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Dynamicanalysis of electrostatically exited micro cantilever beam

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  • Machine Design
  • Design
  • Mathematics
  • Physics


Microcantilever beams find applications in modern micro and nano devices, such as, microswitches, microvalves and atomic force microscopes (AFM). These are generally fabricated from single crystal silicon. Dynamics and pull-in analysis of these cantilever resonators (Beams) is of vital importance before their fabrication. Microbeams are often actuated by several actuation techniques such as piezoelectric, electromagnetic, thermal and electrostatic excitations. In electrostatic actuation a controlled dc voltage is applied together with a harmonic or suddenly applied ac component. The electrostatic force is in fact a non-linear function of displacement of the beam. In such beams when electrostatic force exceeds the elastic restoring force in the beam contact between the beam and supporting substrate occurs. This situation is referred to as pull-in instability which defines the life of a resonator. The study of pull-in is very important to design process of microsystems, such as, microgyroscopes to analyze the frequency response, the dynamic range and sensitivity. In this line, present work attempts to predict the static and dynamic characteristics of a cantilever microbeam resonator. A single-DOF model incorporating squeeze-film damping forces is first considered. Dynamic pull-in voltages are obtained from time-domain analysis and phase trajectories, for values of ac voltage amplitudes. Parametric studies are carried-out to find the effect of ac voltage amplitudes and air film pressure on the intermediate stability of system. For this bifurcation analysis and Poincare maps are employed. The harmonic voltage frequency effects are also illustrated in the form of frequency-response curves. As stiffness of test structure reduces due to applied voltage, the spring –softening behavior is observed in frequency-response curves. Two benchmark cantilever beam geometries available in terature are considered to illustrate the approach.

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