Mechanical Response of a Piezoelectrically Sandwiched Nano-beam Based on the Nonlocal Theory

This article deals with the mechanical analysis of a fixed-fixed nano-beam based on nonlocal theory of elasticity. The nano-beam is sandwiched with two piezoelectric layers through its upper and lower surfaces. The electromechanical coupled equations governing the problem are derived based on nonlocal theory of elasticity considering Euler-Bernoulli beam assumptions. Also, nonlocal piezoelectricity is according to Maxwell's electrostatic equations. The piezoelectric layers are subjected to a voltage to tune the stiffness of the nano-beam. The equations are solved through step by step linearization method and Galerkin's weighted residual method. The results are compared with those of the local model. The effect of piezoelectric voltages on the non-locality of the model is investigated as well.