Versaci Mario, di Barba Paolo, Morabito Francesco Carlo
DICEAM Department, "Mediterranea" University, I-89122 Reggio Calabria, Italy.
Dipartimento di Ingegneria Industriale e dell'Informazione, University of Pavia, I-27100 Pavia, Italy.
Membranes (Basel). 2020 Nov 21;10(11):361. doi: 10.3390/membranes10110361.
The evolution of engineering applications is increasingly shifting towards the embedded nature, resulting in low-cost solutions, micro/nano dimensional and actuators being exploited as fundamental components to connect the physical nature of information with the abstract one, which is represented in the logical form in a machine. In this context, the scientific community has gained interest in modeling membrane Micro-Electro-Mechanical-Systems (MEMS), leading to a wide diffusion on an industrial level owing to their ease of modeling and realization. Physically, once the external voltage is applied, an electrostatic field, orthogonal to the tangent line of the membrane, is established inside the device, producing an electrostatic pressure that acts on the membrane, deforming it. Evidently, the greater the amplitude of the electrostatic field is, the greater the curvature of the membrane. Thus, it seems natural to consider the amplitude of the electrostatic field proportional to the curvature of the membrane. Starting with this principle, the authors are actively involved in developing a second-order semi-linear elliptic model in 1D and 2D geometries, obtaining important results regarding the existence, uniqueness and stability of solutions as well as evaluating the particular operating conditions of use of membrane MEMS devices. In this context, the idea of providing a survey matures to discussing the similarities and differences between the analytical and numerical results in detail, thereby supporting the choice of certain membrane MEMS devices according to the industrial application. Finally, some original results about the stability of the membrane in 2D geometry are presented and discussed.
工程应用的发展正日益朝着嵌入式特性转变，从而产生低成本解决方案，微/纳米尺寸和致动器被用作将信息的物理特性与抽象特性相连接的基本组件，而抽象特性在机器中以逻辑形式呈现。在这种背景下，科学界对膜微机电系统（MEMS）建模产生了兴趣，由于其易于建模和实现，在工业层面得到了广泛传播。从物理角度来看，一旦施加外部电压，在器件内部就会建立一个与膜的切线正交的静电场，产生作用在膜上的静压力，使其变形。显然，静电场的幅度越大，膜的曲率就越大。因此，将静电场的幅度与膜的曲率成正比来考虑似乎是很自然的。基于这一原理，作者积极参与在一维和二维几何结构中开发二阶半线性椭圆模型，在解的存在性、唯一性和稳定性方面取得了重要成果，并评估了膜MEMS器件的特定使用操作条件。在这种背景下，详细讨论分析结果和数值结果之间异同的综述想法逐渐成熟，从而根据工业应用支持对某些膜MEMS器件的选择。最后，给出并讨论了关于二维几何结构中膜稳定性的一些原始结果。
