Abstract：By the progress of micro and nano technologies, nanoscale piezoelectric bimorphs have become extensively popular in various fields including nanosensors, nanoactuators, nanoscale energy recovery devices, and nanoresonators. With the decrease of size, the influence of scale effects becomes more prominent. The aim of this research was to investigate scale effect on the frequency characteristics of nano piezoelectric bimorphs according to scale dependence theory. This work could broaden our understanding of the wave characteristics of piezoelectric nanostructures. According to nonlocal strain gradient theory, wave dispersion properties in nanoscale piezoelectric bimorphs was studied taking into account surface elasticity and residual stress. The upper and lower piezoelectric layers of piezoelectric bimorphs were subjected to an electric field and were deposited on a viscoelastic substrate. Control equation was derived based on Hamilton's principle and sinusoidal shear theory. Motion equation was derived according to 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 numbers, and viscoelastic substrates on piezoelectric bimorphs. Research has revealed that surface residual stress and surface elastic coefficient had a combined effect on the dispersion properties of piezoelectric bimorphs. Research has also suggested that the existence of surface effects was essential for the investigation of the frequency properties of piezoelectric bimorphs. Scale parameters and wave numbers 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 as a means to regulate the center frequency of piezoelectric bimorphs. This work will expand theoretical research on the dispersion mechanism of piezoelectric nano resonators and provide useful reference for the design and manufacturing of piezoelectric nanofilters.
2024, Vol. 45 
