TY - JOUR
T1 - Waves in elastic bodies with discrete and continuous dynamic microstructure
AU - Mishuris, Gennady S.
AU - Movchan, Alexander B.
AU - Slepyan, Leonid I.
N1 - Publisher Copyright:
© 2019 The Authors.
PY - 2020/1/10
Y1 - 2020/1/10
N2 - This paper presents a unified approach to the modelling of elastic solids with embedded dynamic microstructures. General dependences are derived based on Green’s kernel formulations. Specifically, we consider systems consisting of a master structure and continuously or discretely distributed oscillators. Several classes of connections between oscillators are studied. We examine how the microstructure affects the dispersion relations and determine the energy distribution between the master structure and microstructures, including the vibration shield phenomenon. Special attention is given to the comparative analysis of discrete and continuous distributions of the oscillators, and to the effects of non-locality and trapped vibrations. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.
AB - This paper presents a unified approach to the modelling of elastic solids with embedded dynamic microstructures. General dependences are derived based on Green’s kernel formulations. Specifically, we consider systems consisting of a master structure and continuously or discretely distributed oscillators. Several classes of connections between oscillators are studied. We examine how the microstructure affects the dispersion relations and determine the energy distribution between the master structure and microstructures, including the vibration shield phenomenon. Special attention is given to the comparative analysis of discrete and continuous distributions of the oscillators, and to the effects of non-locality and trapped vibrations. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.
KW - Dispersion relations
KW - Dynamic microstructure
KW - Green’s functions
KW - Integral transforms
KW - Wave equations
UR - http://www.scopus.com/inward/record.url?scp=85075510890&partnerID=8YFLogxK
U2 - 10.1098/rsta.2019.0313
DO - 10.1098/rsta.2019.0313
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C2 - 31760902
AN - SCOPUS:85075510890
SN - 1364-503X
VL - 378
JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2162
M1 - 20190313
ER -