Perturbation Solution of a Hyperbolic Equation Governing Longitudinal Wave Propagation in Certain Nonuniform Bars

A perturbation method is used to analyze wave propagation in a class of variable-section bars that can be treated as a perturbation of a uniform bar. The hyperbolic equation of motion is shown to constitute a singular perturbation problem. An existing perturbation method is modified and extended to obtain a uniformly valid asymptotic expansion of the solution.