The wellknown blochfloquet waves bfw are not the only manifestation of periodic structure waves psw resulting from the scattering of structure waves sw in an infinite, uniform, one. Wave propagation in infinite periodic structures taking into account energy absorption darryl mcmahon maritime division, defence science and technology group, hmas stirling, wa 6168, australia email. Electromagnetic wave propagation in periodic structures. Enter your mobile number or email address below and well send you a link to download the free kindle app. It reveals that the periodic structures with a regular array of the scatterers can block the wave propagation at certain frequency or nondimensional wave number ka, which can be used for vibration control and noise reduction in engineering applications. Read wave propagation in continuous periodic structures. Control of longitudinal wave propagation in conical. Higherorder asymptotic analysis versus planewave expansions method.
We present a formalism for optical waveguiding in twodimensional periodic structures by means of bragg reflection. Periodic structures can be modeled like any ordinary structure, but in a periodic structure, the study of the structure behavior of one cell is enough to determine the stop and pass bands of the complete structure independent of the number of cells mohammad tawfik aero631 vibrations of structures. Wave propagation in membranebased nonlinear periodic. Wave propagation in linear and nonlinear periodic media. Buy wave propagation in periodic structures dover phoenix editions on free shipping on qualified orders. Localization of wave propagation in disordered periodic. Additionally, the book provides basic guidelines to design many of the futuristic materials.
Such materials are highly anisotropic and, because of lack of bracing, can present a large contrast between. A successful implementation of such periodictensegrity structures is envisioned to extend the usefulness of tensegrity to vibration isolation problems, as well as to the synthesis of tunable acoustic and elastic wave filters, in both the frequency and spatial domains. Topics are organized in increasing order of complexity for better appreciation of the subject. Eigensolutions of the symplectic matrix are used to analyze. Wave propagation and homogenization in 2d and 3d lattices.
The wave propagation characteristics are estimated by. Eigensolutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear. Wave propagation in sandwich plates with periodic auxetic. Research contributions from southampton, 19641995, journal of sound and vibration on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.
At the same time, the relatively simple geometry of 2d and 3d lattices allows for. Wave propagation in buildings as periodic structures. A theoretical model is developed to describe the wave propagation characteristics and the vibrations of a plate covered by periodic damping structures with simply supported boundary condition along its longitudinal edges. Wave propagation in periodic structures paperback january, 1946. This paper presents an evolution of the semianalytical finite element method, and gives examples that illustrate new improvements and their importance for studying the propagation of waves along. Thus, dispersion parameters such as wavenumber and. Modematching approach and applications in electromagnetic engineering book. Wave propagation in a periodic jointed tunnel model.
Such scalar dynamic effective properties are perhaps surprising since periodic lattice structures support multiple wave types yielding complex dispersion properties described by blochfloquet spectra, particularly band gaps 3, 4 and anisotropic propagation. It is shown in this paper that a special class of flexural wave groups can exist in periodic structures. Prestresscontrolled asymmetric wave propagation and. Wave propagation in periodic structures is closely related to propagation of waves in continuous media. The theory provides analytic expressions for the field modal profiles, dispersion, and attenuation or gain in the waveguide. Mech march, 2015 wave propagation in periodic composites. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. This textbook offers the first unified treatment of wave propagation in electronic and electromagnetic systems and introduces readers to the essentials of the transfer matrix method, a powerful analytical tool that can be used to model and study an array of problems pertaining to wave propagation in electrons and photons.
Variational methods for wave propagation in periodic structures. Negative poissons ratio auxetic core materials of different geometry placed periodically in the plate introduce the proper impedance mismatch necessary to obstruct the propagation of waves over specified frequency bands stop bands and in particular. Both are periodic in the variables x and t with periodicity and t m. The secondneighbor interactions in nondiagonal directions are included to account for the nonlocal effect. Wave propagation in coupled periodic lattices and application. Wave propogation in periodic structures db book online pdf. Consequently, lattice materials behave as frequency and spatial. Structures with periodic arrays of 2d and 3d irregular scatterers. Line defects in twodimensional photonic crystal slabs are used as the principal example. Singular boundary method for wave propagation analysis in. Get your kindle here, or download a free kindle reading app. It is well known that periodic structures by nature act as mechanical filters, allowing waves to propagate within specific frequency bands called pass bands, and blocking wave propagation within other frequency bands called stop bands.
Variational methods for wave propagation in periodic. Wave propagation in twodimensional periodic lattices. A periodic structure consists of a unit cell which repeats itself to form the entire structure. Wave propagation in periodic structures request pdf. The tunnel segment is treated as a pipebeam model based on timoshenko beam theory, while the segment joints are simplified as linearly elastic springs which sustain axial forces and. The application of the method of multiple scales to wave. Wave propagationin periodic structures mcgrawhill book co. For simplicity, it can be approximated as a pipebeam model with periodic joints under elastic foundations.
A number of interesting properties exhibited by periodic structures have been demonstrated analytically and experimentally 1, 2. Abstractelastic wave propagation in highrise buildings is studied using a timoshenko beam model with rigid floor slabs. Wave propagation in materials and structures 1st edition. Floquet waves are waves that naturally propagate in periodic structures and are analogous to the waves that propagate in homogenous structures. The formulation can be applied to both infinite and finite structures, and the amount of damping present may have any value. Asymmetric wave propagation metastructure model designed by the prestress and transfer matrix method result and fe results which represent relative displacement as color intensity with respect to position horizontal axis and time vertical axis.
