Axial vibration analysis of nanorods (carbon nanotubes) embedded in an elastic medium using nonlocal elasticity |
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| Institution: | 1. Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, 410054 Saratov, Politehnicheskaya 77, and Cybernetic Institute, National Research Tomsk Polytechnic University, 634050 Tomsk, Lenin Avenue, 30, Russian Federation;2. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego St., 90-924 Lodz, and Department of Vehicles, Warsaw University of Technology, 84 Narbutta Str., 02-524 Warszawa, Poland;3. Department of Mathematics and Modeling, Saratov State Technical University, Politehnicheskaya 77, 410054 Saratov, Russian Federation |
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| Abstract: | The axial vibration of single walled carbon nanotube embedded in an elastic medium is studied using nonlocal elasticity theory. The nonlocal constitutive equations of Eringen are used in the formulations. The effect of various parameters like stiffness of elastic medium, boundary conditions and nonlocal parameters on the axial vibration of nanorods is discussed. It is obtained that, the axial vibration frequencies of the embedded nanorods are highly over estimated by the classical continuum rod model which ignores the effect of small length scale. |
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