Sharp stopping of time-harmonic wave transmission in elastic structures with defects is considered as a manifestation of the well-known trapped mode effect. It is associated with natural resonance poles lying close to the real axis in the complex frequency plane. Nonresonant wave blocking may also occur due to antiphase combination of the incident and scattered waves. The present paper is aimed to give an insight into such phenomena using an analytically based computer model which strictly takes into account all wave interactions in a cracked structure. Numerical examples are restricted to the case of a line horizontal crack in a half-plane or in a layer (2D in-plane motion), that is, nevertheless, quite enough to demonstrate two kinds of the Rayleigh wave stopping mechanisms (resonant and nonresonant) as well as a possibility of pure real natural resonance frequencies and of a full blocking effect with energy localization.

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The authors deal with low-cost computer implementation of the integral equation method in application to wave excitation, propagation and diffraction phenomena in solids. Typically these are frequency domain problems of seismic and physical acoustics and of nondestructive testing. Fast codes are obtained basing on analytical extracting and taking account of singular and slowly converging components of the solution beforehand. The present paper gives ideas of several such approaches, which have already proved their efficiency in practical applications. More details including numerical examples and discussion of similar methods known from the literature can be found in the surveyed papers.1–12

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Energy vortices in time-averaged energy flows of time-harmonic fields are considered. The purpose of the paper is to verify the supposition that the energy flux along an elastic waveguide with an obstacle is blocked completely at the stop frequencies by the vortices. It is hoped that this work will draw attention to the analogy between energy and fluid flows which is potentially fruitful for understanding various wave phenomena. The normal-mode diffraction by a surface punch on an elastic layer is taken as an example. For tracing energy streamlines in the near field up to the obstacle, a special efficient semianalytical approach has been developed. To illustrate the stated supposition, plots of transmission coefficients versus frequency and figures of the near-field streamline structures are given.