Real natural frequencies and resonance wave localization in an elastic waveguide with a horizontal crack

摘要

Previously developed semi-analytical methods for evaluating elastodynamic diffraction by a horizontal crack in a layer are used to analyze the mechanisms of normal mode transmission, reflection and blocking. It is shown that resonance blocking is accompanied by energy localization near the crack. The dependence of transmission and reflection coefficients on frequency and the size and depth of the crack are analyzed, along with spectral points. The present paper focuses on a search for pure real spectral points and the respective eigenforms of the motion. Some examples of pure real resonance frequencies have been found. The associated eigenforms exhibit strong localization of oscillation near the crack at the resonance frequencies.