Abstract:

In contrast to an acoustical waveguide the distribution of characteristics of normal modes with respect to the cross section in elastic waveguides is strongly dependent on frequency. Such dependence gives rise to several interesting wave phenomena, which take place in inhomogeneous structures. One of them, namely, energy trapping, is quantitatively and qualitatively considered in this report. In terms of the theory of elastic waveguides, this phenomenon manifests itself in an anomaly of the frequency functions of the reflection (transmission) coefficients of energy in the composite waveguides. These functions are calculated for both in-plane and flexural motions in waveguides consisting of two semi-infinite layers with equal thickness. The results are systematized with respect to the ratio of wave impedances of the layers. The frequency bands where the energy trapping is effective are determined. The dependence of these bands on the mechanical characteristics of materials is different for the in-plane and flexural waves. The mechanism of redistribution of energy among the incident and reflected waves is shown. The function of the normal mode with opposite signs of phase and group velocities is illustrated.