Journal article

Approximate determination of Dispersion Relations and Displacement Fields Associated With Elastic Waves in Bars

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Author list: Gradin, Per;Widehammar, Svante

Publication year: 2001

Start page: 853

End page: 876

Number of pages: 24

ISSN: 0022-460X

DOI: http://dx.doi.org/10.1006/jsvi.2001.3714

View additional information: View in Web of Science


Abstract

A method for approximate determination of dispersion relations and displacement fields associated with elastic waves in long prismatic bars is established. The method is based on a matrix formulation of Hamiltons principle and utilizes co-ordinate functions to model the displacements in the bar. The method, which involves the solution of an eigenvalue problem, is suitable for use in a mathematical toolbox. It is applied to wave propagation in bars with square and circular cross-sections. The results obtained agree well with the known exact and approximate solutions. The convergence rate is illustrated by systematically changing the order of the co-ordinate functions.


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