DOI QR코드

DOI QR Code

Vibration Analysis of Smart Embedded Shear Deformable Nonhomogeneous Piezoelectric Nanoscale Beams based on Nonlocal Elasticity Theory

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Barati, Mohammad Reza (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Zenkour, Ashraf M. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • 투고 : 2016.08.02
  • 심사 : 2016.10.21
  • 발행 : 2017.06.30

초록

Free vibration analysis is presented for a simply-supported, functionally graded piezoelectric (FGP) nanobeam embedded on elastic foundation in the framework of third order parabolic shear deformation beam theory. Effective electro-mechanical properties of FGP nanobeam are supposed to be variable throughout the thickness based on power-law model. To incorporate the small size effects into the local model, Eringen's nonlocal elasticity theory is adopted. Analytical solution is implemented to solve the size-dependent buckling analysis of FGP nanobeams based upon a higher order shear deformation beam theory where coupled equations obtained using Hamilton's principle exist for such beams. Some numerical results for natural frequencies of the FGP nanobeams are prepared, which include the influences of elastic coefficients of foundation, electric voltage, material and geometrical parameters and mode number. This study is motivated by the absence of articles in the technical literature and provides beneficial results for accurate FGP structures design.

키워드

참고문헌

  1. Lanhe, W., "Thermal Buckling of a Simply Supported Moderately Thick Rectangular FGM Plate", Composite Structures, Vol. 64, No. 2, 2004, pp. 211-218. DOI:10.1016/j. compstruct.2003.08.004
  2. Ebrahimi, F. and Rastgo, A., "An Analytical Study on the Free Vibration of Smart Circular Thin FGM Plate Based on Classical Plate Theory", Thin-Walled Structures, Vol. 46, No. 12, 2008, pp. 1402-1408. DOI:10.1016/j.tws.2008.03.008
  3. Ke, L. L., Yang, J., Kitipornchai, S. and Xiang, Y., "Flexural Vibration and Elastic Buckling of a Cracked Timoshenko Beam Made of Functionally Graded Materials", Mechanics of Advanced Materials and Structures, Vol. 16, No. 6, 2009, pp. 488-502. DOI:10.1080/15376490902781175
  4. Zhang, D. G., "Nonlinear Bending Analysis of FGM Beams Based on Physical Neutral Surface and High Order Shear Deformation Theory", Composite Structures, Vol. 100, 2013, pp. 121-126. DOI:10.1016/j.compstruct.2012.12.024
  5. Pradhan, K. K. and Chakraverty, S., "Free Vibration of Euler and Timoshenko Functionally Graded Beams by Rayleigh-Ritz Method", Composites Part B: Engineering, Vol. 51, 2013, pp. 175-184. DOI:10.1016/j. compositesb.2013.02.027
  6. Esfahani, S. E., Kiani, Y., Komijani, M. and Eslami, M. R., "Vibration of a Temperature-dependent Thermally Pre/ postbuckled FGM Beam over a Nonlinear Hardening Elastic Foundation", Journal of Applied Mechanics, Vol. 81, No. 1, 2014, 011004. DOI:10.1115/1.4023975
  7. Wattanasakulpong, N. and Chaikittiratana, A., "Flexural Vibration of Imperfect Functionally Graded Beams Based on Timoshenko Beam Theory: Chebyshev Collocation Method", Meccanica, Vol. 50, No. 5, 2015, pp. 1331-1342. DOI:10.1007/ s11012-014-0094-8
  8. Aydogdu, M., "A General Nonlocal Beam Theory: its Application to Nanobeam Bending, Buckling and Vibration", Physica E: Low-dimensional Systems and Nanostructures, Vol. 41, No. 9, 2009, pp. 1651-1655. DOI:10.1016/j. physe.2009.05.014
