Flexural responses of nanobeams with coupled effects of nonlocality and surface energy

This paper proposes a beam model with inclusion of surface and nonlocal effects. Beam-bulk kinematics is formulated within the framework of Euler-Bernoulli beam theory; Eringen nonlocal elasticity theory is employed to account for long-range atomic interactions of a nanoscale beam; and Gurtin-Murdoch surface elasticity theory is used to represent the size-dependent effect inherent to a nanoscale beam. Surface-layer balance equation between the surface and bulk stresses is treated in a consistent manner. Virtual displacement principle is exploited to consistently derive the governing differential equilibrium equation as well as the natural boundary conditions of the problem. The general form of beam bending solution is presented. Two numerical simulations employing the proposed beam model are conducted to study characteristics and behaviors of the nanobeam with various model parameters. The first simulation investigates the coupled effects of nonlocality and surface energy on transverse displacement and bending moment characteristics of nanowires under various support conditions. The second examines the influences of several model parameters as well as the size-dependent effect on the effective bulk Young's modulus of the nanobeam.