Electromechanical Analysis of Flexoelectric Nanosensors Based on Nonlocal Elasticity Theory

Flexoelectric materials have played an increasingly vital role in nanoscale sensors, actuators, and energy harvesters due to their scaling effects. In this paper, the nonlocal effects on flexoelectric nanosensors are considered in order to investigate the coupling responses of beam structures. This nonlocal elasticity theory involves the nonlocal stress, which captures the effects of nonlocal and long-range interactions, as well as the strain gradient stress. Based on the electric Gibbs free energy, the governing equations and related boundary conditions are deduced via the generalized variational principle for flexoelectric nanobeams subjected to several typical external loads. The closed-form expressions of the deflection and induced electric potential (voltage) values of flexoelectric sensors are obtained. The numerical results show that the nonlocal effects have a considerable influence on the induced electric potential of flexoelectric sensors subjected to general transverse forces. Moreover, the induced electric potential values of flexoelectric sensors calculated by the nonlocal model may be smaller or larger than those calculated by the classical model, depending on the category of applied loads. The present research indicates that nonlocal effects should be considered in order to understand or design basic nano-electromechanical components subjected to various external loads.