Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013, Article ID 736148, 16 pages
http://dx.doi.org/10.1155/2013/736148
Research Article

Vibrations of a Slightly Curved Microbeam Resting on an Elastic Foundation with Nonideal Boundary Conditions

1Applied Mathematics and Computation Center, Celal Bayar University, Muradiye, 45140 Manisa, Turkey
2Department of Mechanical Engineering, Celal Bayar University, Muradiye, 45140 Manisa, Turkey

Received 18 January 2013; Accepted 7 May 2013

Academic Editor: Mohammad Younis

Copyright © 2013 Gözde Sarı and Mehmet Pakdemirli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. I. Younis and A. H. Nayfeh, “A study of the nonlinear response of a resonant microbeam to an electric actuation,” Nonlinear Dynamics, vol. 31, no. 1, pp. 91–117, 2003. View at Publisher · View at Google Scholar · View at Scopus
  2. W. Zhang and G. Meng, “Nonlinear dynamical system of micro-cantilever under combined parametric and forcing excitations in MEMS,” Sensors and Actuators A, vol. 119, no. 2, pp. 291–299, 2005. View at Publisher · View at Google Scholar · View at Scopus
  3. R. M. C. Mestrom, R. H. B. Fey, J. T. M. van Beek, K. L. Phan, and H. Nijmeijer, “Modelling the dynamics of a MEMS resonator: simulations and experiments,” Sensors and Actuators A, vol. 142, no. 1, pp. 306–315, 2008. View at Publisher · View at Google Scholar · View at Scopus
  4. X. L. Jia, J. Yang, S. Kitipornchai, and C. W. Lim, “Resonance frequency response of geometrically nonlinear micro-switches under electrical actuation,” Journal of Sound and Vibration, vol. 331, no. 14, pp. 3397–3411, 2012. View at Publisher · View at Google Scholar
  5. S. Abu-Salih and D. Elata, “Electromechanical buckling of a pre-stressed layer bonded to an elastic foundation,” in Proceedings of the NSTI Nanotechnology Conference and Trade Show (NSTI Nanotech '04), pp. 223–226, March 2004. View at Scopus
  6. B. Rivlin and D. Elata, “Design of nonlinear springs for attaining a linear response in gap-closing electrostatic actuators,” International Journal of Solid and Structures, vol. 49, no. 26, pp. 3816–3822, 2012. View at Publisher · View at Google Scholar
  7. S. Kong, S. Zhou, Z. Nie, and K. Wang, “The size-dependent natural frequency of Bernoulli-Euler micro-beams,” International Journal of Engineering Science, vol. 46, no. 5, pp. 427–437, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. H. M. Ouakad and M. I. Younis, “The dynamic behavior of MEMS arch resonators actuated electrically,” International Journal of Non-Linear Mechanics, vol. 45, no. 7, pp. 704–713, 2010. View at Publisher · View at Google Scholar · View at Scopus
  9. J. Casals-Terre and A. Shkel, “Snap-action bistable micromechanism actuated by nonlinear resonance,” in Proceedings of the 4th IEEE Conference on Sensors, pp. 893–896, Irvine, Calif, USA, November 2005. View at Publisher · View at Google Scholar · View at Scopus
  10. J. Qiu, J. H. Lang, and A. H. Slocum, “A curved-beam bistable mechanism,” Journal of Microelectromechanical Systems, vol. 13, no. 2, pp. 137–146, 2004. View at Publisher · View at Google Scholar · View at Scopus
  11. Y. Zhang, Y. Wang, Z. Li, Y. Huang, and D. Li, “Snap-through and pull-in instabilities of an arch-shaped beam under an electrostatic loading,” Journal of Microelectromechanical Systems, vol. 16, no. 3, pp. 684–693, 2007. View at Publisher · View at Google Scholar · View at Scopus
  12. S. Krylov, B. R. Ilic, D. Schreiber, S. Seretensky, and H. Craighead, “The pull-in behavior of electrostatically actuated bistable microstructures,” Journal of Micromechanics and Microengineering, vol. 18, no. 5, pp. 055026–055046, 2008. View at Publisher · View at Google Scholar · View at Scopus
