Size-dependent electromechanical buckling of functionally graded electrostatic nano-bridges

• Electromechanical buckling of nanobridge is investigated by considering the nonlinear geometric effect.
• Electromechanical buckling of nanobridge is investigated by considering intermolecular forces.
• The present model fills the gap between experimental results and the results of classical theories.
• Nanobridge is modeled as functionally graded (FG) narrow nano-beam.

This study explored the electromechanical buckling (EMB) of beam-type nanoelectromechanical systems (NEMS) by considering the nonlinear geometric effect and intermolecular forces (Casimir force and van der Walls force) based on modified couple stress theory. To model the system, a slender nanobeam made of functionally graded material (FGM) with clamped-guided boundary conditions, which is under compressive or tensile axial loads as well as symmetric and nonlinear electrostatic and intermolecular transverse loads, is used. Considering the Euler–Bernoulli beam theory and using the principle of minimum potential energy and the variational approach, the governing equation as well as the related boundary conditions is derived. To discretize the equation and its related boundary conditions, and to solve the equations, the generalized differential quadrature method (GDQM) is employed. Finally, after validation of the results, the effects of size, length, power law index, and the distance between the two fixed and movable electrodes on the bucking of the system are discussed and examined.