Abstract
A numerical investigation of the reflection and transmission of axial waves at stepped nanorods is presented. The scale dependent doublet mechanics theory is used in the analysis. The main difference of the doublet mechanics from other scale dependent models (stress gradient, strain gradient and couple stress theories) is its direct dependence to the micro/nano structure of the solid. Scale parameter is directly related to atomic structure of the material in doublet mechanics theory and it is assumed as carbon-carbon bond length in the present study. However, identification of scale parameters in other scale dependent theories is difficult compared to doublet mechanics theory. Governing equations of stepped nanorods are derived in the framework of doublet mechanics using the Hamilton Principle. The numerical results predicted by doublet mechanics are shown and compared with the classical elasticity.
Highlights
In the last two decades, carbon nanotubes have been attractive due to their excellent mechanical, chemical and thermal properties so they have been used for designing of new nano-electronics devices, nanocomposites, nano electro-mechanical systems (NEMS)
Love’s theory which takes into account the kinetic energy due to lateral motion was used in order to calculate the transmission and reflection coefficients of a stepped rod by Seemann [3]
Wave reflection and transmission of carbon nanotubes have been analysed by using finite difference time domain method [9]
Summary
In the last two decades, carbon nanotubes have been attractive due to their excellent mechanical, chemical and thermal properties so they have been used for designing of new nano-electronics devices, nanocomposites, nano electro-mechanical systems (NEMS). In DM theory, atomic distance of elastic material is directly used as an intrinsic length scale parameter This makes DM model more physical compared to other size-dependent continuum models. Expressions for the propagation, reflection and transmission matrices are derived for waves in stepped nanorods by using DM and elementary rod theories. These reflection and transmission matrices can provide a concise and systematic approach to dynamic analysis of (2). Each node and their neighboring nodes are separated by doublet distance where is the elongation micro stress in the α doublet and is the axial micro strain in doublet and is the tension micro modulus between nodes α and β. It should be noted that doublet term depends on the number of Taylor series expansion in the solid
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