A control approach for vibrations of a nonlinear microbeam system in multi-dimensional form.

*(English)*Zbl 1331.93086Summary: 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.) |

##### Keywords:

microbeam; active control strategy; MEMS; multi-dimensional dynamic system; two-phase control method; chaotic motion
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\textit{L. Dai} et al., Nonlinear Dyn. 77, No. 4, 1677--1692 (2014; Zbl 1331.93086)

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