Exploration into a Clamped-Guided MEMS shallow Arch Design for Sensing Applications

The objective of this proposal is to conduct theoretical and applied research on a newly revisited design of electrostatically actuated Micro-electro-mechanical systems (MEMS) shallow arches of controlled boundary conditions (also called of controlled axial load). The aim of this new design is to explore the possibility of enabling new technologies of smart sensors and actuators and to advance in the fields designing new MEMS devices. The proposed design can be tuned using a variable axial force applied through a second parallel plate capacitor placed in the longitudinal direction of the shallow micro-arch. In this planned investigation, a particular focus will be on studying the nonlinear phenomena in these bi-stable micro-machined shallow arches, and how this design of variable axial load can deteriorate/improve this further. In view of that, these phenomena will be explored to realize smart sensors, which act as electro-mechanical bistable switches when a detected physical/chemical quantities exceed a certain specified onset. One more distinctive attention will be also given to realize smart sensors with multiple and more importantly controllable stable states. Accordingly, in this research project we will focus on commonly used clamped-clamped shallow arched microbeams with a newly revisited design of controllable boundary conditions. Several examples of micro-arches, of various initial shapes and certainly of real devices in the literature will be studied to span a variety of situations. We propose first to start by deriving the governing equations of motion and their respective associated boundary conditions of the designed initially curved beam using the so-called Hamiltons principle. The associated nonlinear integro-partial-differential equations will be then reduced to a nonlinear ordinary differential system using the so-called Differential Quadrature Method (DQM) that discretizes the space derivatives. The limit-cycle solutions will then be acquired using a Finite Difference Method (FDM) that estimates the displacement and velocity solutions over one steady state period. We propose to validate the accuracy and efficiency of the DQM-FDM discretization techniques. In each case, we will examine the number of terms needed for the DQM to converge within an acceptable accuracy. A second numerical approach we would be to use ANSYS (as finite-element software) and then compare the outcomes with those of the DQM method for the static response. After we complete our investigation on the proposed approaches, we propose to exploit them in exploring comprehensively the structural response of such designed micro-arches to axial electrical actuating loads. We will generate curves for the snap-through and pull-in voltages thresholds versus DC/AC voltage amplitudes for various values of the non-dimensional design constraints of the micro-arch. These curves will present valuable information about the interaction between the structural response and the actuating electric forces and how to utilize this interaction to build new sensors and propose new MEMS technologies. In short, this submitted research will afford important information on the exploitation of nonlinear phenomena in MEMS arches to realize smart sensors of distinguished characteristics that are made possible due to the unique controllable axial load of such newly-revisited design. These applications will be utilized after this project to motivate/inspire the PI students of senior levels, and especially those who want to register for independent research course, to discover the fields of Micro-electro-mechanical systems, Nonlinear Structural Dynamics, and Vibrations, as fields of exciting opportunities for creativity and innovations.