Wave propagation in periodic structures electric filters. Wave propagation in periodic structures pdf free download. The dispersion curves for guided waves have been of constant interest in the last decades, because they constitute the starting point for nde ultrasonic applications. Wave propagation and localization in disordered periodic laminated materials composite structures, vol. Control of wave propagation in periodic composite rods. Irisloaded waveguides of standard cross section are then analyzed to obtain an accurate solution for the propagation constant. The doctoral thesis summarizes the study of the propagation of electromagnetic waves in periodic structures, namely in metamaterials, whereas three forms of a.
Abnormal wave propagation behaviors in twodimensional. Conical periodic structure with single cells and multiple subcells is used to control longitudinal wave motion. Citeseerx document details isaac councill, lee giles, pradeep teregowda. This book focuses on basic and advanced concepts of wave propagation in diverse material systems and structures. Abstract many surface acoustic wave saw devices consist of quasiperiodic structures which are designed by successive repetition of a base cell.
Wave propagation in nanoscaled periodic layered structures. We study a onedimensional nonlinear periodic structure which contains two different spring stiffness and an identical mass in each period. Wave propagation in periodic structures dover phoenix. We examine the propagation of electromagnetic waves in periodic dielectric structures by solving the vector maxwell equations with the. Wave propagation in plate covered by periodic damping. Wave propagation in periodic structures 2003 edition. Experimental analysis of wave propagation in periodic grid. Free wave propagation patterns for general threecoupled periodic structures are investigated by means of the transfer matrix approach. Wave propagationin periodic structures brillouin wave propagationin periodic structures brillouin, l. A m odel of inco here nt wave energy propagation in a n infin ite per iodic structure is d iscussed in sub section 3. Pdf wave propagation along transversely periodic structures.
This work presents the experimental investigations of wave propagation in twodimensional 2d periodic lattice structures. Wave propagation in periodic and quasiperiodic structures. Vibration response and wave propagation in periodic structures. Finite element simulation of wave propagation in periodic. Results are shown for the dispersion and beam transfer functions and impulse response functions for. If the address matches an existing account you will receive an email with instructions to reset your password. Wave propagation along transversely periodic structures. We study wave propagation properties in timespatial periodic structures by computing and analyzing band diagrams for said structures. Geometry of the periodic structure and direction of wave. Periodic structures in general feature unique wave propagation characteristics, whereby waves are allowed to propagate only in specific frequency bands, while they are attenuated at frequencies belonging to the socalled band gap. Wave propagation in nanoscaled periodic layered structures ali chen, yuesheng wang. The wave propagation in and the vibration of sandwich plates with cellular core are analyzed and controlled.
Pdf wave propagation in infinite periodic structures. It is shown that an exhaustive description of the propagation domains requires spaces that are stratified in homogeneous regions, whose dimension is given by the number of invariants of the transfer matrix characteristic equation. This work is devoted to the study of the wave propagation in in. The wave propagation in plate covered by periodic damping layers is analyzed and controlled. A few of the properties of electromagnetic waves in periodic structures are considered, with some discussion of propagation in openboundary structures. Chapter 3 onedimensional periodic medium the objective of this chapter is to establish a comprehensive and indepth understanding of the wave propagation in a 1d periodic medium. The linear dispersion relationship we obtain indicates that our periodic structure has obvious advantages compared to other kinds of periodic structures i. The blochfloquet theorem selection from periodic structures.
Electric filters and crystal lattices by brillouin, leon and a great selection of related books, art and collectibles available now at. The precise numerical simulation of such devices including all physical effects is currently beyond the capacity of high end computation. Thus, dispersion parameters such as wavenumber and wave impedance or permeability and permittivity, can be used to describe the propagation of waves in onedimensional periodic structures like loaded or artificial transmission lines and waveguides. Abnormal wave propagation behaviors in twodimensional massspring structures with nonlocal effect this paper considers the propagation of elastic waves in periodic twodimensional massspring structures with diagonal springs. Wave propagation in threecoupled periodic structures. The article presents the study on wave propagation in membranebased nonlinear periodic structures. The wave propagation problem in the nonlinear periodic massspring structure chain is analyzed using the symplectic mathematical method. It is shown that an exhaustive description of the propagation domains requires spaces that are stratified in homogeneous regions, whose dimension is given by the number of invariants of the transfer matrix characteristic equation and whose boundaries are.
Propagation of electromagnetic waves in periodic structures. Wave propagation in periodic structures electric filters and crystal. Effects of the local resonance on the wave propagation in. Then you can start reading kindle books on your smartphone, tablet, or computer. Nonreciprocal elastic wave propagation in spatiotemporal. He presented several fundamental results related to wave propagation in mechanical as well as electrical periodic structures. The approach followed in this work exploits the periodic nature of the considered modulation of the material properties functions and. The relative convergence rates of three fundamental variational principles used for solving elastodynamic eigenvalue problems are studied within the context of elastic wave propagation in periodic composites phononics. A dispersive nonlocal model for inplane wave propagation in laminated composites with periodic structures j. The contributions in this volume present both the theoretical background and an overview of the stateofthe art in wave propagation in linear and nonlinear periodic media in a consistent format. In this paper, a waveletbased method is developed for wavepropagation analysis of a generic multicoupled onedimensional periodic structure ps. Wave propagation in periodic structures springerlink.