Localized waves at a line of dynamic inhomogeneities: General considerations and some specific problems

Gennady S. Mishuris, Alexander B. Movchan, Leonid I. Slepyan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We consider a body, homogeneous or periodic, equipped with a structure composed of dynamic inhomogeneities uniformly distributed along a line, and study free and forced sinusoidal waves (Floquet - Bloch waves for the discrete system) in such a system. With no assumption concerning the wave nature, we show that if the structure reduces the phase velocity, the wave localizes exponentially at the structure line, and the latter can expand the transmission range in the region of long waves. Based on a general solution presented in terms of non-specified Green's functions, we consider the wave localization in some continuous elastic bodies and a regular lattice. We determine the localization-related frequency ranges and the localization degree in dependence on the frequency. While 2D-models are considered throughout the text, the axisymmetric localization phenomenon in the 3D-space is also mentioned. The dynamic field created in such a structured system by an external harmonic force is obtained consisting of three different parts: the localized wave, a diverging wave, and non-spreading oscillations. Expressions for the wave amplitudes and the energy fluxes in the waves are presented.

Original languageEnglish
Article number103901
JournalJournal of the Mechanics and Physics of Solids
StatePublished - May 2020


FundersFunder number
Engineering and Physical Sciences Research CouncilEP/R014604/1, ERC-2013-ADG-340561-INSTABILITIES, EP/L024926/1
Royal Society
Isaac Newton Institute for Mathematical Sciences


    • Green's functions
    • free and forced waves
    • integral transforms
    • structured solids


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