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Effect of Curved Micro-beam on Natural Frequency and Pull-In Voltage Considering Strain Gradient Theory

Derakhshan, Reza | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 46903 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Ahmadiyan, Mohammad Taghi; Firoozbakhsh, Keikhosrow
  7. Abstract:
  8. A microbeam, actuated by electrostatic distributed force, is a flexible beam-shaped element attached to a fixed rigid substrate. Electrostatically actuated microbeams are extensively used in different applications such as signal filtering and mass sensing. When the input voltage exceeds a critical value, called pull-in voltage (V_pi), the flexible microbeam spontaneously deflects towards the rigid plate. Pull-in instability is a basic phenomenon considered in the design of the micro actuators. When the rate of voltage variation is low and consequently inertia has almost no influence on the microsystem behavior, the critical value of voltage is called static pull-in voltage (V_pi). However, when the rate of voltage variation is not negligible, the effect of inertia has to be considered and the critical voltage value is called dynamic pull-in voltage (V_pid). The pull-in instability related to this situation is called dynamic pull-in instability. Studying vibrational behavior of MEMS is quite useful in determining design parameters of these systems. Vibrational characteristics of microbeams have been generally studied assuming small vibrations around a deflected position. Since the classical continuum theory can neither capture the size-dependency observed in micro-scale components nor accurately predict the mechanical behavior of such components, non-classical continuum theory has been emerged and developed. Recently the application of strain gradient theory for study of microbeam is more common. It is very likely that have an initially curved beam due to inappropriate manufacturing process, resulting in many uncertain and unknown parameters of the device. Also curved beams are widely used in the manufacture of mechanical memories and switches. Their main feature is dual stability. Snap-through is a phenomenon that occurs between two stability. In this study, homotopy analysis method is used to derive analytic solutions to predict dynamic snap-through and pull-in instability of an electrostatically-actuated microbeam and imperfect microbeam. The imperfection is expressed modeled by an initially curved beam. The nonlinear governing equation of microbeam affected by an electric field including fringing field effect, based on strain gradient elasticity, couple stress and classical theory is obtained. Influences of different parameters on dynamic pull-in instability are investigated. Equation of motion of double-clamped microbeam is discretized and solved by Galerkin’s method via mode summation. Resulting non-linear differential equation is solved by using homotopy analysis method (HAM). Influence of HAM parameters on accuracy is studied specifically in the vicinity of the snap-through and pull-in voltages. Comparing the results obtained for different theoretical skim indicates at low voltages with respect to snap-through voltage, good agreement exist between numerical, finite element and semi-analytical methods while as voltage increases HAM results are deviated from other two Methods. Findings indicate, considering strain gradient and couple stress theory results in a more stiff microbeam in comparison with classical theory. Effect of auxiliary parameters on convergence of the solutions is also studied. Convergence domain is determined at different voltages and order of HAM approximation
  9. Keywords:
  10. Pull-in Voltages ; Strain Gradient Theory ; Perturbation Method ; Microelectromechanical Systems (MEMS) ; Vibrational Frequency

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