Abstract
In the framework of 2D circular membrane Micro-Electric-Mechanical-Systems (MEMS), a new non-linear second-order differential model with singularity in the steady-state case is presented in this paper. In particular, starting from the fact that the electric field magnitude is locally proportional to the curvature of the membrane, the problem is formalized in terms of the mean curvature. Then, a result of the existence of at least one solution is achieved. Finally, two different approaches prove that the uniqueness of the solutions is not ensured.
Highlights
Introduction to the ProblemIn recent years, a growing demand for embedded engineering applications has convinced researchers to develop low cost micro- to nano-sized components, in which actuators and transducers play important roles
MEMS technology is fully part of the multi-disciplinary field of mathematical physics, allowing for highly varied engineering applications [1,3]. This is mainly due to the fact that it has been supported by sophisticated theoretical models, both static and dynamic [4,5]. Even if these models appear to adhere to reality, they are often structured in an implicit form that does not provide explicit solutions, for which numerical solutions must be necessarily sought [6], or analytical conditions, which ensure the existence, uniqueness, and regularity of the solution must be derived [7,8]
Let us consider a circular membrane MEMS device, which is constituted of two parallel disks with radius R and with mutual distance d
Summary
A growing demand for embedded engineering applications has convinced researchers to develop low cost micro- to nano-sized components, in which actuators and transducers play important roles. Some important models for coupled problems have been developed: ranging from magnetically actuated systems [1,12,13] to thermo-elastic models [14], and from electro-elastic models [15] to micro-fluid models [16], featuring highly complex formulations for the management of different MEMS devices (with plates, membranes, and so on). These theoretical models have had excellent feedback in technology transfer, through.
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