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On the Stability of a Functionally Graded Rectangular Micro-Plate Subjected to Hydrostatic and Nonlinear Electrostatic Pressures

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Abstract

This article studies the stability of a functionally graded clamped-clamped microplate subjected to hydrostatic and electrostatic pressures. Equilibrium positions of the micro-plate are determined and shown in the state control space. To study the stability of the equilibrium positions, the motion trajectories are given for different initial conditions in the phase plane. Effects of the electrostatic and hydrostatic pressure changes on the deflection and stability of the micro-plate for some sample value of k are studied and values of the applied voltage and hydrostatic pressure leading system to unstable conditions by undergoing a saddle node and homoclinic bifurcations are determined.

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References

  1. Koizumi, M., The concept of FGM. Ceramic Transactions, Functionally Gradient Materials, 1993, 34(1): 3–10.

    Google Scholar 

  2. Ferreira, A., Batra, R., Roque, C., Qian, C. and Martins, P., Static analysis of functionally graded plates using third order shear deformation theory and a meshless method. Composite Structures, 2005, 69: 449–457.

    Article  Google Scholar 

  3. Bian, Z., Lim, C. and Chen, W., On functionally graded beams with integrated surface piezoelectric layers. Composite Structures, 2006, 72: 339–351.

    Article  Google Scholar 

  4. Srinivas, S. and Rao, A., Bending vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. International Journal of Solids and Structures, 1970, 6: 1463–1481.

    Article  Google Scholar 

  5. Zhang, D. and Zhou, Y., A theoretical analysis of FGM thin plates based on physical neutral surface. Computational Materials Science, 2008, 44: 716–720.

    Article  Google Scholar 

  6. Vel, S. and Batra, R., Three-dimensional exact solution for the vibration of functionally graded rectangular plates. Journal of Sound and Vibration, 2004, 272: 703–730.

    Article  Google Scholar 

  7. Woo, J., Meguid, S. and Ong, L., Nonlinear free vibration behavior of functionally graded plates. Journal of Sound and Vibration, 2006, 289: 595–611.

    Article  Google Scholar 

  8. Vel, S. and Batra, R., Exact solution for thermoelastic deformations of functionally graded thick rectangular plates. AIAA Journal, 2002, 40: 1421–1433.

    Article  Google Scholar 

  9. Vel, S. and Batra, R., Three-dimensional analysis of transient thermal stresses in functionally graded plates. International Journal of Solids and Structures, 2003, 40: 7181–7196.

    Article  Google Scholar 

  10. Kim, Y., Temperature dependent vibration analysis of functionally graded rectangular plates. Journal of Sound and Vibration, 2005, 284: 531–549.

    Article  Google Scholar 

  11. Rogers, T., Watson, P. and Spencer, A., Exact three-dimensional elasticity solutions for bending of moderately thick inhomogeneous and laminated strips under normal pressure. International Journal of Solids and Structures, 1995, 32: 1659–1673.

    Article  Google Scholar 

  12. Tarn, J. and Wang, Y., Asymptotic thermoelastic analysis of anisotropic inhomogeneous and laminated plates. Journal of Thermal Stresses, 1995, 18: 35–58.

    Article  Google Scholar 

  13. Cheng, Z. and Batra, R., Three-dimensional thermoelastic deformations of a functionally graded elliptic plate. Composites Part B, 2000, 31: 97–106.

    Article  Google Scholar 

  14. Reddy, J. and Cheng, Z., Three-dimensional solutions of smart functionally graded plates. Journal of Applied Mechanics, 2001, 68: 234–241.

    Article  Google Scholar 

  15. Wu, T., Shukla, K. and Huang, J.H., Post-buckling analysis of functionally graded rectangular plates. Composite Structures, 2007, 81: 1–10.

    Article  Google Scholar 

  16. Ferreira, A., Batra, R., Roque, C., Qian, L. and Jorge, R., Natural frequencies of functionally graded plates by a meshless method. Composite Structures, 2006, 75: 593–600.

    Article  Google Scholar 

  17. Batra, R. and Jin, J., Natural frequencies of a functionally graded anisotropic rectangular plate. Journal of Sound and Vibration, 2005, 282: 509–516.

    Article  Google Scholar 

  18. Yang, J., Liew, K. and Kitipornchai, S., Second-order statistics of the elastic buckling of functionally graded rectangular plates. Composites Science and Technology, 2005, 65: 1165–1175.

    Article  Google Scholar 

  19. Abrate, S., Functionally graded plates behave like homogeneous plates. Composites Part B Engineering, 2008, 39: 151–158.

    Article  Google Scholar 

  20. Matsunaga, H., Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory. Composite Structures, 2008, 82: 499–512.

    Article  Google Scholar 

  21. Qian, L., Batra, R. and Chen, L., Static and dynamic deformations of thick functionally graded elastic plate by using higher-order shear and normal deformable plate theory and meshless local Petrov-Galerkin method. Composites Part B Engineering, 2004, 35(6–8): 685–697.

