Abstract
In this work we investigate nonlinear dynamics of an electrostatically actuated microbeam resonator, located between two stationary electrodes, in the regime of supercritical compression. Longitudinal movement of the elastic fastening creates a longitudinal force in the elastic element of the microresonator. The equations of motion of the resonator are supplemented by equations of electrical circuits containing sources of electromotive force and capacitors of variable capacitance formed by fixed electrodes and the elastic element of the resonator. Equilibrium positions depending on the longitudinal displacement of the elastic fastening mechanism are obtained for various configurations of the electric field. With different switched on sources of constant electromotive force either two or three critical values of the force are possible, which differ from the Euler force. A numerical experiment demonstrating the possibility of the occurrence of a self-oscillatory regime was performed.
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References
Eulero, L.: Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solution problematis isoperimetrici latissimo sensu accepti. Lausannae, Genevae. MDCCXLIV (1744)
Lavrent’ev, M.A., Ishlinsky, A.J.: Dynamical modes of stability loss of elastic systems. DAN SSSR 64, 779–782 (1949)
Morozov, N.F., Tovstik, P.E., Tovstik, T.P.: Rod stability with long-term axial compression. Prob. Strength Plast. 77, 40–48 (2015)
Morozov, N.F., Tovstik, P.E.: On the rod dynamic stability loss under the load less that the Eulerian one. DAN 453, 282–285 (2013)
Morozov, N.F., Tovstik, P.E.: Rod dynamics in longitudinal impact. Bull. St. Petersburg Univ. 1, 105–111 (2009)
Morozov, N.F., Tovstik, P.E.: Rod dynamics in a short-term longitudinal impact. Bull. St. Petersburg Univ. 3, 126–130 (2013)
Wang, S., Wei, X., Zhao, Y., Jiang, Z., Shen, Y.: A MEMS resonant accelerometer for low-frequency vibration detection. Sens. Actuators A 283, 151–158 (2018)
Ding, H., Wang, W., Ju, B., Xie, J.: A MEMS resonant accelerometer with sensitivity enhancement and adjustment mechanisms. J. Micromech. Microeng. 27, 115010 (2017)
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Igumnova, V., Shtukin, L., Lukin, A., Popov, I. (2020). Dynamics of the Microresonator in the Regime of Supercritical Compression. In: Indeitsev, D., Krivtsov, A. (eds) Advanced Problems in Mechanics. APM 2019. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-49882-5_14
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DOI: https://doi.org/10.1007/978-3-030-49882-5_14
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