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Response of Double-Clamped Micro-Beams to the Casimir Force and SQFD Resting on Strain Gradient Elasticity Theory

Author Affiliations

  • 1Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

Res. J. Recent Sci., Volume 5, Issue (6), Pages 68-72, June,2 (2016)

Abstract

Present paper shows a numerical assessment to investigate double-clamped micro-beams by considering the Casimir force and SQFD resting on strain gradient elasticity theory using GDQ method. The mathematical formulations are considered to approximately model the non-linear effects of geometry, electrostatic actuation, and Casimir force on the oscillatory system. These equations, in conjunction with boundary conditions, are transformed into dimensionless governing equations and boundary conditions with the aim of simplifying numerical simulations. It is concluded that geometric and material properties both affect the pull-in characteristics of the polysilicon micro-beam. In particular, it is shown that present investigation reveals unexpected influence of the Casimir force on micro-structures.

References

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  25. Shi H., Fan S., Xing W. and Sun J. (2015)., Study of weak vibrating signal detection based on chaotic oscillator in MEMS resonant beam sensor., Mechanical Systems and Signal Processing, 50-51, 535-547.
  26. Caruntu D.I. and Martinez I. (2014)., Reduced order model of parametric resonance of electrostatically actuated MEMS cantilever resonators., International Journal of Non-Linear Mechanics, 66, 28-32.
  27. Hu Y., Shen X., Zhang Y., Wang Z. And Chen, X. (2014)., Research reviews and prospects of MEMS reliability., Integrated Ferroelectrics, 152, 8-21.
  28. Sheng H. and Zhang T. (2015)., MEMS-based low-cost strap-down AHRS research., Measurement, 59, 63-72.
  29. Zahng W.M., Yan H., Peng Z.K. and Meng G. (2014)., Electrostatic pull-in instability in MEMS/NEMS: A review., Sensors and Actuators, 214(A), 187-218.
  30. Joglekar M.M. and Pawaskar D.N. (2011)., Closed-form empirical relations to predict the dynamic pull-in parameters of electrostatically actuated tapered microcantilevers., Journal of Micromechanics and Microengineering, 21, 1-12.
  31. Hasanyan D.J., Batra R.C. and Harutyunyan S. (2008)., Pull-in instability in functionally graded microthermoelectromechanical systems., Journal of Thermal Stresses, 31, 1006-1021.
  32. Jia X.L., Yang J., Kitipornchai S. and Lim C.W. (2012)., Pull-in instability and free vibration of electrically actuated poly-SiGe graded micro-beams with a curved ground electrode., Applied Mathematical Modelling, 36, 1875-1884.
  33. Ai S. and Pelesko J.A. (2007)., Dynamics of a canonical electrostatic MEMS/NEMS system., Journal of Dynamics and Differential Equations, 20(3), 609-641.
  34. Chuang W.C., Lee H.L., Chang P.Z. and Hu Y.C. (2010)., Review on the modelling of electrostatic MEMS., Sensors, 10, 6149-6171.
  35. Sedighi H.M. (2014)., Size-dependent dynamic pull-in instability of vibrating electrically actuated microbeams based on the strain gradient elasticity theory., Acta Astronautica, 95, 111-123.
  36. Son C. and Ziaie B. (2008)., Pull-in instability of parallel-plate electrostatic microactuators under a combined variable charge and voltage configuration., Applied Physics Letters, 92, 1-4.
  37. Yazdanpanahi E., Noghrehabadi A. and Ghalambaz M. (2013)., Balance dielectric layer for micro electrostatic switches in the presence of capillary effect., International Journal of Mechanical Sciences, 74, 83-90.
  38. Altuğ Bıçak M.M. and Rao M.D. (2010)., Analytical modelling of squeeze film damping for rectangular elastic plates using Green’s functions., Journal of Sound and Vibration, 329, 4617-4633.
  39. Homentcovschi D. and Miles R.N. (2010)., Viscous damping and spring force in periodic perforated planar microstructures when the Reynold’s equation cannot be applied., Journal of the Acoustical Society of America, 127(3), 1288-1299.
  40. Buks E. and Roukes M.L. (2001)., Stiction, adhesion energy, and the Casimir force effect in micromechanical systems., Physical Review, 63(B), 1-4.
  41. Bordag M., Mohideen U. and Mostepanenko V.M. (2001)., New developments in the Casimir effect., Physics Reports, 353, 1-205.
  42. Wang Y.G., Lin W.H., Li X.M. and Feng Z.J. (2011)., Bending and vibration of an electrostatically actuated circular microplate in presence of Casimir force., Applied Mathematical Modelling, 35, 2348-2357.
  43. Lam D.C.C., Yang F., Chong A.C.M., Wang J. and Tong P. (2003)., Experiments and theory in strain gradient elasticity., Journal of the Mechanics and Physics of Solids, 51, 1477-1508.
  44. Lamorreaux S.K. (2005)., The Casimir force: background, experiments, and applications., Reports on Progress in Physics, 68, 201-236.
  45. Shu C., Khoo B.C., Chew Y.T. and Yeo K.S. (1996)., Numerical studies of unsteady boundary layer flows past an impulsively started circular cylinder by GDQ and GIQ approaches., Computer Methods in Applied Mechanics and Engineering, 135, 229-241.
  46. Bellman R. and Casti J. (1971)., Differential quadrature and long-term integration., Journal of Mathematical Analysis and Applications, 34, 235-238.
  47. Jia X.L., Yang J. and Kitipornchai S. (2011)., Pull-in instability of geometrically nonlinear micro-switches under electrostatic and Casimir forces., Acta Mechanica, 218, 161-174.
  48. Lin W.H. and Zhao Y.P. (2005)., Casimir effect on the pull-in parameters of nanometer switches., Microsystem Technologies, 11, 80-85.