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## Details

Genre/Form: | Electronic books |
---|---|

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Alexander B Movchan; Natasha V Movchan; Ian S Jones; Daniel J Colquitt |

ISBN: | 1498782108 9781498782104 |

OCLC Number: | 1012311467 |

Description: | 1 online resource : text file, PDF |

Contents: | 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 |

Series Title: | Chapman & Hall/CRC Monographs and Research Notes in Mathematics |

Responsibility: | editors, Natasha V. Movchan, Ian S. Jones. |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

"This book is aimed at specialists in applied mathematics, physics and engineering. The material is based upon the authors' research into waves in structured media, dealing with the dynamic response of elastic structures, cracks and interfaces. The mathematical techniques mostly used are Green's function, asymptotic approximations and numerical simulations. Chapter 1 contains a brief introduction to some ideas and notions and a description of the material in the book. In Chapter 2, dispersion is discussed using linear water waves; also, Bloch-Floquet waves, standing waves and asymptotic lattice approximations are introduced. The elastic problems involving flexural waves on an elastic foundation and waves in chains of particles are discussed. Chapter 3 deals with waves in structured media and ligaments. The asymptotic problems arising from thin interfaces and disintegrating are also dealt with. In Chapter 4, dispersion in periodic structures, dynamic localization and defects in lattices are discussed. Chapter 5 deals with cloaking of waves in which the scattered wave is suppressed by an encompassing structure. In Chapter 6, the models of structured interfaces and chiral media are introduced. Although prerequisite notions are briefly discussed in Chapter 2, some knowledge of asymptotic and singular perturbations and waves in continuous media would be desirable."-Fiazud Din Zaman (Lahore) - Zentralblatt MATH 1397 - 1 Read more...

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