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Free axial vibration of nanorods with elastic medium interaction based on nonlocal elasticity and Rayleigh model
Institution:1. CEA, DEN, DANS, DM2S, SEMT, Laboratoire d’Études de Mécanique Sismique, F-91191 Gif-sur-Yvette, France;2. LMT, ENS Cachan, CNRS, Université Paris-Saclay, 61 avenue du Président Wilson, F-94230 Cachan, France;1. Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, United States;2. Department of Civil Engineering and Computer Science, University of Rome “Tor Vergata”, Via del Politecnico 1, 00133 Rome, Italy;3. Université Pierre et Marie Curie, Institut D’Alembert, UMR 7190 CNRS, 4 Place Jussieu, 75252 Paris Cedex 05, France;1. DEN-Service d''études mécaniques et thermiques (SEMT), CEA, Université Paris-Saclay, F-91191, Gif-sur-Yvette, France;2. LMT, ENS Cachan, CNRS, Université Paris-Saclay, 61 avenue du Président Wilson, F-94230 Cachan, France
Abstract:In this paper, the free axial vibration of single walled carbon nanorod embedded in an elastic medium is investigated by the use of Rayleigh model. The stress gradient model introduced by Eringen is used to formulate the governing equations. Explicit expressions are derived for eigenfrequencies of fixed-fixed and fixed-free boundary conditions.
Keywords:Axial vibration  Carbon nanorod  Nonlocal elastic rod  Rayleigh model
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