Nonlinear Periodic Structures
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Author | : Raj K. Narisetti |
Publisher | : |
Total Pages | : |
Release | : 2010 |
Genre | : Nonlinear theories |
ISBN | : |
A periodic structure consists of spatially repeating unit cells. From man-made multi-span bridges to naturally occurring atomic lattices, periodic structures are ubiquitous. The periodicity can be exploited to generate frequency bands within which elastic wave propagation is impeded. A limitation to the linear periodic structure is that the filtering properties depend only on the structural design and periodicity which implies that the dispersion characteristics are fixed unless the overall structure or the periodicity is altered. : The current research focuses on wave propagation in nonlinear periodic structures to explore tunability in filtering properties such as bandgaps, cut-off frequencies and response directionality. The first part of the research documents amplitude-dependent dispersion properties of weakly nonlinear periodic media through a general perturbation approach. The perturbation approach allows closed-form estimation of the effects of weak nonlinearities on wave propagation. Variation in bandstructure and bandgaps lead to tunable filtering and directional behavior. The latter is due to anisotropy in nonlinear interaction that generates low response regions, or "dead zones," within the structure. The general perturbation approach developed has also been applied to evaluate dispersion in a complex nonlinear periodic structure which is discretized using Finite Elements. The second part of the research focuses on wave dispersion in strongly nonlinear periodic structures which includes pre-compressed granular media as an example. Plane wave dispersion is studied through the harmonic balance method and it is shown that the cut-off frequencies and bandgaps vary significantly with wave amplitude. Acoustic wave beaming phenomenon is also observed in pre-compressed two-dimensional hexagonally packed granular media. Numerical simulations of wave propagation in finite lattices also demonstrated amplitude-dependent bandstructures and directional behavior so far observed.
Author | : Cornelia Denz |
Publisher | : Springer |
Total Pages | : 299 |
Release | : 2010-03-11 |
Genre | : Science |
ISBN | : 3642020666 |
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.
Author | : Francesco Romeo |
Publisher | : Springer Science & Business Media |
Total Pages | : 332 |
Release | : 2013-07-30 |
Genre | : Technology & Engineering |
ISBN | : 3709113091 |
Waves and defect modes in structures media.- Piezoelectric superlattices and shunted periodic arrays as tunable periodic structures and metamaterials.- Topology optimization.- Map-based approaches for periodic structures.- Methodologies for nonlinear periodic media. The contributions in this volume present both the theoretical background and an overview of the state-of-the art in wave propagation in linear and nonlinear periodic media in a consistent format. They combine the material issued from a variety of engineering applications, spanning a wide range of length scale, characterized by structures and materials, both man-made and naturally occurring, featuring geometry, micro-structural and/or materials properties that vary periodically in space, including periodically stiffened plates, shells and beam-like as well as bladed disc assemblies, phononic metamaterials, photonic crystals and ordered granular media. Along with linear models and applications, analytical methodologies for analyzing and exploiting complex dynamical phenomena arising in nonlinear periodic systems are also presented.
Author | : Anatoli? Mikha?lovich Kamchatnov |
Publisher | : World Scientific |
Total Pages | : 399 |
Release | : 2000 |
Genre | : Science |
ISBN | : 981024407X |
Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to treat various problems in nonlinear wave theory. Therefore it is topical to describe recent developments of the Whitham theory in a clear and simple form suitable for applications in various branches of physics.This book develops the techniques of the theory of nonlinear periodic waves at elementary level and in great pedagogical detail. It provides an introduction to a Whitham's theory of modulation in a form suitable for applications. The exposition is based on a thorough analysis of representative examples taken from fluid mechanics, nonlinear optics and plasma physics rather than on the formulation and study of a mathematical theory. Much attention is paid to physical motivations of the mathematical methods developed in the book. The main applications considered include the theory of collisionless shock waves in dispersive systems and the nonlinear theory of soliton formation in modulationally unstable systems. Exercises are provided to amplify the discussion of important topics such as singular perturbation theory, Riemann invariants, the finite gap integration method, and Whitham equations and their solutions.
Author | : Jianhong Feng |
Publisher | : |
Total Pages | : 64 |
Release | : 1994 |
Genre | : |
ISBN | : |
Author | : Peyman Sarrafi |
Publisher | : |
Total Pages | : |
Release | : 2014 |
Genre | : |
ISBN | : |
Author | : Gang Bao |
Publisher | : Springer Nature |
Total Pages | : 361 |
Release | : 2021-11-22 |
Genre | : Mathematics |
ISBN | : 9811600619 |
This book addresses recent developments in mathematical analysis and computational methods for solving direct and inverse problems for Maxwell’s equations in periodic structures. The fundamental importance of the fields is clear, since they are related to technology with significant applications in optics and electromagnetics. The book provides both introductory materials and in-depth discussion to the areas in diffractive optics that offer rich and challenging mathematical problems. It is also intended to convey up-to-date results to students and researchers in applied and computational mathematics, and engineering disciplines as well.
Author | : Matthew A. Davies |
Publisher | : |
Total Pages | : 430 |
Release | : 1993 |
Genre | : |
ISBN | : |
Author | : |
Publisher | : |
Total Pages | : 67 |
Release | : 1995 |
Genre | : |
ISBN | : |
The optical properties of two examples of nonlinear periodic structures experimentally studied: colloidal crystals used as nonlinear distributed feedback structures and nonlinear volume holographic elements. The transmission of the colloidal crystals was found to be dramatically modified by an incident field whose frequency was tuned within or near the stop gap of the crystal. Optical limiting was observed when the frequency of the incident field was tuned to the high frequency edge of the stop gap. Optical switching and bistability were observed when the frequency was tuned to within the stop gap. The switching intensity was seen to decrease as the frequency of the incident light was tuned further into the stop gap. This result can not be explained by the simple model of a nonlinear distributed feedback structure. The transmission was also found to exhibit temporal fluctuations at high intensities. The nonlinear volume holographic structures consisted of a porous photopolymer in which a permanent grating was recorded and then was imbibed with a nematic liquid crystal. The diffraction efficiency of the grating was switched from high to low using a control beam power of 8.4 mW. The response time of the switching was limited by the response time of the thermal nonlinearity of the liquid crystal and was measured to be approximately 1 ms. (MM).
Author | : C W Cai |
Publisher | : World Scientific |
Total Pages | : 280 |
Release | : 2002-03-25 |
Genre | : Technology & Engineering |
ISBN | : 9814488747 |
By using the U-transformation method, it is possible to uncouple linear simultaneous equations, either algebraic or differential, with cyclic periodicity. This book presents a procedure for applying the U-transformation technique twice to uncouple the two sets of unknown variables in a doubly periodic structure to achieve an analytical exact solution.Explicit exact solutions for the static and dynamic analyses for certain engineering structures with doubly periodic properties — such as a continuous truss with any number of spans, cable network and grillwork on supports with periodicity, and grillwork with periodic stiffening members or equidistant line supports — can be found in the book. The availability of these exact solutions not only helps with the checking of the convergence and accuracy of numerical solutions, but also provides a basis for optimization design for these types of structures.The study of the force vibration and mode shape of periodic systems with nonlinear disorder is yet another research area which has attained considerable success by the U-transformation method. This book illustrates the analytical approach and procedure for the problems of localization of the mode shape of nearly periodic systems together with the results.