    Article  Google Scholar 

  22. Zhong, Z. and Yu, T., Vibration of a simply supported functionally graded piezoelectric rectangular plate. Smart Materials & Structures, 2006, 15: 1404–1412.

    Article  Google Scholar 

  23. Roque, C., Ferreira, A. and Jorge, R., A radial basis function approach for the free vibration analysis of functionally graded plates using a refined theory. Journal of Sound and Vibration, 2007, 300: 1048–1070.

    Article  Google Scholar 

  24. Zhao, X., Lee, Y. and Liew, K., Free vibration analysis of functionally graded plates using the element-free kp-Ritz method. Journal of Sound and Vibration, 2009, 319: 918–939.

    Article  Google Scholar 

  25. Pradyumna, S. and Bandyopadhyay, J., Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation. Journal of Sound and Vibration, 2008, 318: 176–192.

    Article  Google Scholar 

  26. Chen, X. and Liew, K., Buckling of rectangular functionally graded material plates subjected to nonlinearly distributed in-plane edge loads. Smart Materials & Structures, 2004, 13: 1430–1437.

    Article  Google Scholar 

  27. Batra, R. and Aimmanee, S., Vibrations of thick isotropic plates with higher order shear and normal deformable plate theories. Computers and Structures, 2005, 83: 934–955.

    Article  Google Scholar 

  28. Woo, J. and Meguid, S., Nonlinear analysis of functionally graded plates and shallow shells. International Journal of Solids and Structures, 2001, 38(42–43): 7409–7421.

    Article  Google Scholar 

  29. Hao, Y., Chen, L., Zhang, W. and Lei, J., Nonlinear oscillations, bifurcations and chaos of functionally graded materials plate. Journal of Sound and Vibration, 2008, 312(4–5): 862–892.

    Article  Google Scholar 

  30. Liew, K., Yang, J. and Kitipornchai, S., Postbuckling of Piezoelectric FGM plates subject to thermo-electromechanical loading. International Journal of Solids and Structures, 2003, 40: 3869–3892. (doi:10.1016/S0020-7683(03)00096-9).

    Article  Google Scholar 

  31. Shen, H., Post buckling of FGM plates with piezoelectric actuators under thermo-electro-mechanical loadings. International Journal of Solids and Structures, 2005, 42: 6101–6121.

    Article  Google Scholar 

  32. Zhang, Y., Ikehara, T., Lu, J., Kobayashi, T., Ichiki, M., Itoh, T., et al. Novel MEMS-based thermometer with low power consumption for health-monitoring network application. SPIE, 2008, 1: 6800.

    Google Scholar 

  33. Craciunescu, C. and Wuttig, M., New ferromagnetic and functionally grade shape memory alloys. Journal of Optoelectronics Advanced Materials, 2003, 5(1): 139–146.

    Google Scholar 

  34. Fu, Y., Du, H. and Zhang, S., Functionally graded TiN/TiNi shape memory alloy films. Journal of Materials Letters, 2003, 57(20): 2995–2999.

    Article  Google Scholar 

  35. Fu, Y., Du, H., Huang, W., Zhang, S. and Hu, M., TiNi-based thin films in MEMS applications: a review. Sensors and Transducers Journal (A), 2004, 112(2–3): 395–408.

    Article  Google Scholar 

  36. Witvrouw, A. and Mehta, A., The use of functionally graded poly-SiGe layers for MEMS applications. Journal of Functionally Graded Materials, 2005, (8): 492–493: 255–260.

    Google Scholar 

  37. Lee, Z., Ophus, C., Fischer, L., Nelson-Fitzpatrick, N., Westra, K., Evoy, S. et al., Metallic NEMS components fabricated from nano-composite Al-Mo films. Journal of Nanotechnology, 2006, 17(12): 3063–3070.

    Article  Google Scholar 

  38. Rahaeifard, M., Kahrobaiyan, M. and Ahmadian, M., Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials. In: DETC2009-86254, 3rd International Conference on Micro and Nano-Systems (MNS3) 2009, San Diego, CA, USA, 2009.

  39. Mohammadi-Alasti, B., Rezazadeh, G, Borgheei, A., Minaei, S. and Habibifar, R., On the mechanical behavior of a functionally graded micro-beam subjected to a thermal moment and nonlinear electrostatic pressure. Composite Structures, 2011, 93: 1516–1525.

    Article  Google Scholar 

  40. Zhou, M. et al., A novel capacitive pressure sensor based on sandwich structures. Journal of Micro Electro Mechanical System, 2005, 14:1272–1281.

    Article  MathSciNet  Google Scholar 

  41. Rajalingham, C. and Bhat, R., Influence of electric field on diaphragm stability and vibration in a condenser microphone. Journal of Sound and Vibration, 1998, 211(5): 819–827.

