NONLOCAL FINITE ELEMENT ANALYSIS FOR FREE VIBRATION OF ELASTICALLY SUPPORTED NANOBEAMS

Resumo

Nanobeams are nanoscale structures extensively used in nanotechnology applications. Due
to the small scale effect, this nanostructures cannot be accurately modelled by traditional elastic theory.
To overcome this difficulty, several continuous models including the material length scale effect were
developed, like nonlocal elasticity theory. In this paper, a nonlocal finite element model for elastically
supported Euler-Bernoulli (EBT) and Timoshenko (TBT) nanobeams is developed. Nonlocal differential
constitutive equations of Eringen are considered to account for the small scale effect. The stiffness and
mass matrices for a two-node nonlocal beam element with two degrees of freedom per node are obtained
based upon Hamilton’s principle. The influence of nonlocal parameter, slenderness ratio and support
stiffness on the free vibration characteristics is investigated. Numerical results obtained are discussed
and compared with results obtained by other researchers.