Ii by using the expression derived in a companion paper. Wave propagation in periodic structures 2003 edition. Elastic wave scattering by periodic structures of spherical objects. Free wave propagation patterns for general threecoupled periodic structures are investigated by means of the transfer matrix approach. In this work, we studied the nonreciprocal elastic wave propagation in timespace periodic beams, of which, the youngs modulus is periodically modulated in both time and space. Kochmann 1graduate aerospace laboratories, california institute of technology, pasadena, california 91125, usa.
This is commonly achieved through the generation of bandgaps or stop bands. A hybrid structure is defined as a combination of two independent structures with different properties, in this case a periodic and an aperiodic structure, to form a structure with superior features. Wave propagation in periodic structures dover phoenix. Electric filters and crystal lattices mcgrawhill, 1946 dover, 1953, 2003 les tenseurs en mecanique et en elasticite. We assume that medium variation occurs over two distinct length scales. Waves in periodic curved pipes in this section, we consider three types of structures. Apr 04, 2018 wave propagation in buildings as periodic structures. Propagation of electromagnetic waves in periodic and fibonacci photonic loop structures. Mead department of aeronautics and astronautics, university of southampton, southampton s09 5 nh, england received 17 october 1984 a response function is found for an. Hexagonal honeycomb left with a selected primitive unit cell middle and the. Pcs have periodic inclusions that inhibit wave propagation due to the inclusions destructive interference from scattering. A few of the properties of electromagnetic waves in periodic structures are considered, with some discussion of propagation in openboundary structures. Dynamics of periodic mechanical structures containing. The problem of wave propagation in periodic structures is receiving increasing attention because of the ability of these systems to effectively filter elastic waves 1.
To apply the floquet theory and find propagation constants, the. Waves in random and complex media effective propagation. Wave propagation in periodic structures cern document server. A limited discussion of the transfer matrix then follows, after which the method of spaceharmonics is introduced as the method best suited to the prediction of sound radiated from a vibrating periodic structure.
Note that this periodic structure is made of infinite repetition of the unit cell. Wave propagation in materials and structures crc press book. Highly nonlinear wave propagation in elastic woodpile periodic. Wave interactions in periodic structures and periodic. Unit cell consists of a transmission line of a length d at the center of which a lumped shunt admittance b. This paper studies wave propagation in a periodic parallelplate waveguide with equilateral triangular holes. Consequently, lattice materials behave as frequency and spatial. Boyce1 1department of mechanical engineering, massachusetts institute of technology, cambridge, massachusetts 0294307, usa. Thus the brillouin zones pass andor stopbands separate phase lags, which correspond to standing waves.
Classical wave propagation in periodic and random media by. The proposed approach is capable of handling scattering from the array filled with different media in different layers. We study a onedimensional nonlinear periodic structure which contains two different spring stiffness and an identical mass in each period. Coupling of flexural and longitudinal wave motion in a periodic. Spectral analysis using fast discrete fourier transforms james f. 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. Related content application of magnetoelastic materials in spatiotemporally modulated phononic crystals for nonreciprocal wave propagation. I for a simple model problem a speed up by a factor of 103 has been achieved in comparison to the supercell approach. Wave propagation in nanoscaled periodic layered structures. Wave propagation in buildings as periodic structures. A new method of analyzing wave propagation in periodic. Wave dynamics in locally periodic structures by multiscale.
Electric filters and crystal lattices by brillouin, leon and a great selection of related books, art and collectibles available now at. Dynamics of periodic mechanical structures containing bistable elastic elements. The propagation of waves through nonhomogeneous elastic material, with a periodic structure of elastic constants and density variation, can be conveniently treated in terms of floquet waves. This work is concerned with a general analysis of wave interactions in periodic structures and particularly periodic thin film dielectric waveguides. Wave dynamics in locally periodic structures by multiscale analysis. Irisloaded waveguides of standard cross section are then analyzed to obtain an accurate solution for the propagation constant. Wave propagation in periodic structures electric filters and crystal lattices first edition by leon brillouin. Boyce1 1department of mechanical engineering, massachusetts institute of technology, cambridge, massachusetts 0294307, usa 2multi scale mechanics msm, ts, ctw, universiteit twente, p. Wave propagation in threecoupled periodic structures. A modematching method is implemented to analyze the dispersion diagram of the. Buy wave propagation in periodic structures dover phoenix editions on free shipping on qualified orders. Pdf wave propagation in periodic metallic structures. Wave propagation in periodic structures electric filters. Nonreciprocal elastic wave propagation in timespace.
