Mathematical Modelling of Waves in Multi-Scale Structured Media /
editors, Natasha V. Movchan, Ian S. Jones.
- First edition.
- 1 online resource : text file, PDF.
- Chapman & Hall/CRC Monographs and Research Notes in Mathematics .
""Cover ""; ""Half title ""; ""Published Titles""; ""Title ""; ""Copyright ""; ""Contents""; ""Preface ""; ""Chapter 1 Introduction""; ""1.1 Blochâ#x80;#x93;Floquet waves ""; ""1.2 Structured interfaces and localisation ""; ""1.3 Multi-physics problems and phononic crystal structures ""; ""1.4 Designer multi-scale materials "" ""1.5 Dynamic anisotropy and defects in lattice systems """"1.6 Models and physical applications in materials science ""; ""1.7 Structure of the book ""; ""Chapter 2 Foundations, methods of analysis of waves and analytical approaches to modelling of multi-scale solids""; ""2.1 Wave dispersion ""; ""2.2 Blochâ#x80;#x93;Floquet waves "" ""2.3 Asymptotic lattice approximations """"2.4 Transmission and reflection ""; ""2.5 Wave localisation and dynamic defect modes ""; ""2.6 Dynamic localisation in a biatomic discrete chain ""; ""2.7 Asymptotic homogenisation ""; ""Chapter 3 Waves in structured media with thin ligaments and disintegrating junctions"" ""3.1 Structures with undamaged multi-scale resonators """"3.2 Singular perturbation analysis of fields in solids with disintegrating junctions ""; ""3.3 Structures with damaged multi-scale resonators ""; ""Chapter 4 Dynamic response of elastic lattices and discretised elastic membranes"" ""4.1 Stop-band dynamic Greenâ#x80;#x99;s functions and exponential localisation """"4.2 Dynamic anisotropy and localisation near defects ""; ""4.3 Localisation near cracks/inclusions in a lattice ""; ""Chapter 5 Cloaking and channelling of elastic waves in structured solids""; ""5.1 A cloak is not a shield ""
"The book presents novel analytical and numerical models of waves in structured elastic media, with emphasis on the asymptotic analysis of phenomena such as dynamic anisotropy, localisation, filtering and polarisation as well as on the modelling of photonic and phononic/platonic crystals. Can we bend a wave? How to avoid rattle and shake in a building or a long bridge? Can a dinner table act as an earthquake protection resonator? (It would not work as a dinner table though on that occasion.) Cloaking - what is it? These and many other fascinating questions may attract a potential reader to this book."--Provided by publisher.