  9. Thai, H. T., "A Nonlocal Beam Theory for Bending, Buckling, and Vibration of Nanobeams", International Journal of Engineering Science, Vol. 52, 2012, pp. 56-64. DOI:10.1016/j.ijengsci.2011.11.011
  10. Yan, Z. and Jiang, L., "Size-dependent Bending and Vibration Behaviour of Piezoelectric Nanobeams due to Flexoelectricity", Journal of Physics D: Applied Physics, Vol. 46, No. 35, 2013, 355502. DOI:10.1088/0022-3727/46/35/355502
  11. Ke, L. L., Wang, Y, S,, Yang, J. and Kitipornchai, S., "Nonlinear Free Vibration of Size-dependent Functionally Graded Microbeams", International Journal of Engineering Science, Vol. 50, No. 1, 2012, pp. 256-267. DOI:10.1016/j. ijengsci.2010.12.008
  12. Ansari, R., Shojaei, M. F., Gholami, R., Mohammadi, V. and Darabi, M. A., "Thermal Postbuckling Behavior of Sizedependent Functionally Graded Timoshenko Microbeams", International Journal of Non-Linear Mechanics, Vol. 50, 2013, pp. 127-135. DOI:10.1016/j.ijnonlinmec.2012.10.010
  13. Eltaher, M. A., Emam, S. A. and Mahmoud, F. F., "Static and Stability Analysis of Nonlocal Functionally Graded Nanobeams", Composite Structures, Vol. 96, 2013, pp. 82-88. DOI:10.1016/j.compstruct.2012.09.030
  14. Simsek, M. and Yurtcu, H. H., "Analytical Solutions for Bending and Buckling of Functionally Graded Nanobeams Based on the Nonlocal Timoshenko Beam Theory", Composite Structures, Vol. 97, 2013, pp. 378-386. DOI:10.1016/j. compstruct.2012.10.038
  15. Sharabiani, P. A. and Yazdi, M. R. H., "Nonlinear Free Vibrations of Functionally Graded Nanobeams with Surface Effects", Composites Part B: Engineering, Vol. 45, No. 1, 2013, pp. 581-586. DOI:10.1016/j.compositesb.2012.04.064
  16. Uymaz, B., "Forced Vibration Analysis of Functionally Graded Beams Using Nonlocal Elasticity", Composite Structures, Vol. 105, 2013, pp. 227-239. DOI:10.1016/j. compstruct.2013.05.006
  17. Rahmani, O. and Pedram, O., "Analysis and Modeling the Size Effect on Vibration of Functionally Graded Nanobeams Based on Nonlocal Timoshenko Beam Theory", International Journal of Engineering Science, Vol. 77, 2014, pp. 55-70. DOI:10.1016/j.ijengsci.2013.12.003
  18. Zenkour, A. M. and Abouelregal, A. E., "Vibration of FG Nanobeams Induced by Sinusoidal Pulse-heating via a Nonlocal Thermoelastic Model", Acta Mechanica, Vol. 225, No. 12, 2014, pp. 3409-3421. DOI:10.1007/s00707-014-1146-9
  19. Ebrahimi, F., Ghadiri, M., Salari, E., Hoseini, S. A. H. and Shaghaghi, G. R. "Application of the Differential Transformation Method for Nonlocal Vibration Analysis of Functionally Graded Nanobeams", Journal of Mechanical Science and Technology, Vol. 29, 2015, pp. 1207-1215. DOI:10.1007/s12206-015-0234-7
  20. Ebrahimi, F. and Salari, E., "A Semi-analytical Method for Vibrational and Buckling Analysis of Functionally Graded Nanobeams Considering the Physical Neutral Axis Position", CMES: Computer Modeling in Engineering & Sciences, Vol. 105, 2015, pp. 151-181. DOI:10.3970/cmes.2015.105.151
  21. Zenkour, A. M. and Abouelregal, A. E., "Thermoelastic Interaction in Functionally Graded Nanobeams Subjected to Time-dependent heat Flux", Steel and Composite Structures, Vol. 18, No. 4, 2015, pp. 909-924. DOI: 10.12989/ scs.2015.18.4.909
  22. Ansari, R., Pourashraf, T. and Gholami, R., "An Exact Solution for the Nonlinear Forced Vibration of Functionally Graded Nanobeams in Thermal Environment Based on Surface Elasticity Theory", Thin-Walled Structures, Vol. 93, 2015, pp. 169-176. DOI:10.1016/j.tws.2015.03.013
