Wave propagation in an elastic longitudinally inhomogeneous cylinder

The problem of the propagation of stationary waves in an elastic waveguide that is inhomogeneous along its length is examined. A mathematical foundation is given for the algorithm for solving the problem to determine the wave fields in piecewise-homogeneous waveguides. Results of computations of the wave reflection and transmission coefficients in a strip with two interface boundaries of the material properties are presented. A relation is obtained between the extremal properties of these coefficients and the different resonance phenomena originating in a longitudinally inhomogeneous waveguide.