Development of autooscillating system of vibration frequency sensors with mechanical resonator
DOI:
https://doi.org/10.15587/1729-4061.2017.93335Keywords:
vibration frequency sensor, auto-oscillating system, nonlinear amplifier, analytical stability criterionAbstract
At present, resonator sensors with an auto-oscillating system have a number of advantages in comparison with the known sensors with frequency output. In this case, developed auto-oscillating systems of resonator sensors are very specific; their elements are oriented toward a particular type of resonator and possess a certain degree of nonlinearity, which makes studying and modeling such systems impossible.
In the present work, analytical expressions were obtained for the reduction of parameters of mechanical systems of resonators to the lumped ones. This allowed us to apply the methods of research into nonlinear systems of control to the analysis of AOS and to receive the expression of transfer function of nonlinear resonator with consideration to the nonisochronicity. A structure of auto-oscillating system with a nonlinear resonator is devised, which was not explored earlier.
With the purpose of selecting the character of nonlinearity in the elements of feedback and mechanical resonator of the assigned type in AOS to warrant the assigned stability of frequency and amplitude of auto-oscillations, we performed imitation simulation in the Matlab Simulink programming environment.
The simulation demonstrated that a nonlinear amplifier at work with a nonlinear mechanical resonator provide for the auto-oscillating system that is stable by frequency and amplitude. Thus, auto-oscillating system of the devised structure can be used in the design of vibration frequency sensors.
References
- Sharapov, V. M., Polishhuk, E. S. (2012). Datchiki. Moscow: Tehnosfera, 624.
- Jetkin, L. G. (2004). Vibrochastotnye datchiki. Teorija i praktika. Moscow: MGTU im. N. Je. Baumana, 408.
- Matsuzuka, N., Hara, T., Isono, Y. (2016). Semi-empirical calculation for design of flexural mode silicon mechanical resonator with variable cross section. Sensors and Actuators A: Physical, 243, 25–34. doi: 10.1016/j.sna.2016.02.044
- Hao, Z., Erbil, A., Ayazi, F. (2003). An analytical model for support loss in micromachined beam resonators with in-plane flexural vibrations. Sensors and Actuators A: Physical, 109 (1-2), 156–164. doi: 10.1016/j.sna.2003.09.037
- Holmes, C. A., Meaney, C. P., Milburn, G. J. (2012). Synchronization of many nanomechanical resonators coupled via a common cavity field. Physical Review E, 85 (6). doi: 10.1103/physreve.85.066203
- Malas, A., Chatterjee, S. (2016). Modal self-excitation by nonlinear acceleration feedback in a class of mechanical systems. Journal of Sound and Vibration, 376, 1–17. doi: 10.1016/j.jsv.2016.04.029
- Malas, A., Chatterjee, S. (2015). Analysis and synthesis of modal and non-modal self-excited oscillations in a class of mechanical systems with nonlinear velocity feedback. Journal of Sound and Vibration, 334, 296–318. doi: 10.1016/j.jsv.2014.09.011
- Eichler, A., Moser, J., Chaste, J., Zdrojek, M., Wilson-Rae, I., Bachtold, A. (2011). Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene. Nature Nanotechnology, 6 (6), 339–342. doi: 10.1038/nnano.2011.71
- Taranenko, Ju. K. (2006). Avtokolebatel'naja sistema vibrochastotnogo izmeritelja plotnosti zhidkosti s mehanicheskim rezonatorom. Izv. Vuzov Radiojelektronika, 49 (12), 29–45.
- Taranenko, Ju. K. (2008). Formirovanie optimal'noj harakteristiki dlja avtokolebatel'nyh sistem vibrochastotnyh plotnomerov. Izv. Vuzov Radiojelektronika, 51 (7), 47–58.
- Shpoljanskij, V. A. (1974). Hronometrija. Moscow: Mashinostroenie, 656.
- Abramchuk, V. S., Abramchuk, I. V., Mozgovoj, A. V. (2013). Analiz mehanicheskih kolebanij s uchetom rassejanija vnutrennej jenergii. Izv. Tul'skogo gos. universiteta, 11 (3), 103–108.
- Biderman, V. L. (1980). Teorija mehanicheskih kolebanij. Moscow: Vysshaya shkola, 456.
- Sirota, A. A. (2016). Metody i algoritmy analiza dannyh i ih modelirovanie v MATLAB. Sankt-Peterburg, 384.
- Shah, P., Patel, J. B. (2012). Learning of Nonlinear Control System Using -'nonlintool'. 2012 IEEE Fourth International Conference on Technology for Education. doi: 10.1109/t4e.2012.32
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2017 Olga Oliynyk, Yuri Taranenko, Alexander Shvachka, Olena Chorna
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.
