Gap Dependent Bifurcation Behavior of a Nano-Beam Subjected to a Nonlinear Electrostatic Pressure

Abstract

This paper presents a study on the gap dependent bifurcation behavior of an electro statically-actuated nano-beam. The sizedependent behavior of the beam was taken into account by applying the couple stress theory. Two small and large gap distance regimes have been considered in which the intermolecular vdW and Casimir forces are dominant, respectively. It has been shown that changing the gap size can affect the fundamental frequency of the beam. The bifurcation diagrams for small gap distance revealed that by changing the gap size, the number and type of the fixed points can change. However, for large gap regime, where the Casimir force is the dominant intermolecular force, changing the gap size does not affect the quality of the bifurcation behavior.

Comprehensive nonlinear electromechanical analysis of nanobeams under DC/AC voltages based on consistent couple-stress theory

“…applications not their simultaneous applications. This is the point that some researchers did not consider it [23][24][25]. The transition regime is not considered in this study.…”

“…(16) as: (23) where A is the cross-sectional area and L is the length of the nanobeam. where I is the moment of inertia and is the mass of the nanobeam.…”

“…(28a) and (29a) results in: (34) where (35) for doubly clamped nanobeams and for cantilever nanobeams and As mentioned before, the interatomic force can be either vdW or Casimir. Simultaneous application of both of them is against the physical concepts behind the problem that was not considered in some research [23][24][25] leading to unreliable results. The nondimensional form of the vdW and Casimir forces are formulated as:…”

The size-dependent electromechanical instability of double-sided and paddle-type actuators in centrifugal and Casimir force fields

“…In order to overcome this shortcoming, the non-classical theories, such as nonlocal elasticity [35], Couple Stress Theory (CST) [36][37][38], strain gradient theory [39], modi ed couple stress theory [40], etc., have been developed to consider the size e ect on theoretical continuum models. Despite other size-dependent theories, limited research has been conducted on modeling the ultra-small structures using the CST [41][42][43].…”