Nonlinear beam formulation incorporating surface energy and size effect： application in nano-bridges

A nonlinear beam formulation is presented based on the Gurtin-Murdoch surface elasticity and the modified couple stress theory. The developed model theoretically takes into account coupled effects of the energy of surface layer and microstructures size- dependency. The mid-plane stretching of a beam is incorporated using von-Karman nonlinear strains. Hamilton＇s principle is used to determine the nonlinear governing equation of motion and the corresponding boundary conditions. As a case study, pull-in instability of an electromechanical nano-bridge structure is studied using the proposed formulation. The nonlinear governing equation is solved by the analytical reduced order method （ROM） as well as the numerical solution. Effects of various parameters including surface layer, size dependency, dispersion forces, and structural damping on the pull- in parameters of the nano-bridges are discussed. Comparison of the results with the literature reveals capability of the present model in demonstrating the impact of nano- scale phenomena on the pull-in threshold of the nano-bridges.