This research deals with the amplitude–frequency response of primary resonance of electrostatically actuated, angled nanoelectromechanical systems (NEMS) cantilever resonators. These devices feature a uniform cantilever beam inclined relative to a ground plate. Under primary resonance conditions, when the frequency of the applied alternating current (AC) voltage is near half the beam’s natural frequency, resonant vibrations of the cantilever resonator occur. The investigation considers electrostatic forces, viscous damping, fringing field effects, and the Casimir force, a quantum phenomenon significant at nanoscale gaps. The resonator’s behavior is modeled using a nonlinear partial differential equation. Two modeling approaches are employed: 1) a single-mode Reduced-Order Model (ROM) solved via the Method of Multiple Scales (MMS), and 2) a three-mode ROM (3 T-ROM) solved using numerical integration, and AUTO a continuation and bifurcation software package. This research reports the effects of beam angle, applied voltage, damping, fringing fields, and Casimir forces on the amplitude–frequency response. Key nonlinear phenomena, such as bifurcations and pull-in instability (collapse of the resonator onto the ground plate), are also investigated. Results show that beam angles significantly affect the response. Positive angles show an increase in vibration amplitudes, while negative angles show a reduction in amplitudes with stronger nonlinear behavior, broadening the resonance bandwidth. MMS aligns well with 3 T-ROM results in the case of soft actuation, small amplitudes, small damping, and weak nonlinearities, but diverges for larger amplitudes and stronger nonlinearities. The findings suggest that beam angle can be used as a design parameter to tune NEMS performance. This investigation assumes slender beams (length ≥ 100× thickness) and gaps under 1 μm where Casimir force is relevant.

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Angled NEMS Uniform Cantilever Beams: Amplitude-Frequency Response of Primary Resonance to Include Casimir Effect

  • Dumitru I. Caruntu,
  • Benjamin M. Huerta

摘要

This research deals with the amplitude–frequency response of primary resonance of electrostatically actuated, angled nanoelectromechanical systems (NEMS) cantilever resonators. These devices feature a uniform cantilever beam inclined relative to a ground plate. Under primary resonance conditions, when the frequency of the applied alternating current (AC) voltage is near half the beam’s natural frequency, resonant vibrations of the cantilever resonator occur. The investigation considers electrostatic forces, viscous damping, fringing field effects, and the Casimir force, a quantum phenomenon significant at nanoscale gaps. The resonator’s behavior is modeled using a nonlinear partial differential equation. Two modeling approaches are employed: 1) a single-mode Reduced-Order Model (ROM) solved via the Method of Multiple Scales (MMS), and 2) a three-mode ROM (3 T-ROM) solved using numerical integration, and AUTO a continuation and bifurcation software package. This research reports the effects of beam angle, applied voltage, damping, fringing fields, and Casimir forces on the amplitude–frequency response. Key nonlinear phenomena, such as bifurcations and pull-in instability (collapse of the resonator onto the ground plate), are also investigated. Results show that beam angles significantly affect the response. Positive angles show an increase in vibration amplitudes, while negative angles show a reduction in amplitudes with stronger nonlinear behavior, broadening the resonance bandwidth. MMS aligns well with 3 T-ROM results in the case of soft actuation, small amplitudes, small damping, and weak nonlinearities, but diverges for larger amplitudes and stronger nonlinearities. The findings suggest that beam angle can be used as a design parameter to tune NEMS performance. This investigation assumes slender beams (length ≥ 100× thickness) and gaps under 1 μm where Casimir force is relevant.