الفهرس 
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Abstract
ABSTRACT
In this thesis, natural frequencies of 1D nanostructures have been determined using the dynamic stiffness matrix method. The analysis is based on the Bernoulli-Euler theory. The nanoscale analysis is based on Eringen’s nonlocal elasticity theory. In this work, two models have been investigated; longitudinal vibration of multi-stepped nanorod embedded in several elastic media and lateral vibration of multi-stepped nanobeam. Verification of the results have been presented by carrying out a comparison with published results and good agreement is found.
In the first model, the case of two-segment nanorod embedded in two elastic media has been deeply investigated. Two boundary conditions: clamped-clamped (C-C) and clamped-free (C-F) have been studied. Furthermore, the effect of nonlocal parameter, the first elastic media stiffness and the elastic media stiffness ratios have been examined. The results showed that the dimensionless natural frequencies are proportional to the elastic media stiffness and the elastic media stiffness ratio. Furthermore, the dimensionless natural frequencies are found to be inversely proportional to the nonlocal parameter. The nonlocal parameter effect is minor at low modes and increases at high modes.