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.

Citation

Kaplunov. (2017). A robust approach for analysing dispersion of elastic waves in an orthotropic cylindrical shell. Journal of Sound and Vibration, 23 - 35. https://doi.org/10.1016/j.jsv.2017.04.028

• 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