Dispersion Analysis of Waves in Nanoscale Piezoelectric Double Crystals Considering Surface Effects
Due to progress in micro and nano technologies,nanoscale piezoelectric bimorphs have gained extensive popularity in various fields such as nanosensors,nanoactuators,nanoscale energy recover-y devices,and nanoresonators.With a decrease in size,the influence of scale effect becomes more promi-nent.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 under-standing 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 ac-count 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 re-vealed 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 bi-morphs were influenced by a combination of surface residual stress and surface elastic coefficient.The ex-istence of surface effects was found to be essential for the investigation of the frequency properties of piezo-electric bimorphs.Scale parameters and wave number also had a combined effect on dispersion characteris-tics,and the influences of elastic coefficient,damping coefficient,and piezoelectric layer thickness on fre-quency 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.
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