Size-dependent free flexural vibration behavior of functionally graded nanoplates

S. Natarajan, S. Chakraborty, M. Thangavel, S. Bordas, T. Rabczuk

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227 Citations (Scopus)


In this paper, size dependent linear free flexural vibration behavior of functionally graded (FG) nanoplates are investigated using the iso-geometric based finite element method. The field variables are approximated by non-uniform rational B-splines. The nonlocal constitutive relation is based on Eringen's differential form of nonlocal elasticity theory. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG plate are computed using Mori-Tanaka homogenization scheme. The accuracy of the present formulation is demonstrated considering the problems for which solutions are available. A detailed numerical study is carried out to examine the effect of material gradient index, the characteristic internal length, the plate thickness, the plate aspect ratio and the boundary conditions on the global response of the FG nanoplate. From the detailed numerical study it is seen that the fundamental frequency decreases with increasing gradient index and characteristic internal length.

Original languageEnglish
Pages (from-to)74-80
Number of pages7
JournalComputational Materials Science
Publication statusPublished - 2012 Dec


  • Eringen's gradient elasticity
  • Finite element
  • Functionally graded
  • Internal length
  • Mori-Tanaka
  • Partition of unity

ASJC Scopus subject areas

  • General Computer Science
  • General Chemistry
  • General Materials Science
  • Mechanics of Materials
  • General Physics and Astronomy
  • Computational Mathematics


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