APPROXIMATE DETERMINATION OF DISPERSION RELATIONS AND DISPLACEMENT FIELDS ASSOCIATED WITH ELASTIC WAVES IN BARS: Method Based on Matrix Formulation of Hamiltons Principle
✍ Scribed by S. WIDEHAMMAR; P.A. GRADIN; B. LUNDBERG
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 395 KB
- Volume
- 246
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
A method for approximate determination of dispersion relations and displacement "elds associated with elastic waves in long prismatic bars is established. The method is based on a matrix formulation of Hamilton's 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.
2001 Academic Press