Wave Propagation in Linear and Nonlinear Periodic Media PDF Download
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Author: Francesco Romeo
Publisher: Springer Science & Business Media
ISBN: 3709113091
Category : Technology & Engineering
Languages : en
Pages : 332
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Book Description
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: Francesco Romeo
Publisher: Springer Science & Business Media
ISBN: 3709113091
Category : Technology & Engineering
Languages : en
Pages : 332
Get Book Here
Book Description
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: Spencer P Kuo
Publisher: World Scientific
ISBN: 9811231656
Category : Science
Languages : en
Pages : 206
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Book Description
Waves are essential phenomena in most scientific and engineering disciplines, such as electromagnetism and optics, and different mechanics including fluid, solid, structural, quantum, etc. They appear in linear and nonlinear systems. Some can be observed directly and others are not. The features of the waves are usually described by solutions to either linear or nonlinear partial differential equations, which are fundamental to the students and researchers.Generic equations, describing wave and pulse propagation in linear and nonlinear systems, are introduced and analyzed as initial/boundary value problems. These systems cover the general properties of non-dispersive and dispersive, uniform and non-uniform, with/without dissipations. Methods of analyses are introduced and illustrated with analytical solutions. Wave-wave and wave-particle interactions ascribed to the nonlinearity of media (such as plasma) are discussed in the final chapter.This interdisciplinary textbook is essential reading for anyone in above mentioned disciplines. It was prepared to provide students with an understanding of waves and methods of solving wave propagation problems. The presentation is self-contained and should be read without difficulty by those who have adequate preparation in classic mechanics. The selection of topics and the focus given to each provide essential materials for a lecturer to cover the bases in a linear/nonlinear wave course.
Author: Raj K. Narisetti
Publisher:
ISBN:
Category : Nonlinear theories
Languages : en
Pages :
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Book Description
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: Ricardo A. Delgadillo
Publisher:
ISBN: 9781369146974
Category :
Languages : en
Pages : 96
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Book Description
Lastly, we will propose a time-splitting FGA-based artificial boundary conditions for solving the one-dimensional nonlinear Schrodinger equation (NLS) on an unbounded domain. The NLS will be split into two parts, the linear and nonlinear parts. For the linear part we will use the following absorbing boundary strategy: eliminate Gaussian functions whose centers are too distant to a fixed domain.
Author: Brian R Seymour
Publisher: World Scientific
ISBN: 9813100354
Category : Technology & Engineering
Languages : en
Pages : 420
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Book Description
This unique book aims to treat a class of nonlinear waves that are reflected from the boundaries of media of finite extent. It involves both standing (unforced) waves and resonant oscillations due to external periodic forcing. The waves are both hyperbolic and dispersive. To achieve this aim, the book develops the necessary understanding of linear waves and the mathematical techniques of nonlinear waves before dealing with nonlinear waves in bounded media. The examples used come mainly from gas dynamics, water waves and viscoelastic waves.
Author: Julian L. Davis
Publisher: Princeton University Press
ISBN: 0691223378
Category : Mathematics
Languages : en
Pages : 411
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Book Description
Earthquakes, a plucked string, ocean waves crashing on the beach, the sound waves that allow us to recognize known voices. Waves are everywhere, and the propagation and classical properties of these apparently disparate phenomena can be described by the same mathematical methods: variational calculus, characteristics theory, and caustics. Taking a medium-by-medium approach, Julian Davis explains the mathematics needed to understand wave propagation in inviscid and viscous fluids, elastic solids, viscoelastic solids, and thermoelastic media, including hyperbolic partial differential equations and characteristics theory, which makes possible geometric solutions to nonlinear wave problems. The result is a clear and unified treatment of wave propagation that makes a diverse body of mathematics accessible to engineers, physicists, and applied mathematicians engaged in research on elasticity, aerodynamics, and fluid mechanics. This book will particularly appeal to those working across specializations and those who seek the truly interdisciplinary understanding necessary to fully grasp waves and their behavior. By proceeding from concrete phenomena (e.g., the Doppler effect, the motion of sinusoidal waves, energy dissipation in viscous fluids, thermal stress) rather than abstract mathematical principles, Davis also creates a one-stop reference that will be prized by students of continuum mechanics and by mathematicians needing information on the physics of waves.
Author: Jan Askne
Publisher:
ISBN:
Category :
Languages : sv
Pages : 28
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Book Description
Author: Alan Jeffrey
Publisher:
ISBN:
Category : Magnetohydrodynamics
Languages : en
Pages : 388
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Book Description
Author: D. S. Drumheller
Publisher: Cambridge University Press
ISBN: 9780521587464
Category : Science
Languages : en
Pages : 546
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Book Description
Waves occur widely in nature and have innumerable commercial uses. Pressure waves are responsible for the transmission of speech, bow waves created by meteors can virtually ignite the earth's atmosphere, ultrasonic waves are used for medical imaging, and shock waves are used for the synthesis of new materials. This book provides a thorough, modern introduction to the study of linear and nonlinear waves. Beginning with fundamental concepts of motion, the book goes on to discuss linear and nonlinear mechanical waves, thermodynamics, and constitutive models. It covers gases, liquids, and solids as integral parts of the subject. Among the important areas of research and application are impact analysis, shock wave research, explosive detonation, nonlinear acoustics, and hypersonic aerodynamics. Graduate students, as well as professional engineers and applied physicists, will value this clear, comprehensive introduction to the study of wave phenomena.
Author: Jianke Yang
Publisher: SIAM
ISBN: 0898717051
Category : Science
Languages : en
Pages : 452
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Book Description
Nonlinear Waves in Integrable and Nonintegrable Systems presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind. This book is intended for researchers and graduate students working in applied mathematics and various physical subjects where nonlinear wave phenomena arise (such as nonlinear optics, Bose-Einstein condensates, and fluid dynamics).
