Date of Award
Master of Engineering Science
Dr. S. F. Asokanthan
Dr. L. Y. Jiang
The aim of this thesis is to develop suitable mathematical models for the purpose of investigating nonlinear instabilities in Micro-Electro-Mechanical (MEM) and Nano- Electro-Mechanical (NEM) electrostatic switches. The proposed models capture the influence of electric field fringing, intermolecular forces, surface stress and surface elasticity.
Based on Euler-Bernoulli assumptions, a surface elasticity model and the generalized Young-Laplace equation, effects of surface stress and surface elasticity are incorporated in the models, while the intermolecular force effects are modelled using quantum mechanics. The derived governing equation representing static pull-in behaviour of switches is inherently nonlinear due to the driving electrostatic force and intermolecular forces which become dominant at nanoscale. Since no exact solutions are available for the resulting nonlinear differential equation, an approach based on homotopy perturbation method (HPM) is proposed to construct approximate analytical solutions, as well as to characterize the instability behaviour. Numerical solutions obtained via finite difference method (FDM) are employed for validating the analytical results.
HPM in conjunction with Adomian decomposition method (ADM) has been employed for approximate analytical predictions. To this end, the solutions for the fourth-order two- point boundary value problem (BVP) representing MEM/NEM electrostatic switches are constructed in terms of a convergent series. The pull-in parameters, including pull-in voltage, detachment length and low-voltage actuation windows, are investigated in detail using the above methods and also via a lumped parameter model. HPM analytical solutions are found to be more accurate and reliable compared to those predicted via the lumped parameter model. HPM solutions also tend to overestimate the static deflection, and underestimate pull-in voltage and detachment length compared to the FDM numerical solutions. However, its relative differences to the FDM numerical solutions are within an acceptable range for design purposes. HPM is concluded to work well for the static pull-in in parameter determination, and is preferred since it is straightforward to implement and could save computation efforts while not losing accuracy.
Predictions via HPM and FDM also revealed that the influence of surface effects on the pull-in instability of MEM/NEM switches is significant and the exclusion of surface effects in the analysis may result in an erroneous estimation of the pull-in parameters. Further, the concept of Casimir actuated switches is proposed for the purpose of ensuring the physical realization of a new class of the switchable devices using pure Casmir force actuation. To this end, a new idea of Casimir-force actuation window has been introduced for the purpose of ensuring designs that yield functional Casimir actuated switches.
The present study is envisaged to be beneficial for the design and applications of MEM/NEM electrostatic as well as Casimir actuated switches. The methodology presented in this thesis may be also used for the analysis of actuation systems, which may involve other types of nonlinear actuation forces.
Ma, Jianming Bryan, "NONLINEAR INSTABILITIES IN MEM/NEM ELECTROSTATIC SWITCHES" (2011). Digitized Theses. 3445.