Vibration analysis of three-layered nanobeams based on nonlocal elasticity theory

In this paper, the first investigation on free vibration analysis of three-layered nanobeams
with the shear effect incorporated in the mid-layer based on the nonlocal theory and both Euler
Bernoulli and Timoshenko beams theories is presented. Hamilton’s formulation is applied
to derive governing equations and edge conditions. In order to solve differential equations of
motions and to determine natural frequencies of the proposed three-layered nanobeams with
different boundary conditions, the generalized differential quadrature (GDQM) is used. The
effect of the nanoscale parameter on the natural frequencies and deflection modes shapes of
the three layered-nanobeams is discussed. It appears that the nonlocal effect is important
for the natural frequencies of the nanobeams. The results can be pertinent to the design and
application of MEMS and NEMS.