Analysis of nonlocal nonlinear behavior of graphene sheet circular nanoplate actuators subject to uniform hydrostatic pressure

Abstract

This study investigates the scale effect on nonlinear behavior of a clamped-clamped circular graphene sheet nanoplate actuator, which is electrostatically actuated by various vdW forces, tensile loads, and hydrostatic pressures. The circular nanoplate model is developed by using Eringen's nonlocal elasticity theory. The nonlinear behavior of the circular nanoplate actuator subject to nonlocal effect, electrostatic vdW forces, tensile loads, and hydrostatic pressures, is then carefully derived, analyzed and presented. A proposed hybrid differential transformation/finite difference method is first introduced to characterize the influence of scale effect on nonlinear behavior of the circular nanoplate subject to DC loads. The modeling result shows that the pull-in voltage deviates less than 2.71% as compared to that appeared in the literature obtained by using a different approach. The validity of the proposed hybrid method is thus verified and can thus be employed to further characterize the effect of small scale for different electrostatic actuation of tensile loads and hydrostatic pressures in greater details. The structural modeling results indicate that the pull-in voltage increases obviously with increasing scale effects. Overall, the results also reveal that the hybrid method presented in this paper is effective and can be used to accurately quantify the pull-in voltage in circular nanoplate systems under different associated actuation.

Investigation of pull-in behavior of circular nanoplate actuator based on the modified couple stress theory

“…This is because these theories do not take into account the size effect when modelling in nanostructures, and it has been proven that the pull-in behavior of nanostructures are size dependent (Sadeghian et al , 2009). To overcome this problem, some unconventional continuum theories have been developed that can combine size effects (Lin et al , 2018a, 2018b; Lim et al , 2015; Thai et al , 2020; Eringen, 1983; Eringen, 2002). Nonlocal elasticity theory was first considered by Eringen (1983, 2002).…”

“…The theory assumes that the stress at a point is dependent on the strain at all points. Lin et al (2018a, 2018b) investigated nonlocal effects on nonlinear behavior of a clamped–clamped circular graphene sheet nanoplate actuator. Lim et al (2015) developed the nonlocal strain gradient theory to bring both the length scales and nonlocal scales into a single theory.…”

“…Wang et al (2015) studied the combined surface elasticity theory and modified couple stress theory in the rectangular nanoplate context, where it was shown that the material and surface parameters increase the pull-in values. Lin et al (2018a, 2018b) adopted DTM and FDM to investigate surface effects on the electrostatically actuated circular nanoplate. Fleck and Hutchinson (2001) reformulated the strain gradient theory using the Mindlin model with a strain tensor.…”

“…In MEMS and NEMS, the characteristics subjected to the combined hydrostatically and electrostatically actuated plates have been the main focus of investigation by different researchers in numerical simulations (Mohammadi et al , 2013; Lin et al , 2018a, 2018b; Ansari et al , 2014; Nabian et al , 2008). Ansari et al (2014) analyzed the pull-in behavior of a geometrically nonlinear plate considering the surface stress effects subjected to hydrostatic and electrostatic actuations.…”

Super and subcritical nonlinear nonlocal analysis of NSGT nanotubes conveying nanofluid

“…The vibration response of macroscale structures has widely been explored via the classical elasticity (Ghayesh et al 2013a;Ghayesh and Moradian 2011;Malekzadeh 2007;Malekzadeh and Vosoughi 2009). However, since classical continuum-based models lead to size-independent results for small-scale structures, they are modified to include size effects (Babaei and Yang 2019;Ebrahimi and Barati 2019;Farajpour et al 2018b;Farajpour et al 2018c; Ghayesh and Farajpour 2018b;Lin et al 2018;Sahmani and Aghdam 2018), and accurately estimate the mechanical behaviour at small-scales (Farokhi et al 2018a;Farokhi et al 2018b;Ghayesh 2018;Ghayesh 2019;Kamali et al 2018;Pradiptya and Ouakad 2018;Yayli 2018). Various modified continuum-based models involving the nonlocal Reddy 2010), couple stress (Ghayesh et al 2016;Nejad et al 2017) and a theory incorporating the gradient of strain (Akgöz and Civalek 2011;Ghayesh et al 2013b) have been developed and utilised for small-scale structures.…”