Free vibration analysis of functionally graded rectangular nanoplates considering spatial variation of the nonlocal parameter

Ghassabı A. A., Dağ S., Ciğeroğlu E.

ARCHIVES OF MECHANICS, cilt.69, ss.105-130, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 69
  • Basım Tarihi: 2017
  • Dergi Adı: ARCHIVES OF MECHANICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.105-130
  • Anahtar Kelimeler: functionally graded materials, nanoplates, nonlocal elasticity, differential quadrature method, free vibrations, SHEAR DEFORMATION-THEORY, DIFFERENT BOUNDARY-CONDITIONS, NONLINEAR FREE-VIBRATION, WALLED CARBON NANOTUBES, TIMOSHENKO BEAM THEORY, CIRCULAR MICRO-PLATES, ISOGEOMETRIC ANALYSIS, BUCKLING ANALYSIS, ELASTICITY THEORY, NANOBEAMS
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

WE PRESENT A NEW NONLOCAL ELASTICITY-BASED ANALYSIS METHOD for free vibrations of functionally graded rectangular nanoplates. The introduced method allows taking into account spatial variation of the nonlocal parameter. Governing partial differential equations and associated boundary conditions are derived by employing the variational approach and applying Hamilton's principle. Displacement field is expressed in a unified way to be able to produce numerical results pertaining to three different plate theories, namely Kirchhoff, Mindlin, and third-order shear deformation theories. The equations are solved numerically by means of the generalized differential quadrature method. Numerical results are generated by considering simply-supported and cantilever nanoplates undergoing free vibrations. These findings demonstrate the influences of factors such as dimensionless plate length, plate theory, power-law index, and nonlocal parameter ratio upon vibration behavior.