Analysis of Euler-Bernoulli Beam on Elastic Foundation Considering Nonlocal Effects in Nano Scale

Nano-beam is one of the most important nano-structures with applications in different fields such as NEMS (Nano electromechanical systems) considering their low weight, low energy consumption and high sensitivity for use in medical, computer, bio-sensors and etc. Since the behavior of material in nano scale is different from usual scales, new methods are innovated to study the mechanical behavior of material in nano scale which one of them is nonlocal model. In this paper, nonlocal elasticity theory is used to describe the behavior of beam on the nonlinear elastic foundation. The Euler-Bernoulli beam theory is used to modeling the beam. The governing equations are obtained using principle of virtual displacements and analytical solution is used to solve governing equations. Maximum deflection, critical buckling load and natural frequencies for simply supported boundary condition and different spring constant, and nonlocal parameter is presented. The obtained results show that deflection is increased and critical buckling load and natural frequencies are decreased by considering nonlocal effects. Also elastic foundation decreases deflection and increases critical buckling load and natural frequencies.