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Abstract
This article is concerned with the mathematical analysis of models for Micro-Electro-Mechanical Systems (MEMS). These models arise in the form of coupled partial differential equations with a moving boundary. Although MEMS devices are often operated in non-isothermal environments, temperature is often neglected in the mathematical investigations. In light of this finding the focus of our modelling is to incorporate temperature and the related material properties. We derive a full model for this coupling and discuss a simplified version as well. Lastly, we prove local well-posedness in time and also global well-posedness under additional assumptions on the model’s parameters.
Highlights
The technology of Micro-ElectroMechanical Systems (MEMS) is concerned with microscopic devices that function by combining electrostatic with mechanical features
To the best of our knowledge no analytical work has been done that takes into account temperature effects on the dynamics of the above described idealized MEMS device
We show how the different parameters influence the deflection of the membrane and in particular report significant differences between our model and the model M0 which neglects temperature effects
Summary
The technology of MEMS is concerned with microscopic devices that function by combining electrostatic with mechanical features. Assuming a small aspect ratio makes it possible to decouple the electro and mechanical effects and consider a problem with a fixed boundary. In [KHT16] the authors derive a model for the thermoelastic behaviour of a micro-beam resonator They solve the resulting equation analytically and show a good agreement to already available numerical data. To the best of our knowledge no analytical work has been done that takes into account temperature effects on the dynamics of the above described idealized MEMS device. Space variations of the temperature and damping of the membrane is neglected In both chapters the authors neither consider the question of well-posedness nor perform a numerical analysis. The resulting governing equation for the membrane will turn out to be quasilinear We end both sections by proving local and global well-posedness of the derived problem under different assumptions. We show how the different parameters influence the deflection of the membrane and in particular report significant differences between our model and the model M0 which neglects temperature effects
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