On wave equations for elastic rods

Journal article, 2000

The derivation of one-dimensional wave equtions for axially symmetric waves in elastic rods is discussed. By series expansions in the radial coordinate a hierarchy of wave equations are derived. As the lowest reasonable approximation the usual simple wave equation for the rod is recovered. At the next level a fourth order wave equation is obtained. The dispersion relation and the displacements for these approximations and for Love's equation are compared with the lowest branch of the exact Pochhammer-Chree equation. An excitation with a shear force is also solved and compared among the theories.