Arab J Sci Eng (2016) 41:4397–4410 DOI 10.1007/s13369-016-2135-1 RESEARCH ARTICLE - MECHANICAL ENGINEERING A Nonlinear Model for Incorporating the Coupled Effects of Surface Energy and Microstructure on the Electromechanical Stability of NEMS Maryam Keivani 1 · Ali Koochi 2 · Hamid M. Sedighi 3 · Ahmadreza Abadian 4 · Mohamadreza Abadyan 2 Received: 19 August 2015 / Accepted: 24 March 2016 / Published online: 16 April 2016 © King Fahd University of Petroleum & Minerals 2016 Abstract Surface energy and size phenomenon can play significant roles in physical performance of nano-electro- mechanical systems. Herein, the static and dynamic pull-in behavior of nano-tweezers and nano-switch fabricated from conductive cylindrical nano-wires is studied. The Gurtin– Murdoch surface elasticity in combination with the couple stress theory is employed to incorporate the coupled effects of surface energy and microstructure dependency (size phe- nomenon). Using Green–Lagrange strain, the higher-order surface stress components are incorporated in the nonlinear governing equation. The effect of gas damping is considered in the model as well as structural damping. The govern- ing equation is solved using the reduced order method. The effects of various parameters on the static and dynamic pull- in parameters, phase plans and stability threshold of the nano-structures are demonstrated. Keywords Couple stress theory · Surface effect · Cylindrical nano-wire · Dynamic pull-in instability B Mohamadreza Abadyan abadyan@yahoo.com 1 Shahrekord University of Medical Sciences, Shahrekord, Iran 2 Shahrekord Branch, Islamic Azad University, Sharekord, Iran 3 Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran 4 Mechanical Engineering Group, Kashan Branch, Islamic Azad University, Kashan, Iran List of symbols E Young’s modulus of the nano-wire ν Poisson ratio of the nano-wire μ = E /2(1 + ν) Shear modulus of the nano-wire l Material length scale parameter δ Size effect non-dimensional parameter E 0 Surface elastic modulus e 0 Surface elastic modulus non-dimensional parameter τ 0 Surface residual stress t 0 Surface residual stress non-dimensional parameter c s Structural damping coefficient c f Gas damping coefficient μ f Flow viscosity γ = 0.5572 Euler’s constant K n Knudsen number St Stokes number R Radius of the nano-wire L Length of the nano-wire D Initial gap f elec Electrical force V Applied voltage ε = 8.854 × 10 −12 Permittivity of vacuum C 2 N −1 m −2 β Applied voltage non-dimensional parameter f vdW van der Waals force ¯ A = (0.4−4) × 10 −19 Hamaker constant η Van der Waals force non-dimensional parameter W Nano-wire deflection t Time 123