Effect of High Electrostatic Actuation on Thermoelastic Damping in Thin Rectangular Microplate Resonators

Mohammadi, Ardeshir Karami; Ali, Nassim Ale

doi:10.15632/jtam-pl.53.2.317

Cited by 14 publications

(9 citation statements)

References 17 publications

(18 reference statements)

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“…Condition (65) has an important physical meaning. In fact, taking into account (14), (65) can be written as follows:…”

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

confidence: 99%

“…In the field of MEMS technologies, the scientific community has been actively engaged both in the development of theoretical models and in technology transfer. In particular, 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…”

Section: Introduction To the Problemmentioning

confidence: 99%

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

2019

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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 ...

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“…Condition (65) has an important physical meaning. In fact, taking into account (14), (65) can be written as follows:…”

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

confidence: 99%

Section: Introduction To the Problemmentioning

confidence: 99%

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

2019

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“…During the years, the advancement in MEMS technology has gone hand in hand with the development of sophisticated the-oretical models that more and more adhering to the physics underlying the operation of these devices [2], [5]. Recently, some remarkable results have been achieved in several relevant cases, such as thermo-elastic [11], electro-elastic [12], and magnetically actuated systems [13]. However, almost all these models are often structured in an implicit form that does not allow to evaluate explicit analytic solutions [14].…”

Section: Introductionmentioning

confidence: 99%

Electrostatic Micro-Electro-Mechanical-Systems (MEMS) Devices: A Comparison Among Numerical Techniques for Recovering the Membrane Profile

2020

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In this work, numerical techniques based on Shooting procedure, Relaxation scheme and Collocation technique have been used for recovering the profile of the membrane of a 1D electrostatic Micro-Electro-Mechanical-Systems (MEMS) device whose analytic model considers |E| proportional to the membrane curvature. The comparison among these numerical techniques has put in evidence the pros and cons of each numerical procedure. Furthermore, useful convergence conditions which ensure the absence of ghost solutions, and a new condition of existence and uniqueness for the solution of the considered differential MEMS model, are obtained and discussed.

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“…In particular, micro-transducers' and micro-actuators' results are of paramount importance due to their role of micro-devices' interfaces [1,2]. In recent years, circular membrane MEMS technology has been exploited to this aim in a wide variety of technological fields such as thermo-elasticity [2][3][4], microfluidics [2,[5][6][7], electroelasticity [8][9][10][11][12], and biomedical engineering [13][14][15]. The focus on this geometry can mainly be attributed to the availability of theoretical models in both steady-state and dynamical conditions (see [16][17][18] and references within).…”

Section: Introduction and Problem Statementmentioning

confidence: 99%

Recovering of the Membrane Profile of an Electrostatic Circular MEMS by a Three-Stage Lobatto Procedure: A Convergence Analysis in the Absence of Ghost Solutions

2020

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In this paper, a stable numerical approach for recovering the membrane profile of a 2D Micro-Electric-Mechanical-Systems (MEMS) is presented. Starting from a well-known 2D nonlinear second-order differential model for electrostatic circular membrane MEMS, where the amplitude of the electrostatic field is considered proportional to the mean curvature of the membrane, a collocation procedure, based on the three-stage Lobatto formula, is derived. The convergence is studied, thus obtaining the parameters operative ranges determining the areas of applicability of the device under analysis.

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Effect of High Electrostatic Actuation on Thermoelastic Damping in Thin Rectangular Microplate Resonators

Cited by 14 publications

References 17 publications

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

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

Electrostatic Micro-Electro-Mechanical-Systems (MEMS) Devices: A Comparison Among Numerical Techniques for Recovering the Membrane Profile

Recovering of the Membrane Profile of an Electrostatic Circular MEMS by a Three-Stage Lobatto Procedure: A Convergence Analysis in the Absence of Ghost Solutions

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