Structural Engineering and Mechanics

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Dynamic buckling of FGM viscoelastic nano-plates resting on orthotropic elastic medium based on sinusoidal shear deformation theory

  • Arani, A. Ghorbanpour (Faculty of Mechanical Engineering, University of Kashan) ;
  • Cheraghbak, A. (Faculty of Mechanical Engineering, University of Kashan) ;
  • Kolahchi, R. (Faculty of Mechanical Engineering, University of Kashan)
  • Received : 2015.09.19
  • Accepted : 2016.09.09
  • Published : 2016.11.10
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Abstract

Sinusoidal shear deformation theory (SSDT) is developed here for dynamic buckling of functionally graded (FG) nano-plates. The material properties of plate are assumed to vary according to power law distribution of the volume fraction of the constituents. In order to present a realistic model, the structural damping of nano-structure is considered using Kelvin-Voigt model. The surrounding elastic medium is modeled with a novel foundation namely as orthotropic visco-Pasternak medium. Size effects are incorporated based on Eringen'n nonlocal theory. Equations of motion are derived from the Hamilton's principle. The differential quadrature method (DQM) in conjunction with Bolotin method is applied for obtaining the dynamic instability region (DIR). The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, orthotropic visco-Pasternak foundation, power index of FG plate, structural damping and boundary conditions on the dynamic instability of system. The results are compared with those of first order shear deformation theory and higher-order shear deformation theory. It can be concluded that the proposed theory is accurate and efficient in predicting the dynamic buckling responses of system.

Keywords

Acknowledgement

Supported by : University of Kashan

References

  1. Amabili, M. (2004), "Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments", Comput. Struct., 82, 2587-2605. https://doi.org/10.1016/j.compstruc.2004.03.077
  2. Bolotin, V.V. (1964), "The dynamic stability of elastic systems. in: the dynamic stability of elastic systems", Holden-Day, San Francisco.
  3. Chakraverty, S. and Behera L. (2015), "Small scale effect on the vibration of non-uniform nanoplates", Struct. Eng. Mech., 55, 495-510. https://doi.org/10.12989/sem.2015.55.3.495
  4. Chien, R.D. and Chen, C.S. (2006), "Nonlinear vibration of laminated plates on an elastic foundation", Thin Wall. Struct., 44, 852-860. https://doi.org/10.1016/j.tws.2006.08.016
  5. Ebraheem, O., Ashraf, A. and Zenkour, M. (2013), "Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium", Compos. Struct., 105, 163-172. https://doi.org/10.1016/j.compstruct.2013.04.045
  6. Ebrahimi, F. and Salari, E. (2015), "Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment", Acta Astronaut., 113, 29-50. https://doi.org/10.1016/j.actaastro.2015.03.031
  7. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803
  8. Ghorbanpour Arani, A., Kolahchi, R., Mosallaie Barzoki, A.A., Mozdianfard, M.R. and Noudeh Farahani, S.M. (2012), "Elastic foundation effect on nonlinear thermo-vibration of embedded double-layered orthotropic grapheme sheets using differential quadrature method", Inst. Mech. Eng. Part C, J. Mech. Eng. Sci., 227, 862-879.
  9. Ghorbanpour Arani, A., Mosallaie Barzoki, A.A., Kolahchi, R. and Loghman, A. (2011), "Pasternak foundation effect on the axial and torsional waves propagation in embedded DWCNTs using nonlocal elasticity cylindrical shell theory", J. Mech. Sci. Tech., 25, 2385-2391. https://doi.org/10.1007/s12206-011-0712-5
  10. Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011a), "A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates", Int. J. Mech. Sci., 53, 11-22. https://doi.org/10.1016/j.ijmecsci.2010.10.002
  11. Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011b), "Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure", Compos. Struct., 93, 722-735. https://doi.org/10.1016/j.compstruct.2010.08.007
  12. Karlicic, D., Adhikari, S., Murmu, T. and Cajic, M. (2014), "Exact closed-form solution for non-local vibration and biaxial buckling of bonded multi-nanoplate system", Compos. Part B: Eng., 66, 328-339. https://doi.org/10.1016/j.compositesb.2014.05.029
  13. Kutlu, A. and Omurtag, M.H. (2012), "Large deflection bending analysis of elliptic plates on orthotropic elastic foundation with mixed finite element method", Int. J. Mech. Sci., 65, 64-74 https://doi.org/10.1016/j.ijmecsci.2012.09.004
  14. Lanhe, W., Hongjun, W. and Daobin, W. (2007), "Dynamic stability analysis of FGM plates by the moving least squares differential quadrature method", Compos. Struct., 77, 383-394. https://doi.org/10.1016/j.compstruct.2005.07.011
  15. Lei, J., He, Y., Zhang, B., Gan, Z. and Zeng, P.C. (2013a), "Bending and vibration of functionally graded sinusoidal microbeams based on the strain gradient elasticity theory", Int. J. Eng. Sci., 72, 36-52. https://doi.org/10.1016/j.ijengsci.2013.06.012
  16. Lei, Y., Adhikari, S. and Friswell, M.I. (2013b), "Vibration of nonlocal Kelvin-Voigt viscoelastic damped Timoshenko beams", Int. J. Eng. Sci., 66, 1-13.
  17. Li, J.J. and Cheng, C.J. (2005), "Differential quadrature method for nonlinear vibration of orthotropic plates with finite deformation and transverse shear effect", J. Sound Vib., 281, 295-309. https://doi.org/10.1016/j.jsv.2004.01.016
  18. Lu, P., Zhang, P.Q., Lee, H.P., Wang, C.M. and Reddy, J.N. (2007), "Non-local elastic plate theories", Proc. R. Soc. A, 463, 3225-3240. https://doi.org/10.1098/rspa.2007.1903
  19. Malekzadeh, P. (2008), "Nonlinear free vibration of tapered Mindlin plates with edges elastically restrained against rotation using DQM", Thin Wall. Struct., 46.11-26. https://doi.org/10.1016/j.tws.2007.08.016
  20. Nami, M.R. and Janghorban, M. (2013), "Static analysis of rectangular nanoplates using trigonometric shear deformation theory based on nonlocal elasticity theory", Beilstein J. Nanotechnol., 4, 968-973. https://doi.org/10.3762/bjnano.4.109
  21. Nami, M.R. and Janghorban, M. (2014), "Static analysis of rectangular nanoplates using exponential shear deformation theory based on strain gradient elasticity theory", Iran. J. Mat. Form., 1, 1-13.
  22. Narendar, S. (2011), "Buckling analysis of micro/nano-scale plates based on two-variable refined plate theory incorporating nonlocal scale effects", Compos. Struct., 93, 3093-3103. https://doi.org/10.1016/j.compstruct.2011.06.028
  23. Wang, Y.Z. and Li, F.M. (2012), "Static bending behaviors of Nanoplate embedded in elastic matrix with small scale effects", Mech. Res.Commun., 41, 44-48. https://doi.org/10.1016/j.mechrescom.2012.02.008
  24. Zenkour, A.M. (2009), "The refined sinusoidal theory for FGM plates on elastic foundations", Int. J. Mech. Sci., 51, 869-880. https://doi.org/10.1016/j.ijmecsci.2009.09.026

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