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Complex oscillations and chaos in electrostatic microelectromechanical systems under superharmonic excitations
1Department of Mechanical and Industrial Engineering Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA.
Physical Review Letters
|August 11, 2005
Summary
Complex oscillations were observed in electrostatic microelectromechanical systems (MEMS) due to superharmonic excitation. Researchers found period doubling bifurcations leading to chaotic transitions, driven by the nonlinear electrostatic force.
Area of Science:
- Nonlinear dynamics
- Microelectromechanical systems (MEMS)
- Complex oscillations
Background:
- Electrostatic microelectromechanical systems (MEMS) are susceptible to nonlinear behaviors.
- Superharmonic excitation can lead to complex dynamic responses in MEMS devices.
Purpose of the Study:
- To investigate the formation of complex oscillations in MEMS under superharmonic excitation.
- To analyze the period doubling bifurcations and chaotic transitions in these systems.
Main Methods:
- Applying a DC bias and an AC signal at the Mth superharmonic frequency to MEMS.
- Observing the system's response, specifically the number of oscillations per period.
- Analyzing the transitions in oscillation patterns as AC amplitude is increased.
Main Results:
- M oscillations per period were observed with specific DC and AC signal amplitudes.
- Increasing AC voltage induced period doubling bifurcations, leading to 2n M oscillations per period.
- Chaotic transitions, including 1-band and 2-band chaos, were identified during the initial period doubling bifurcation.
Conclusions:
- The nonlinear nature of the electrostatic force is the primary cause of these complex oscillations and bifurcations.
- Superharmonic excitation in MEMS can exhibit rich nonlinear dynamics, including chaos.
- Understanding these phenomena is crucial for designing stable and predictable MEMS devices.