Electromechanical buckling of functionally graded electrostatic nanobridges using strain gradient theory

• We model nonlinear electromechanical buckling of nanobridge.
• We examine effect of van der Waals force on electromechanical buckling.
• We study size effect by modified strain gradient theory.
• We model clamped-guided functionally graded narrow nano-beam.
• New model fills the gap between experimental results and classical theories.

Electromechanical buckling (EMB) of beam-type nanoelectromechanical systems (NEMSs) is investigated based on modified strain gradient theory. The system is modeled as a clamped-guided nanobeam which is under compressive or tensile axial loads as well as the effect of nonlinear electrostatic and van der Waals symmetric transverse forces. In addition, the beam is considered to be made of axially and transverse functionally graded materials. Here, FGM is Poly-SiGe, of which the general properties change gradually from silicon to germanium based on a simple power-law method. Considering the Euler–Bernoulli beam theory and using the principle of minimum potential energy, the governing equations and corresponding boundary conditions are established. After validation of results, the effects of power law index, variation of size effect parameters, length-thickness ratio and the distance between the two fixed and movable electrodes on the buckling response of the system are discussed.