THE INFLUENCE OF THE SYMMETRY OF OSCILLATIONS AND THE RATIO OF THE HALF-LAYER WIDTHS ON THE TRANSPARENCY OF THE BOUNDARY IN A STEPPED WAVEGUIDE

Abstract

The article is devoted to the analysis of the scattered field at the boundary of a stepped waveguide formed by the rigid contact of two half-layers with the same mechanical characteristics, but with different widths. The wave field is excited by the first normal wave propagating from infinity in the narrower half-layer. Mathematical difficulties of the posed boundary problem are due to the presence of a local singularity in the stresses at the point of change of the boundary conditions at the boundary of the two hemispheres. The solution is built by the superposition method, which allows taking into account the local singularity due to the asymptotic features of the unknowns. The quality criterion of the obtained solution was the control of the accuracy of the fulfillment of the conjugation conditions at the boundary of the two half-layers. The main attention in the work is focused on the established conditions for changing the transpar[1]ency of the boundary depending on the frequencies, the symmetry of the oscillations, and the ratio of the half-layer widths. It was shown in the work that for both symmetric and antisymmetric oscillations of a stepped waveguide, there are frequency ranges in which the transparency of the boundary changes significantly. For both types of symmetry, in the frequency range up to the critical frequency for the third propagating normal wave, there are two frequency ranges in which the transparency of the boundary increases rather sharply. The frequencies at which local energy maxima are observed in the reflected field are different for symmetric and anti-symmetric oscillations. For symmetric oscillations, the first energy maximum in the reflected field is observed at the frequency when only one wave can propagate in both half-layers. This effect is due to the increase in the role of inhomogeneous waves in the transmitted field. The second energy maximum in the reflected field is due to the transformation of the energy of the incident wave into propagating waves of higher orders. In the case of antisymmetric oscillations, both maxima are due to the energy features of propa[1]gating waves of higher orders. The quality of energy resonance in the reflected field was also significantly dependent on the symmetry of the oscillations. The established features of the scattered field make it possible to develop recommenda[1]tions for controlling the transparency of the boundary in a stepped waveguide