Bending and Vibration of Layered Piezoelectric Semiconductor Nanoplates with Flexoelectric Effect

By considering the flexoelectric effect, bending deformation and vibration of three-dimensional (3D) piezoelectric semiconductor (PS) layered nanoplates are investigated. The final governing equation is derived based on the pseudo-Stroh formulation and the propagator matrix method. Analytical solutions of the extended displacement (i.e. mechanical displacement, electric potential and electron concentration perturbation) and extended stress (i.e. stress, higher-order stress, electric displacement and electron current density) for bending deformation of the nanoplates, the natural frequencies for free vibration and the extended displacement for harmonic response are obtained. The effects of initial carrier concentration, flexoelectric coefficient and forced frequency on the electron concentration perturbation distribution are analyzed by some numerical examples. The results demonstrate that the flexoelectric effect exerts a significant influence at the micro- and nanoscale, and the initial carrier concentration plays an important role in PS materials. The present study not only deepens the understanding of the physical mechanism of the size-dependent electromechanical coupling behavior of PS nanomaterials, but also provides an important theoretical basis for the optimal design of novel PS nanodevices.