Modelling of the flexoelectric effect on rotating nanobeams with geometrical imperfection

Flexoelectricity is the phenomenon of electric polarization caused by the strain gradient, which usually has a huge effect on nanoscale structures. This paper firstly combines the finite element method (FEM) with a novel third-order shear deformation beam theory (TSDT) to simulate the static bending and free vibration responses of rotating (around one fixed axis) piezoelectric nanobeams with geometrical imperfection considering flexoelectric effects, where the structures are placed on the Pasternak’s elastic foundations. Based on two-node beam elements, the Lagrange and Hermit interpolation functions, the proposed approach shows high accuracy through the comparative results of this work and published references. A wide range of parameter studies is conducted such as the rotational speed, shape imperfection, flexoelectric effect, and so on to evaluate the influences on the static bending and free vibration behaviors of the structures. The novel investigation points out that when the beams are rotating around one fixed axis, the mechanical responses, in this case, are not similar to those of normal cases when the rotational speed is zero. This is a new study that can be referenced when designing nanoscale beam structures in practice. © 2021, The Brazilian Society of Mechanical Sciences and Engineering.