Frequency domain analysis of nonlocal rods embedded in an elastic medium

S. Adhikari, T. Murmu, M.A. McCarthy

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)


A novel dynamic finite element method is carried out for a small-scale nonlocal rod which is embedded in an elastic medium and undergoing axial vibration. Eringen's nonlocal elasticity theory is employed. Natural frequencies are derived for general boundary conditions. An asymptotic analysis is carried out. The stiffness and mass matrices of the embedded nonlocal rod are obtained using the proposed finite element method. Nonlocal rods embedded in an elastic medium have an upper cut-off natural frequency which is independent of the boundary conditions and the length of the rod. Dynamic response for the damped case has been obtained using the conventional finite element and dynamic finite element approaches. The present study would be helpful for developing nonlocal finite element models and study of embedded carbon nanotubes for future nanocomposite materials.
Original languageEnglish
Pages (from-to)33-40
Number of pages8
JournalPhysica E: Low-dimensional Systems and Nanostructures
Publication statusPublished - May 2014
Externally publishedYes


  • Nano-structure
  • Elastic medium, vibration
  • Finite element analysis
  • Nonlocal elasticity


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