APPROXIMATE DETERMINATION OF DISPERSION RELATIONS AND DISPLACEMENT FIELDS ASSOCIATED WITH ELASTIC WAVES IN BARS: Method Based on Matrix Formulation of Hamiltons Principle

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 Hamiltonʹs 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.