Nonlinear Dynamic Analysis of Nanoscale Beams inLiquid Electrolytes using Nonlocal Elasticity TheoryConsidering Casimir Effect

Electrostatic actuators are commonly used in gas or vacuum. As a result, there has been littleattempt to develop MEMS and NEMS actuators capable of operating in liquids. Whereasthere are several practical applications in which the N/MEMS devices have to operate in aliquid, and therefore, more effort is needed to analyze such systems. In this study, thenonlinear dynamic behaviour of electrochemically actuated nanobeams is investigated basedon a nonlinear modified continuum beam model subjected to nonlinear forces. An elasticbeam suspended horizontally over a substrate in liquid electrolyte is subjected to electric,osmotic, van der Waals, and Casimir forces. The equation of motion is derived based on thenonlocal theory of elasticity for the nonlinear Euller-Bernoulli beam theory. It should benoted that, the nonlinearity of the beam theory is due to contemplating the von Karmanstrains leading to more realistic results for some specific boundary conditions by taking thelongitudinal stretching force into account. To the best of our knowledge, dynamic analysis ofthe system considering the nonlocal theory of elasticity along with taking account of allpreviously stated nonlinear forces in the nonlinear Euller-Bernoulli beam theory is performedfor the first time. The generalized differential quadrature (GDQ) method along with theNewmark integration scheme converts the nonlinear governing equation into a system ofalgebraic equations. Then this system of equations is linearized with the assistance ofiterative Newton-Raphson method. The present research investigates the size effect on the thedynamic behaviour of the nano-beam under DC voltage using nonlocal elasticity theory. Theinteresting outcomes obtained in this study are useful in modelling and design process of electrochemically actuated micron- and submicron-scale beams.

Keywords:

nanoscale beam , nonlocal elasticity , electrochemical and Casimir forces , GDQ method