Dynamic response of a tunable MEMS accelerometer based on repulsive force

Daeichin, Meysam; Ozdogan, Mehmet; Towfighian, Shahrzad; Miles, Ronald N.

doi:10.1016/j.sna.2019.02.007

Cited by 38 publications

(27 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As mentioned above, θ is a parameter proportional to the applied voltage V and λ 2 takes into account the electro-mechanical properties of the material constituting the membrane. Figure 3 depicts the zone of existence, in the plane d * − θλ 2 , of at least one solution for the problem (5). In particular, the line of equation θλ 2 = R 2 d * 2 2V 2 0 k , shown in Figure 3 as a black line, separates the area of existence of at least one solution to Model (5) (light green area) from the area where at least a solution to the model (5) is not guaranteed (light red area).…”

Section: A Results Of the Existence Of At Least One Solution To The Prmentioning

confidence: 99%

“…where d * is the critical security distance, which ensures that the deflection of the membrane does not produce contact between the membrane itself and the fixed upper plate. Then, we prove a theorem of the existence of the solution to the model (5). However, as we will prove below, the uniqueness of the solution to the problem (5) is not guaranteed.…”

Section: From the Cassani Model To The Proposed Modelmentioning

confidence: 97%

“…B = 0, and m = 0, we obtain the model (5). We focus our attention on achieving conditions that ensure both the existence and uniqueness of the solution for Model (5). Section 8 describes a very interesting existence result for Problem (5).…”

Section: General Formulation Of the Problemmentioning

confidence: 99%

“…We focus our attention on achieving conditions that ensure both the existence and uniqueness of the solution for Model (5). Section 8 describes a very interesting existence result for Problem (5). For this purpose, let us introduce some preliminary Lemmas.…”

Section: General Formulation Of the Problemmentioning

confidence: 99%

“…At present, 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]. However, even if these models appear to adhere to reality, they are often structured in an implicit form that does not provide explicit solutions (except in particular cases), for which numerical solutions must be necessarily sought [6], or analytical conditions, which ensure the existence, uniqueness, and regularity (up to the desired order) of the solution must be derived [7,8].…”

Section: Introduction To the Problemmentioning

confidence: 99%

See 4 more Smart Citations

A 2D Non-Linear Second-Order Differential Model for Electrostatic Circular Membrane MEMS Devices: A Result of Existence and Uniqueness

2019

View full text Add to dashboard Cite

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.Mathematics 2019, 7, 1193 2 of 18 the design, realization, and distribution of the MEMS devices used in the various applications [17]. Biomedical diagnostics increasingly require efficient, low-cost, and reliable micro-components, which can be of help to health-care personnel both in on-line and off-line modes [18,19]. Many mathematical models have been theoretically conceived of in special functional spaces, in order to provide the conditions of the existence and uniqueness of the solutions, which are otherwise difficult to detect [20,21]. Cassani et al. [22] built a sophisticated mathematical model of a MEMS device constituted of two metallic plates (one fixed and one deformable), which was clumped at the edges and subjected to a drop voltage, which deformed the deformable plate towards the other one. Obviously, determining a solution for this model is very difficult, and some simplifications were necessarily required. In particular, neglecting the inertial and non-local effects, Cassani et al. obtained a simplified model in [23], which was studied using Steklov boundary conditions to achieve Dirichlet and Navier boundary conditions. Starting from this simplified model, the authors studied a new elliptical semi-linear dimensionless model for a 1D membrane MEMS, based on the proportionality between the electric field magnitude |E| and the curvature of the membrane, achieving results of the existence and uniqueness for the solution. In particular, in [7], the algebraic condition ensuring the uniqueness of the solution did not depend on the electro-mechanical properties of the material constituting the membrane. Consequently, in [10], the authors achieved a new algebraic condition depending on these properties, ensuring the uniqueness of the solution.In this work, for applicative reasons, the authors focus their attention on a 2D circular membrane MEMS device, which is useful in several industrial and/or biomedical applications [1,19]. In addition, the authors consider |E| to be proportional to the mean curvature of the membrane of the device, in order to achieve a non-linear second-order differential model with singularity in the steady-state case. Finally, an algebraic condition, depending on both the mechanical and electrical properties of the membrane, guarantees the existence of at least one solution to the proposed model. However, the uniqueness of the solution is not ensured.The paper is structured as follows. After presenting how the proposed model was achieved in ...

show abstract

Section: A Results Of the Existence Of At Least One Solution To The Prmentioning

confidence: 99%

Section: From the Cassani Model To The Proposed Modelmentioning

confidence: 97%