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

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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.


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


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