作用规律。研究表明,表面效应的存在对压电纳米双晶频率特性的研究至关重要,尺度参数和波数对频散特性具有耦合作用,弹性系数、阻尼系数和压电层厚度对频率的作用表现出区域性。

Due to progress in micro and nano technologies,nanoscale piezoelectric bimorphs have gained extensive popularity in various fields such as nanosensors,nanoactuators,nanoscale energy recovery devices,and nanoresonators.With a decrease in size,the influence of scale effect becomes more prominent.The aim of this research was to investigate the scale effect on the frequency characteristics of nanoscale piezoelectric bimorphs according to scale-dependent theory.This work may broaden our understanding of the wave characteristics of piezoelectric nanostructures.On the basis of nonlocal strain gradient theory,the wave dispersion properties in nanoscale piezoelectric bimorphs were studied,taking into account surface elasticity and residual stress.The upper and lower piezoelectric layers of the bimorphs were subjected to an electric field and deposited on a viscoelastic substrate.The control equation was derived based on Hamilton's principle and sinusoidal shear theory.The equation of motion was derived according to the scale-dependent constitutive equation with nonlocal and length scale parameters,and the corresponding characteristic equation was solved by incorporating harmonic solutions.The obtained numerical results revealed the effects of surface elasticity,residual stress,scale parameters,wave number,and viscoelastic substrate on piezoelectric bimorphs.The research showed that the dispersion properties of piezoelectric bimorphs were influenced by a combination of surface residual stress and surface elastic coefficient.The existence of surface effects was found to be essential for the investigation of the frequency properties of piezoelectric bimorphs.Scale parameters and wave number also had a combined effect on dispersion characteristics,and the influences of elastic coefficient,damping coefficient,and piezoelectric layer thickness on frequency exhibited regional characteristics.Therefore,it is possible to use appropriate substrate materials to regulate the center frequency of piezoelectric bimorphs.This work contributes to the theoretical research on the dispersion mechanism of piezoelectric nanoresonators and provides useful reference for the design and manufacturing of piezoelectric nanofilters.