Abstract
Dispersion of elastic waves in a thin orthotropic cylindrical shell is considered, within the framework of classical 2D Kirchhoff-Love theory. In contrast to direct multi-parametric analysis of the lowest propagating modes, an alternative robust approach is proposed that simply requires evaluation of the evanescent modes (quasi-static edge effect), which, at leading order, do not depend on vibration frequency. A shortened dispersion relation for the propagating modes is then derived by polynomial division and its accuracy is numerically tested against the full Kirchhoff-Love dispersion relation. It is shown that the same shortened relation may be also obtained from a refined dynamic version of the semi-membrane theory for cylindrical shells. The presented results may be relevant for modelling various types of nanotubes which, according to the latest experimental findings, possess strong material anisotropy.
Highlights
A fresh interest in mechanics of thin elastic shells has emerged in the last few decades due to advanced applications in nanotechnology, e.g. see [1, 2, 3, 4, 5]
This paper presents a low-frequency analysis of the propagating modes in an orthotropic cylindrical shell
The investigation is partly motivated by recent experimental findings indicating that carbon and oxidic nanotubes possess strong anisotropic material properties
Summary
A fresh interest in mechanics of thin elastic shells has emerged in the last few decades due to advanced applications in nanotechnology, e.g. see [1, 2, 3, 4, 5]. In [10] multi-walled carbon nanotube mechanical properties are determined through atomic force microscopy and it is found that for ordered arcgrown tubes the radial elastic constant is roughly one third of the axial constant This result is well expected because of strong anisotropy of graphite [11]. Amended hypotheses in the aforementioned semi-membrane shell theory are formulated on the basis of two-term expansions for the eigenforms As it might be expected, the variationally reduced PDE following from the amended hypotheses supports the same shortened dispersion relation as that developed in the previous section. This PDE seemingly has a potential to be a useful model for tackling various modern problems in anisotropic shell dynamics
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