  23. Rahmani, O. and Jandaghian, A. A., "Buckling Analysis of Functionally Graded Nanobeams Based on a Nonlocal Third-order Shear Deformation Theory", Applied Physics A, Vol. 119, 2015, pp. 1019-1032. DOI:10.1007/s00339-015- 9061-z
  24. Ebrahimi, F. and Salari, E., "Thermal Buckling and Free Vibration Analysis of Size Dependent Timoshenko FG Nanobeams in Thermal Environments", Composite Structures, Vol. 128, 2015, pp. 363-380. DOI:10.1016/j. compstruct.2015.03.023
  25. Zenkour, A. M. and Sobhy, M., "A Simplified Shear and Normal Deformations Nonlocal Theory for Bending of Nanobeams in Thermal Environment", Physica E, Vol. 70, 2015, pp. 121-128. DOI:10.1016/j.physe.2015.02.022
  26. Mashat, D. S., Zenkour, A. M. and Sobhy, M., "Investigation of Vibration and Thermal Buckling of Nanobeams Embedded in an Elastic Medium Under Various Boundary Conditions", Journal of Mechanics, Vol. 32, No. 3, 2016, pp. 277-287. DOI:10.1017/jmech.2015.83
  27. Doroushi, A., Eslami, M. R. and Komeili, A. "Vibration Analysis and Transient Response of an FGPM Beam Under Thermo-electro-mechanical Loads Using Higherorder Shear Deformation Theory", Journal of Intelligent Material Systems and Structures, Vol. 22, 2011, pp. 231-243. DOI:10.1177/1045389X11398162
  28. Kiani, Y., Rezaei, M., Taheri, S. and Eslami, M. R., "Thermo-electrical Buckling of Piezoelectric Functionally Graded Material Timoshenko Beams", International Journal of Mechanics and Materials in Design, Vol. 7, 2011, pp. 185-197. DOI:10.1007/s10999-011-9158-2
  29. Komijani, M., Kiani, Y., Esfahani, S. E. and Eslami, M. R., "Vibration of Thermo-electrically Postbuckled Rrectangular Functionally Graded Piezoelectric Beams", Composite Structures, Vol. 98, 2013, pp. 143-152. DOI:10.1016/j.compstruct.2012.10.047
  30. Lezgy-Nazargah, M., Vidal, P. and Polit, O., "An Efficient Finite Element Model for Static and Dynamic Analyses of Functionally Graded Piezoelectric Beams", Composite Structures, Vol. 104, 2013, pp. 71-84. DOI:10.1016/j. compstruct.2013.04.010
  31. Shegokar, N. L. and Lal, A., "Stochastic Finite Element Nonlinear Free Vibration Analysis of Piezoelectric Functionally Graded Materials Beam Subjected to Thermopiezoelectric Loadings with Material Uncertainties", Meccanica, Vol. 49, No. 5, 2014, pp. 1039-1068. DOI:10.1007/ s11012-013-9852-2
  32. Touratier, M., "An Efficient Standard Plate Theory", International Journal of Engineering Science, Vol. 29, 1991, pp. 901-916. DOI:10.1016/0020-7225(91)90165-Y
  33. Soldatos, K. P., "A Transverse Shear Deformation Theory for Homogeneous Monoclinic Plates", Acta Mechanica, Vol. 94, No. 3-4, 1992, pp. 195-220. DOI:10.1007/ BF01176650
  34. Reddy, J. N., "Nonlocal Theories for Bending, Buckling and Vibration of Beams", International Journal of Engineering Science, Vol. 45, No. 2, 2007, pp. 288-307. DOI:10.1016/j. ijengsci.2007.04.004
  35. Eringen, A. C. and Edelen, D. G. B., "On Nonlocal Elasticity", International Journal of Engineering Science, Vol. 10, No. 3, 1972, pp. 233-248. DOI:10.1016/0020- 7225(72)90039-0
  36. Eringen, A. C., "Nonlocal Polar Elastic Continua", International Journal of Engineering Science, Vol. 10, No. 1, 1972, pp. 1-16. DOI:10.1016/0020-7225(72)90070-5
  37. Eringen, A. C., "On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves", Journal of Applied Physics, Vol. 54, No. 9, 1983, pp. 4703-4710. DOI:10.1063/1.332803

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