×

zbMATH — the first resource for mathematics

A control approach for vibrations of a nonlinear microbeam system in multi-dimensional form. (English) Zbl 1331.93086
Summary: Microbeams are widely seen in micro-electro-mechanical systems and their engineering applications. An active control strategy based on the fuzzy sliding mode control is developed in this research for controlling and stabilizing the nonlinear vibrations of a micro-electro-mechanical beam. An Euler-Bernoulli beam with a fixed-fixed boundary is employed to represent the microbeam, and the geometric nonlinearity of the beam and loading nonlinearity from the electrostatic force are considered. The governing equation of the microbeam is established and transformed into a multi-dimensional dynamic system with the third-order Galerkin method. A stability analysis is provided to show the necessity of the derived multi-dimensional dynamic system, and a chaotic motion is discovered. Then, a control approach is proposed, including a control strategy and a two-phase control method. For describing the application of the control approach developed, control of a chaotic motion of the microbeam is presented. The effectiveness of the active control approach is demonstrated via controlling and stabilizing the nonlinear vibration of the microbeam.
MSC:
93C10 Nonlinear systems in control theory
74F15 Electromagnetic effects in solid mechanics
37N35 Dynamical systems in control
70J50 Systems arising from the discretization of structural vibration problems
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Choi, B., Lovell, E.G.: Improved analysis of microbeams under mechanical and electrostatic loads. J. Micromech. Microeng. 7, 14-29 (1997) · Zbl 06942204
[2] Ramezani, S.: Nonlinear vibration analysis of micro-plates based on strain gradient elasticity theory. Nonlinear Dyn. 73, 1399-1421 (2013) · Zbl 1281.74014
[3] Wang, YC; Adams, SG; Thorp, JS; MacDonald, NC; Hartwell, P; Bertsch, F, Chaos in mems, parameter estimation and its potential application, IEEE Trans. Circuits Syst. I Fundam. Theory Appl., 45, 1013-1020, (1998)
[4] Azizi, S., Ghazavi, M.R., Khadem, S.E., Rezazadeh, G., Cetinkaya, C.: Application of piezoelectric actuation to regularize the chaotic response of an electrostatically actuated micro-beam. Nonlinear Dyn. 73, 853-867 (2013) · Zbl 1281.74027
[5] Younis, MI; Nayfeh, AH, A study of the nonlinear response of a resonant microbeam to an electric actuation, Nonlinear Dyn., 31, 91-117, (2003) · Zbl 1047.74027
[6] Mestrom, RMC; Fey, RHB; Beek, JTM; Phan, KL; Nijmeijer, H, Modelling the dynamics of a mems resonator: simulations and experiments, Sens. Actuators A., 142, 306-315, (2008)
[7] Alsaleem, FM; Younis, MI; Quakad, HM, On the nonlinear resonances and dynamic pull-in of electrostatically actuated resonators, J. Micromech. Microeng., 19, 040513, (2009)
[8] Utkin, V.I.: Sliding Modes in Control and Optimization. Springer, Berlin (1992) · Zbl 0748.93044
[9] Yau, HT; Kuo, CL; Yan, JJ, Fuzzy sliding mode control for a class of chaos synchronization with uncertainties, Int. J. Nonlinear Sci. Numer. Simul., 7, 333-338, (2006) · Zbl 06942204
[10] Kuo, CL, Design of an adaptive fuzzy sliding-mode controller for chaos synchronization, Int. J. Nonlinear Sci. Numer. Simul, 8, 631-636, (2007) · Zbl 06942314
[11] Yau, HT; Wang, CC; Hsieh, CT; Cho, CC, Nonlinear analysis and control of the uncertain micro-electro-mechanical system by using a fuzzy sliding mode control design, Comput. Math. Appl., 61, 1912-1916, (2011) · Zbl 1219.93062
[12] Haghighi, HS; Markazi, AHD, Chaos prediction and control in mems resonators, Commun. Nonlinear Sci. Numer. Simul., 15, 3091-3099, (2010)
[13] Tusset, AM; Balthazar, JM; Bassinello, DG; Pointes, BR; Felix, JLP, Statements on chaos control designs, including a fractional order dynamical system, applied to a “mems” comb-drive actuator, Nonlinear Dyn., 69, 1837-1857, (2012) · Zbl 1263.93105
[14] Dai, L, Chen, C., Sun, L.: An active control strategy for vibration control of an axially translating beam. J. Vib. Control (2013) (in press) · Zbl 1349.93196
[15] Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley, New York (1979) · Zbl 0418.70001
[16] Abou-Rayan, AM; Nayfeh, AH; Mook, DT, Nonlinear response of a parametrically excited buckled beam, Nonlinear Dyn., 4, 499-525, (1993)
[17] Dai, L.: Nonlinear Dynamics of Piecewise Constant Systems and Implementation of Piecewise Constant Arguments. World Scientific, New Jersey (2008) · Zbl 1154.70001
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.