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

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

*Awdur cyfatebol y gwaith hwn

Allbwn ymchwil: Cyfraniad at gyfnodolynErthygladolygiad gan gymheiriaid


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.

Iaith wreiddiolSaesneg
Rhif yr erthygl103901
CyfnodolynJournal of the Mechanics and Physics of Solids
Dyddiad ar-lein cynnar12 Chwef 2020
Dynodwyr Gwrthrych Digidol (DOIs)
StatwsCyhoeddwyd - 01 Mai 2020

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