Wave motions in non-uniform one-dimensional waveguides

Wave approach is used in the analysis of wave motions in one-dimensional non-uniform waveguides. Under assumptions of constant wave velocity and no wave conversion, one class of non-uniform rods including four different profiles results. The obtained results indicate kinetic energy is preserved as constant and wave amplitude is inversely proportional to square root of the cross-section area of the rod. The obtained spectrograms and dispersion relations indicate that under certain conditions there exists a cut-off frequency, below which waves do not propagate along the non-uniform waveguides. The conclusions are similar for high frequency longitudinal wave motions of arbitrary non-uniform rods. For a Euler-Bernoulli beam with exponent variation in geometry and material variation, the bending wave motion is also analyzed including its cut-off frequencies.