  13. K. Das and R. C. Batra, “Pull-in and snap-through instabilities in transient deformations of microelectromechanical systems,” Journal of Micromechanics and Microengineering, vol. 19, no. 3, pp. 035008–035027, 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. M. I. Younis, E. M. Abdel-Rahman, and A. Nayfeh, “A reduced-order model for electrically actuated microbeam-based MEMS,” Journal of Microelectromechanical Systems, vol. 12, no. 5, pp. 672–680, 2003. View at Publisher · View at Google Scholar · View at Scopus
  15. L. Ruzziconi, A. M. Bataineh, M. I. Younis, and S. Lenci, “Theoretical and experimental investigation of the nonlinear response of an electrically actuated imperfect microbeam,” in Proceedings of the International Conference on Structural Nonlinear Dynamics and Diagnosis (CSNDD '12), vol. 1, 2012.
  16. L. Ruzziconi, M. I. Younis, and S. Lenci, “An electrically actuated imperfect microbeam: dynamical integrity for interpreting and predicting the device response,” Meccanica, 2013. View at Publisher · View at Google Scholar
  17. H. O. Ekici and H. Boyaci, “Effects of non-ideal boundary conditions on vibrations of microbeams,” Journal of Vibration and Control, vol. 13, no. 9-10, pp. 1369–1378, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. H. R. Öz, M. Pakdemirli, E. Özkaya, and M. Yilmaz, “Non-linear vibrations of a slightly curved beam resting on anon-linear elastic foundation,” Journal of Sound and Vibration, vol. 212, no. 2, pp. 295–309, 1998. View at Google Scholar · View at Scopus
  19. H. R. Öz and M. Pakdemirli, “Two-to-one internal resonances in a shallow curved beam resting on an elastic foundation,” Acta Mechanica, vol. 185, no. 3-4, pp. 245–260, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. M. Pakdemirli and H. Boyaci, “Vibrations of a stretched beam with non-ideal boundary conditions,” Mathematical and Computational Applications, vol. 6, no. 3, pp. 217–220, 2001. View at Google Scholar · View at Scopus
  21. M. Pakdemirli and H. Boyaci, “Effect of non-ideal boundary conditions on the vibrations of continuous systems,” Journal of Sound and Vibration, vol. 249, no. 4, pp. 815–823, 2002. View at Publisher · View at Google Scholar · View at Scopus
  22. M. Pakdemirli and H. Boyaci, “Non-linear vibrations of a simple-simple beam with a non-ideal support in between,” Journal of Sound and Vibration, vol. 268, no. 2, pp. 331–341, 2003. View at Publisher · View at Google Scholar · View at Scopus
  23. M. Pakdemirli and H. Boyaci, “Vibrations of a simply supported beam with a non-ideal support at an intermediate point,” Mathematical and Computational Applications, vol. 8, no. 1–3, pp. 159–164, 2003. View at Google Scholar · View at Scopus
  24. D. J. Griffiths, Introduction to Electrodynamics, Prentice Hall, Englewood Cliffs, NJ, USA, 1981.
  25. A. H. Nayfeh, J. F. Nayfeh, and D. T. Mook, “On methods for continuous systems with quadratic and cubic nonlinearities,” Nonlinear Dynamics, vol. 3, no. 2, pp. 145–162, 1992. View at Publisher · View at Google Scholar · View at Scopus
  26. M. Pakdemirli, S. A. Nayfeh, and A. H. Nayfeh, “Analysis of one-to-one autoparametric resonances in cables-Discretization vs. direct treatment,” Nonlinear Dynamics, vol. 8, no. 1, pp. 65–83, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  27. M. Pakdemirli, “A comparison of two perturbation methods for vibrations of systems with quadratic and cubic nonlinearities,” Mechanics Research Communications, vol. 21, no. 2, pp. 203–208, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. M. Pakdemirli and H. Boyaci, “The direct-perturbation method versus the discretization-perturbation method: linear systems,” Journal of Sound and Vibration, vol. 199, no. 5, pp. 825–832, 1997. View at Google Scholar · View at Scopus
  29. A. H. Nayfeh, Introduction to Perturbation Techniques, Wiley, New York, NY, USA, 1981. View at MathSciNet