Abstract
The derivation of one-dimensional wave equations for axially symmetric waves in elastic rods is discussed. By series expansions in the radial coordinate a hierarchy of wave equations is 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 problem with a shear force is also solved and compared among the theories.
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