Nonlinear Lattice Structures

Provides a comprehensive introduction to the dynamic response of lattice materials, covering the fundamental theory and applications in engineering practice Offers comprehensive treatment of dynamics of lattice materials and periodic materials in general, including phononic crystals and elastic metamaterials Provides an in depth introduction to elastostatics and elastodynamics of lattice materials Covers advanced topics such as damping, nonlinearity, instability, impact and nanoscale systems Introduces contemporary concepts including pentamodes, local resonance and inertial amplification Includes chapters on fast computation and design optimization tools Topics are introduced using simple systems and generalized to more complex structures with a focus on dispersion characteristics

Optical information processing of the future is associated with a new generation of compact nanoscale optical devices operating entirely with light. Moreover, adaptive features such as self-guiding, reconfiguration and switching become more and more important. Nonlinear devices offer an enormous potential for these applications. Consequently, innovative concepts for all-optical communication and information technologies based on nonlinear effects in photonic-crystal physics and nanoscale devices as metamaterials are of high interest. This book focuses on nonlinear optical phenomena in periodic media, such as photonic crystals, optically-induced, adaptive lattices, atomic lattices or metamaterials. The main purpose is to describe and overview new physical phenomena that result from the interplay between nonlinearities and structural periodicities and is a guide to actual and future developments for the expert reader in optical information processing, as well as in the physics of cold atoms in optical lattices.

This book is a printed edition of the Special Issue "Non-Linear Lattice" that was published in Entropy

Second edition of the English translation (first published in 1981) from the Japanese (1978) deals with waves in lattices composed of particles interacting by nonlinear forces. New areas elucidated include such problems as integrability, generalized lattices, and the Bethe ansatz. Annotation copyrig

Cette thèse est consacrée à la modélisation des structures fibreuses avec des milieuxcontinus généralisés. Dans l'Introduction, l'état de l'art concernant les milieuxcontinus généralisée et applications aux structures fibreuses sont décrits et lesproblèmes ouverts pertinents sont mis en évidence. Dans le Chapitre 1 et 2, uneprocédure d'homogénéisation rigoureuse basée sur des arguments de Gammaconvergenceest appliquée à une structure en treillis et à un model de poutrediscrétisé. Dans le Chapitre 3, un traitement variationnel est utilisé pour formuler unapproche favorable du point de vue numérique. Dans le Chapitre 4 sont discutées lesrésultats expérimentaux concernant le comportement de la structure dans différentstypes de déformation. Cela à motivé les études effectuées dans le Chapitre 5, ou lesMéthodes directes de calcul des variations sont appliquées à poutres d'Euler engrandes déformations.

The aim of this book is to provide a unified presentation of modern mechanics of structures in a form which is suitable for graduate students as well as for engineers and scientists working in the field of applied mechanics. Traditionally, students at technical universities have been taught subjects such as continuum mechanics, elasticity, plates and shells, frames or finite element techniques in an entirely separate manner. The authors' teaching experience clearly suggests that this situation frequently tends to create in students' minds an incomplete and inconsistent picture of the contemporary structural mechanics. Thus, it is very common that the fundamental laws of physics appear to students hardly related to simplified equations of different "technical" theories of structures, numerical solution techniques are studied independently of the essence of mechanical models they describe, and so on. The book is intended to combine in a reasonably connected and unified manner all these problems starting with the very fundamental postulates of nonlinear continuum mechanics via different structural models of "engineer ing" accuracy to numerical solution methods which can effectively be used for solving boundary-value problems of technological importance. The authors have tried to restrict the mathematical background required to that which is normally familiar to a mathematically minded engineering graduate.

This book deals with waves in lattices composed of particles interacting by nonlinear forces. Since motion in a lattice with exponential interac tion between nearest neighbors can be analyzed rigorously, it is treated as the central subject to be discussed. From the idea that the fundamentals of the mathematical methods for nonlinear lattices would be elucidated by rigorous results, I was led in 1966 to the lattice with exponential interaction, which has since proved to be a subject of intensive investigation by many researchers. Therefore I have tried to describe the development of the study of this lattice. The presentation is intended to be coherent and self-contained. Chapter 1 starts with a rather historical exposition, and deals with the motion in the lattices and in continuous systems in general. Funda mental concepts necessary for later chapters, including the partic1elike behavior of stable pulses (solitons), the most characteristic entities of the nonlinear waves, are introduced. The dual transformation, which exchanges the roles of particles and interaction, is described for devel opment in the next chapter.