Investigation of Size-Dependent Vibration Behavior of Piezoelectric Composite Nanobeams Embedded in an Elastic Foundation Considering Flexoelectricity Effects

This article investigates the size dependent on piezoelectrically layered perforated nanobeams embedded in an elastic foundation considering the material Poisson’s ratio and the flexoelectricity effects. The composite beam is composed of a regularly squared cut-out elastic core with two piezoelectric face sheet layers. An analytical geometrical model is adopted to obtain the equivalent geometrical variables of the perforated core. To capture the Poisson’s ratio effect, the three-dimensional continuum mechanics adopted to express the kinematics are kinetics relations in the framework of the Euler–Bernoulli beam theory (EBBT). The nonlocal strain gradient theory is utilized to incorporate the size-dependent electromechanical effects. The Hamilton principle is applied to derive the nonclassical electromechanical dynamic equation of motion with flexoelectricity impact. A closed form solution for resonant frequencies is obtained. Numerical results explored the impacts of geometrical and material characteristics on the nonclassical electromechanical behavior of nanobeams. Obtained results revealed the significant effects of the mechanical, electrical, and elastic foundation parameters on the dynamic behavior of piezoelectric composite nanobeams. The developed procedure and the obtained results are helpful for many industrial purposes and engineering applications, such as micro/nano-electromechanical systems (MEMS) and NEMS.