Size-dependent free flexural vibration behavior of functionally graded nanoplates

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

Research output: Contribution to journalArticle

141 Citations (Scopus)

Abstract

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
Volume65
DOIs
Publication statusPublished - 2012 Dec 1
Externally publishedYes

Fingerprint

Free Vibration
Splines
Aspect ratio
Elasticity
Materials properties
Boundary conditions
Finite element method
vibration
Dependent
Paper size
Numerical Study
Nonlocal Elasticity
Gradient
Internal
gradients
Effective Properties
Fundamental Frequency
Elasticity Theory
Constitutive Relations
Differential Forms

Keywords

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

ASJC Scopus subject areas

  • Materials Science(all)
  • Chemistry(all)
  • Computer Science(all)
  • Physics and Astronomy(all)
  • Computational Mathematics
  • Mechanics of Materials

Cite this

Size-dependent free flexural vibration behavior of functionally graded nanoplates. / Natarajan, S.; Chakraborty, S.; Thangavel, M.; Bordas, S.; Rabczuk, Timon.

In: Computational Materials Science, Vol. 65, 01.12.2012, p. 74-80.

Research output: Contribution to journalArticle

Natarajan, S. ; Chakraborty, S. ; Thangavel, M. ; Bordas, S. ; Rabczuk, Timon. / Size-dependent free flexural vibration behavior of functionally graded nanoplates. In: Computational Materials Science. 2012 ; Vol. 65. pp. 74-80.
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