Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix

Samir Belmahi, Mohamed Zidour, Mustapha Meradjah, Tayeb Bensattalah and Ahmed Dihaj

Abstract

In this study, we investigate the vibration of single-walled carbon nanotubes embedded in a polymeric matrix using nonlocal elasticity theories with account arbitrary boundary conditions effects. A Winkler type elastic foundation is employed to model the interaction of nanobeam and the surrounding elastic medium. Influence of all parameters such as nonlocal small-scale effects, Winkler modulus parameter, vibration mode and aspect ratio of nanobeam on the vibration frequency are analyzed and discussed. The mechanical properties of carbon nanotubes and polymer matrix are treated and an analytical solution is derived using the governing equations of the nonlocal Euler-Bernoulli beam models. Solutions have been compared with those obtained in the literature and The results obtained show that the non-dimensional natural frequency is significantly affected by the small-scale coefficient, the vibrational mode number and the elastic medium.

Key Words

non-local; frequency; Winkler; boundary conditions; nanobeam

Address

Samir Belmahi: 1) University of Ibn Khaldoun,PB 78 Zaaroura, 14000 Tiaret, Algeria 2) Laboratory of Materials and Hydrology, University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria Mohamed Zidour and Tayeb Bensattalah: 1) University of Ibn Khaldoun,PB 78 Zaaroura, 14000 Tiaret, Algeria 2) Laboratory of Geomatics and Sustainable Development, University of Ibn Khaldoun Tiaret, Algeria Mustapha Meradjah and Ahmed Dihaj: Laboratory of Materials and Hydrology, University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria

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