×

Nonlinear dynamics and chaos in micro/nanoelectromechanical beam resonators actuated by two-sided electrodes. (English) Zbl 1448.74054

Summary: We investigate theoretically the nonlinear dynamics and the emergence of chaos in suspended beam micro/nanoelectromechanical (MEMS/NEMS) resonators actuated by two-sided electrodes. Through the analysis of phase diagrams we have found that the system presents a rich and complex nonlinear behavior. Multistability is observed in a significant region of the relevant parameter space, involving periodic and chaotic attractors. Complex and varied routes to chaos were also found. Basins of attraction with strongly intermingled attractors provide further evidence of multistability. The basins are analyzed in greater detail. Their fractal dimensions and uncertainty exponent are calculated using the well known box counting and uncertainty methods. The results for the uncertainty exponent are compared with those obtained with yet another approach, based on the recently proposed basin entropy method. The comparison provides a test for the new approach, which we conclude that is a reliable alternative method of calculation. Very low uncertainty exponents have been obtained, indicating that some basins have extremely intermingled attractors, what may have significant influence in the experimental investigation and practical applications of the resonators. We also conclude that the observation of chaos in this system is favored by lower frequencies of excitation and comparatively small quality factors (larger dissipation).

MSC:

74H65 Chaotic behavior of solutions to dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74F15 Electromagnetic effects in solid mechanics
37N15 Dynamical systems in solid mechanics
37M05 Simulation of dynamical systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Huang, X. M.H.; Feng, X. L.; Zorman, C. A.; Mehregany, M.; Roukes, M. L., VHF, UHF and microwave frequency nanomechanical resonators, New J Phys, 7, 247 (2005)
[2] Uranga, A.; Verd, J.; Barniol, N., CMOS-MEMS resonators: from devices to applications, Microelectron Eng, 132, 58-73 (2015)
[3] Almog, R.; Zaitsev, S.; Shtempluck, O.; Buks, E., Signal amplification in a nanomechanical duffing resonator via stochastic resonance, Appl Phys Lett, 90, 013508 (2007)
[4] Antonio, D.; Zanette, D. H.; López, D., Frequency stabilization in nonlinear micromechanical oscillators, Nat Commun, 3, 806 (2012)
[5] Rhoads, J.; Shaw, S. W.; Turner, K. L., Nonlinear dynamics and its applications in micro- and nanoresonators, Proceedings of 2008 ASME Dynamic Systems and Control Conference,October 20-22 (2008)
[6] De S., K.; Aluru, N. R., Complex oscillations and chaos in electrostatic microelectromechanical systems under superharmonic excitations, Phys Rev Lett, 94, 204101 (2005)
[7] Amorim, T. D.; Dantas, W. G.; Gusso, A., Analysis of the chaotic regime of MEMS/NEMS fixed – fixed beam resonators using an improved 1DOF model, Nonlinear Dyn, 79, 967-981 (2015)
[8] Barceló, J.; Rosselló, J. L.; Bota, S.; Segura, J.; Verd, J., Electrostatically actuated microbeam resonators as chaotic signal generators: a practical perspective, Commun Nonlinear Sci Numer Simulat, 30, 316-327 (2016) · Zbl 1489.94025
[9] Alemansour, H.; Miandoab, E. M.; Pishkenari, H. N., Effect of size on the chaotic behavior of nano resonators, Commun Nonlinear Sci Numer Simulat, 44, 495-505 (2017) · Zbl 1455.74045
[10] Dantas, W. G.; Gusso, A., Analysis of the chaotic dynamics of MEMS/NEMS doubly clamped beam resonators with two-sided electrodes, Int J Bifurc Chaos, 28, 1850122 (2018) · Zbl 06958265
[11] Karabalin, R. B.; Cross, M. C.; Roukes, M. L., Nonlinear dynamics and chaos in two coupled nanomechanical resonators, Phys Rev B, 79, 165309 (2009)
[12] Wang, Y. C.; Adams, S. G.; Thorp, J. S.; MacDonald, N. C.; Hartwell, P.; Bertsch, F., Chaos in MEMS, parameter estimation and its potential application, IEEE Trans Circuits Syst I, 45, 1013-1020 (1998)
[13] Haghighi, H. S.; Markazi, A. H.D., Chaos prediction and control in MEMS resonators, Commun Nonlinear Sci Numer Simulat, 15, 3091-3099 (2010)
[14] Siewe, M. S.; Hegazy, U. H., Homoclinic bifurcation and chaos control in MEMS resonators, Appl Math Model, 35, 5533-5552 (2011) · Zbl 1228.70015
[15] Gusso, A.; Dantas, W. G.; Ujevic, S., Prediction of robust chaos in micro and nanoresonators under two-frequency excitation, Chaos, 29, 033112 (2019)
[16] Younis, M. I., MEMS linear and nonlinear statics and dynamics (2011), New York: Springer
[17] Fu, Y.; Zhang, J.; Jiang, Y., Influences of the surface energies on the nonlinear static and dynamic behaviors of nanobeams, Phys. E, 42, 2268-2273 (2010)
[18] Arecchi, F. T.; Badii, R.; Politi, A., Generalized multistability and noise-induced jumps in a nonlinear dynamical system, Phys Rev A, 32, 402-408 (1985)
[19] Cleland, A. N., Foundations of nanomechanics (2002), Berlin: Springer
[20] Alligood, K. T.; Sauer, T. D.; Yorke, J. A., Chaos: an introduction to dynamical systems (1997), New York: Springer
[21] Aguirre, J.; Viana, R. L.; Sanjuán, M. A.F., Fractal structures in nonlinear dynamics, Rev Mod Phys, 81, 333-386 (2009)
[22] McDonald, S. W.; Grebogi, C.; Ott, E.; Yorke, J. A., Fractal basin boundaries, Physica D, 17, 125-153 (1985) · Zbl 0588.58033
[23] Daza, A.; Wagemakers, A.; Georgeot, B.; Guéry-Odelin, D.; Sanjuán, M. A.F., Basin entropy: a new tool to analyze uncertainty in dynamical systems, Sci Rep, 6, 31416 (2016)
[24] Górskia, A. Z.; Drozdza, S.; Mokrzyckac, A.; Pawlik, J., Accuracy analysis of the box-counting algorithm, Acta Phys Pol A, 121, 28-30 (2012)
[25] Zaitsev, S.; Shtempluck, O.; Buks, E.; Gottlieb, O., Nonlinear damping in a micromechanical oscillator, Nonlinear Dyn, 67, 859-883 (2012) · Zbl 1314.70027
[26] Gusso, A., Nonlinear damping in doubly clamped beam resonators due to the attachment loss induced by the geometric nonlinearity, J Sound Vib, 372, 255-265 (2016)
[27] Gusso, A.; Pimentel, J. D., Nonlinear damping in MEMS/NEMS beam resonators resulting from clamping loss, Proceedings of the sixth international conference on nonlinear science and complexity (2016)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.