Vibration analysis of multi-walled carbon nanotubes embedded in elastic medium
Pattabhi R. BUDARAPU1,*(),Sudhir Sastry YB2,Brahmanandam JAVVAJI3,D. Roy MAHAPATRA3
1. Institute of Structural Mechanics, Bauhaus University of Weimar, Weimar 99423, Germany 2. Deptarment of Aeronautical Engineering, Institute of Aeronautical Engineering, Hyderabad 500043, India 3. Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India
We propose a method to estimate the natural frequencies of the multi-walled carbon nanotubes (MWCNTs) embedded in an elastic medium. Each of the nested tubes is treated as an individual bar interacting with the adjacent nanotubes through the inter-tube Van der Waals forces. The effect of the elastic medium is introduced through an elastic model. The mathematical model is finally reduced to an eigen value problem and the eigen value problem is solved to arrive at the inter-tube resonances of the MWCNTs. Variation of the natural frequencies with different parameters are studied. The estimated results from the present method are compared with the literature and results are observed to be in close agreement.
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