    Article  Google Scholar 

  42. Bay, J., Hansen, O. and Bouwstra, S., Micromachined double backplate differential capacitive microphone. Journal of Micromechanics and Microengineering, 1999, 9(1): 30–33.

    Article  Google Scholar 

  43. Soleymani, P., Sadeghian, H., Tahmasebi, A. and Rezazadeh, G., Pull-in Instability Investigation of Circular Micro Pump Subjected to Nonlinear Electrostatic Force. Sensors & Transducers Journal, 2006, 69(7): 622–628.

    Google Scholar 

  44. Rezazadeh, G., Tayefe-Rezaei, S., Ghesmati, J. and Tahmasebi, A., Investigation of the pull-in phenomenon in drug delivery micropump using Galerkin method. Sensors and Transducers Journal, 2007, 78(4): 1098–107.

    Google Scholar 

  45. Zhang, Y. and Zhao, Y., Numerical and analytical study on the pull-in instability of microstructure under electrostatic loading. Journal of Sensors and Actuators (A) Physical, 2006, 127: 366–367.

    Article  Google Scholar 

  46. Rezazadeh, G., Khatami, F. and Tahmasebi, A., Investigation of the torsion and bending effects on static stability of electrostatic torsional micromirrors. Microsystem Technologies, 2007, 13(7): 715–722.

    Article  Google Scholar 

  47. Sazonova, V., A Tunable Carbon Nanotube Resonator. Ph.D. dissertation, university of Cornell, 2006.

  48. Kao, P., Dai, C., Hsu, C. and Lee, C., Fabrication and characterization of a tunable in-plane resonator with low driving voltage. Sensors, 2009, 9: 2062–2075.

    Article  Google Scholar 

  49. Dai, C. and Chen, Y., Modeling and manufacturing of micromechanical RF switch with inductors. Sensors, 2007, 7: 2660–2670.

    Article  Google Scholar 

  50. Hasanyan, D., Batra, R. and Harutyunyan, S., Pull-in instabilities in functionally graded micro thermo electromechanical systems. Journal of Thermal Stresses, 2008, 31: 1006–1021.

    Article  Google Scholar 

  51. Jia, X., Yang, J. and Kitipornchai, S., Characterization of FGM micro-switches under electrostatic and Casimir forces. Materials Science and Engineering, 2010, 10: 012178.

    Google Scholar 

  52. Talebian, S., Rezazadeh, G., Fathalilou, M. and Toosi, B., Effect of temperature on pull-in voltage and natural frequency of an electrostatically actuated microplate. Journal of Mechatronics, 2010, 20: 666–673.

    Article  Google Scholar 

  53. Sadeghian, H., Rezazadeh, G. and Osterberg, P., Application of the generalized differential quadrature method to the study of pull-in phenomena of MEMS switches. IEEE/ASME Journal of Microelectromechanical System, 2007, 16(6): 1334–1340.

    Article  Google Scholar 

  54. Rezazadeh, G., Tahmasebi, A. and Zubtsov, M., Application of piezoelectric layers in electrostatic MEM actuators: controlling of pull-in voltage. Microsystem Technologies, 2006, 12: 1163–1170.

    Article  Google Scholar 

  55. Nabian, A., Rezazadeh, G., Haddad-derafshi, M. and Tahmasebi, A., Mechanical behavior of a circular micro plate subjected to uniform hydrostatic and non-uniform electrostatic pressure. Microsystem Technologies, 2008, 14: 235–240.

    Article  Google Scholar 

  56. Nabian, A., Rezazadeh, G., Haddad-derafshi, M. and Tahmasebi, A., Investigation of pull-in phenomenon of rectangular micro-plate subjected to nonlinear electrostatic pressure. Sensors & Transducers Journal, 2006, 73(11): 810–818.

    Google Scholar 

  57. Azizi, S., Design of Micro Accelerometer to Use as Airbag Activator. MSc thesis, Mechanical Engineering Department, Tarbiat Modares University, Tehran, Iran, 2008: 53–54.

    Google Scholar 

  58. Seydel, R., Practical Bifurcation and Stability Analysis, Third Edition. Springer, aDOI 10.1007/978-1-4419-1740-9.

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Authors and Affiliations

  1. Department of Agricultural Machinery Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Adel Nabian, Morteza Almassi & Ali-Mohammad Borgheei

  2. Department of Mechanical Engineering, Urmia University, Urmia, Iran

    Ghader Rezazadeh

Authors
  1. Adel Nabian
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  2. Ghader Rezazadeh
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  3. Morteza Almassi
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  4. Ali-Mohammad Borgheei
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Correspondence to Adel Nabian.

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Nabian, A., Rezazadeh, G., Almassi, M. et al. On the Stability of a Functionally Graded Rectangular Micro-Plate Subjected to Hydrostatic and Nonlinear Electrostatic Pressures. Acta Mech. Solida Sin. 26, 205–220 (2013). https://doi.org/10.1016/S0894-9166(13)60020-8

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  • DOI: https://doi.org/10.1016/S0894-9166(13)60020-8

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