This research is on the nonlinear dynamics of a two-sided electrostatically actuated capacitive micro-beam. The micro-resonator is composed of silicon and PZT as a piezoelectric material. PZT is functionally distributed along the height of the micro-beam according to the power law distribution. The micro-resonator is simultaneously subjected to DC piezoelectric and two-sided electrostatic actuations. The DC piezoelectric actuation leads to the generation of an axial force along the length of the micro-beam and this is used as a tuning tool to shift the primary resonance of the micro-resonator. The governing equation of the motion is derived by the minimization of the Hamiltonian and generalized to the viscously damped systems. The periodic solutions in the vicinity of the primary resonance are detected by means of the shooting method and their stability is investigated by determining the so-called Floquet exponents of the perturbed motions. The basins of attraction corresponding to three individual periodic orbits are determined. The results depict that the higher the amplitude of the periodic orbit, the smaller is the area of the attractor.
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2.
Abdel-Rahman EM, Nayfeh AH and Younis MI (2003a) Dynamics of an electrostatically actuated resonant microsensor. In: International Conference on MEMS, NANO and Smart Systems (ICMENS'03), IEEE, 20–23 July 2003.
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Abdel-Rahman EM, Younis MI and Nayfeh AH (2003b) A nonlinear reduced order model for electrostatic MEMS. ASME 2003 Design Engineering Technical Conferences and Computers and Information in Engineering. Chicago, Illinois, USA, 2–6 September 2003, pp. 1771–1778.
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