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Article information
2016 , Volume 21, ¹ 2, p.63-87
Fadeev S.I., Kostsov E.G., Pimanov D.O.
Study of the mathematical model for a microelectromechanical resonator of the Platform type
The results of mathematical modelling of the microelectromechanical high frequency resonator of “Platform” type are presented. The resonator consists of a fixed electrode coated with dielectric film and movable electrode in the form of stiff (nondeformable) platform attached to an elastic beam with rigidly fixed ends. The mathematical model is represented by the formulations of nonlinear initial-boundary value problem describing the oscillations of the moveable electrode. The auto-oscillations originate during the start up under the influence of intensity of the electrostatical field between the movable and fixed electrodes in the micro-gap. At the end of the start up, auto-oscillations are transformed into natural oscillations. The conditions for initialisation of the oscillations are determined numerically. These conditions appear to be close to the case when the mass of the platform is much greater than the mass of the elastic element. Therefore we can obtain formulas in analytical form, describing the main characteristics of microresonator’s behavior with a good precision. Similar studies are carried out for the microresonators of “Platform” type with elastic elements in form of cantilever beam and strained film. The article presents an example for calculation of the microresonator’s parameters. We have shown that the obtained values of parameters satisfy the current MEMS technology. The results can be useful in the technological design of the device.
[full text]
Keywords: electrostatical attraction, cylindrical flexure of elastic beam, method of lines, auto-oscillations and natural oscillations, Greens functions, natural frequency, Fourier method
Author(s):
Fadeev Stanislav Ivanovich
Dr. , Professor
Position: General Scientist
Office: Sobolev Institute of Mathematics of SB RAS, Novosibirsk state university
Address: 630090, Russia, Novosibirsk, Prospekt Academika Koptyga, 4
Phone Office: (383) 329-76-80
E-mail: fadeev@math.nsc.ru
Kostsov Eduard Gennadevich
Dr.
Position: Head of Laboratory
Office: Institute of Automation and Electrometry SB RAS
Address: 630090, Russia, Novosibirsk, 1 Academician Koptug avenue
Phone Office: (383) 330-79-86
E-mail: kostsov@iae.nsk.su
Pimanov Daniil Olegovich
Position: Student
Office: Novosibirsk state university
Address: 630090, Russia, Novosibirsk, 2 Pirogov st.
E-mail: pimanov-daniil@yandex.ru
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Bibliography link:
Fadeev S.I., Kostsov E.G., Pimanov D.O. Study of the mathematical model for a microelectromechanical resonator of the Platform type // Computational technologies. 2016. V. 21. ¹ 2. P. 63-87
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