A robust approach for analysing dispersion of elastic waves in an orthotropic cylindrical shell

Kaplunov

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.

• Acceptance Date: Apr 19, 2017
• Publication Date: Aug 4, 2017
• Journal: Journal of Sound and Vibration
• Print ISSN: 0022-460X
• Publisher: Elsevier
• Pages: 23 - 35
• DOI: https://doi.org/10.1016/j.jsv.2017.04.028
• Keywords: Thin-shell; Vibration; Anisotropy; Nanotube; Elastic; Low-frequency
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0022460X17303541