Parametric excitation of a piezoelectrically actuated system near Hopf bifurcation

DOI10.1016/j.apm.2011.09.031zbMath1243.74081OpenAlexW2033643796WikidataQ58483252 ScholiaQ58483252MaRDI QIDQ437938

Ghader Rezazadeh, Mohammad-Reza Ghazavi, Saber Azizi, Siamak Esmaeilzadeh Khadem

Publication date: 20 July 2012

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2011.09.031

zbMATH Keywords

Mathieu equationHopf bifurcationFloquet theoryMEMSflutter instabilitymicro-beam

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Control, switches and devices (``smart materials) in solid mechanics (74M05) Stability of dynamical problems in solid mechanics (74H55) Electromagnetic effects in solid mechanics (74F15) Micromechanical theories (74A60)

Related Items (6)

Dynamic stability in parametric resonance of vibrating beam micro-gyroscopes ⋮ Dynamic stability analysis of reduced delaminated planar beam structures using extended Craig-Bampton method ⋮ Application of piezoelectric actuation to regularize the chaotic response of an electrostatically actuated micro-beam ⋮ Nonlinear vibration and stability analysis of the curved microtube conveying fluid as a model of the micro coriolis flowmeters based on strain gradient theory ⋮ Tuning the primary resonances of a micro resonator, using piezoelectric actuation ⋮ Parametric amplification performance analysis of a vibrating beam micro-gyroscope with size-dependent and fringing field effects

Cites Work

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• Stabilizing the pull-in instability of an electro-statically actuated micro-beam using piezoelectric actuation
• Perturbation solution for secondary bifurcation in the quadratically-damped Mathieu equation
• Vibration and stability of an axially moving Rayleigh beam
• Nonlinear Mathieu equation and coupled resonance mechanism
• Dynamic stability of axially accelerating Timoshenko beam: averaging method
• The damped nonlinear quasiperiodic Mathieu equation near 2:2:1 resonance
• Parametric resonance of Hopf bifurcation
• Periodic solutions and stability for a weakly damped nonlinear Mathieu equation

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