On the coupled bending–torsional analysis of flexoelectric microbeams

The present research performed a static and free vibration analysis of a flexoelectric micro-beam with bending–torsion coupling for the first time. Microbeams are used in various microstructures, such as micro-sensors, micro-actuators, and micro-switches. Hence, a study of the static and free vibration behavior of flexoelectric micro-beams with bending–torsion coupling seems necessary. In this study, the governing equations were obtained based on the non-classical size-dependent flexoelectric theory using Hamilton’s principle. Furthermore, the Laplace transform technique was employed to solve the problems in the static case. Additionally, the generalized differential quadrature (GDQ) method was used to solve for the vibration response. Subsequently, the impact of various parameters, such as the size effect, on the static response under direct and inverse flexoelectric effect and the free vibration response were discussed. To validate the results, they were compared to data from previous studies, whereby a good agreement.