Asymptotic approximations for vibrational modes of helices

T. Tarnopolskaya, F.R. de Hoog

Abstract


The free vibrations in the plane normal to the helical axis are studied under the assumption that the helical pitch is small. Asymptotic approximations for eigenvalues and eigenfunctions are derived for both small and large numbers of helical turns. The analytic approximations reveal interesting features of helix vibrations and the connection between the vibrational modes of a helix and the flexural modes of a curved beam. Comparison with numerical calculations shows that the approximations derived cover with sufficient accuracy a wide range of number of helical turns.

Full Text:

PDF


DOI: http://dx.doi.org/10.21914/anziamj.v42i0.651



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.