TY - JOUR
T1 - Localized waves at a line of dynamic inhomogeneities
T2 - General considerations and some specific problems
AU - Mishuris, Gennady S.
AU - Movchan, Alexander B.
AU - Slepyan, Leonid I.
N1 - Funding Information:
ABM would like to acknowledge the support of the EPSRC Program grant EP/L024926/1 . GM acknowledges financial support from the ERC Advanced Grant ”Instabilities and nonlocal multiscale modelling of materials”, ERC-2013-ADG-340561-INSTABILITIES. GM is also thankful to the Royal Society for the Wolfson Research Merit Award.
Funding Information:
ABM would like to acknowledge the support of the EPSRC Program grant EP/L024926/1. GM acknowledges financial support from the ERC Advanced Grant ?Instabilities and nonlocal multiscale modelling of materials?, ERC-2013-ADG-340561-INSTABILITIES. GM is also thankful to the Royal Society for the Wolfson Research Merit Award. GM and LS are thankful to the Isaac Newton Institute for Mathematical Sciences, Cambridge, for Simon's Fellowship. All authors also would like to thank the Isaac Newton Institute for the support and hospitality during the programme ?Bringing pure and applied analysis together via the Wiener-Hopf technique, its generalisations and applications? where work on this paper was mainly completed. The programme was supported by EPSRC grant EP/R014604/1.
Funding Information:
GM and LS are thankful to the Isaac Newton Institute for Mathematical Sciences, Cambridge, for Simon’s Fellowship. All authors also would like to thank the Isaac Newton Institute for the support and hospitality during the programme ”Bringing pure and applied analysis together via the Wiener-Hopf technique, its generalisations and applications” where work on this paper was mainly completed. The programme was supported by EPSRC grant EP/R014604/1 .
Publisher Copyright:
© 2020 Elsevier Ltd
PY - 2020/5/1
Y1 - 2020/5/1
N2 - 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.
AB - 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.
KW - free and forced waves
KW - Green's functions
KW - integral transforms
KW - structured solids
UR - http://www.scopus.com/inward/record.url?scp=85079690281&partnerID=8YFLogxK
U2 - 10.1016/j.jmps.2020.103901
DO - 10.1016/j.jmps.2020.103901
M3 - Article
AN - SCOPUS:85079690281
SN - 0022-5096
VL - 138
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
M1 - 103901
ER -