# Free Vibrations of Stepped Nano-Beams

Free Vibrations of Stepped Nano-Beams

Jaan Lellep Artur Lenbaum

Institute of Mathematics and Statistics, University of Tartu, Estonia

Page:
716-725
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DOI:
https://doi.org/10.2495/CMEM-V6-N4-716-725
N/A
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Accepted:
N/A
| | Citation

OPEN ACCESS

Abstract:

Free vibrations of beams and rods made of nano-materials are investigated. It is assumed that the dimensions of cross sections of nano-beams are piecewise constant and that the beams are weakened with cracks. It is expected that the vibrational behaviour of the nano-material can be described within the non-local theory of elasticity and that the crack induces additional local compliance. The latter is coupled with the stress intensity coefficient at the crack tip.

Keywords:

beam, crack, non-local elasticity, nano-material, vibration

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