The photonic energy band structure of periodic composite materials, consisting of regular spherical arrays or scaffoldings of one kind of dielectric material in a different background material, are studied using the plane wave expansion method in order to determine, among other things, the optimum conditions crystal structure, dielectric constant ratio, filling ratio etc. Journal of sound and vibration 1986 104 l, 927 a new method of analyzing wave propagation in periodic structures. Pdf wave propagation in periodic metallic structures with. The periodic structure used was a brass plate with periodic gratings on one side. Pdf propagation of electromagnetic waves in periodic and. Nonlinear propagation of light in one dimensional periodic. It is shown in this paper that a special class of flexural wave groups can exist in periodic structures. Wave propagation analysis in 2d nonlinear periodic structures. Jan 01, 2003 classic treatment of wave propagation covers a broad variety of problems with a common mathematical background, from solid state physics to propagation along electric lines, xrays, rest rays, certain optical reflections, electrical engineering, and wave mechanics of the spinning electron. Wave propagation in nanoscaled periodic layered structures ali chen, yuesheng wang. Abstractelastic wave propagation in highrise buildings is studied using a timoshenko beam model with rigid floor slabs. This book deals not with a special branch of physical science but with a general method and its applications to different problems. The formulation can be applied to both infinite and finite structures, and. As we previously men tioned, for the periodic part we choose the classical bm structure, while for the aperiodic we chose the fn one.
The amle system considered incorporates the effects. Chan, and ping sheng department of physics, the hong kong university of science and technology, clear water bay, kowloon, hong kong, china. We examine the propagation of electromagnetic waves in periodic dielectric structures by solving the vector maxwell equations with the. This thesis presents the results of numerical studies of scalar and electromagnetic wave propagation in periodic and random dielectric media. On waves in composite materials with periodic structure. Modematching approach and applications in electromagnetic engineering presents the scattering and guiding characteristics of periodic structures using the modematching approach and their applications in electromagnetic engineering. 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. Nonreciprocal elastic wave propagation in spatiotemporal periodic structures to cite this article. It is convenient to introduce the nondimensional parameters 1 2 2 1 1 1 2 e h, 1 1 h l, 1 2 l l, 1 2 h h, 1 2, 1 2 e e hereafter 1 2 0. Waves in random and complex media 2010, 122, ifirst effective propagation in a onedimensional perturbed periodic structure. The dimensions of the structure are shown in the schematic diagram and photograph in figs. Nonreciprocal elastic wave propagation in timespace periodic. Additionally, the book provides basic guidelines to design many of the futuristic materials. Oneway propagation of acoustic waves through a periodic.
Wave propagation in periodic structures electric filters and crystal lattices brillouin. The formulation can be applied to both infinite and finite structures, and the amount of damping present may have any value. Wave propagation and tunneling through periodic structures. Pdf wave propagation in infinite periodic structures. Coupling of flexural and longitudinal wave motion in a. The linear dispersion relationship we obtain indicates that our periodic structure has obvious advantages compared to other kinds of periodic structures i. Sample curves of the propagation and attenuation constants pertaining to these structures are presented. Wave propagation in periodic structures electric filters and.
Classical wave propagation in periodic and random media. Topics are organized in increasing order of complexity for better appreciation of the subject. 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 finite element method, periodic structures, local perturbations. A periodic plate a propagation of the stationary plane flexural wave at a circular frequency is considered, so that dynamics of a plate is, in effect, reduced to the dynamics of a beam. Read wave propagation in continuous periodic structures. Coupling of flexural and longitudinal wave motion in a finite. The book is structured so that the first three chapters provide an introduction and prepare. 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.
We study the propagation of waves in spatially nonhomogeneous media focusing on schrodingers equation of quantum mechanics and maxwells equations of electromagnetism. Book title wave propagation in periodic structures. In the case of the periodic structure, with a lattice defect, the defect was made by inserting a dielectric ring between two regular periodic structures of equal length fig. In order to navigate out of this carousel please use your. Wave propagation in twodimensional periodic lattices. Highly nonlinear wave propagation in elastic woodpile periodic structures. In the first part of this dissertation, the integral equation approaches are developed to analyze the wave propagation in periodic structures. A wave finite elementbased approach for the modeling of periodic. The wavelength of light is selected to be in resonance with the periodic structure bragg resonance. The scattering matrix for guided acoustical propagation has been computed. Covers guided and leaky mode propagation in periodic surroundings, from fundamentals to practical device applications.
The basis vectors of the direct lattice e iand the reciprocal lattice e are also shown. From elastic to solitary wave propagation neel nadkarni, 1chiara daraio,2 and dennis m. Results are shown for the dispersion and beam transfer functions and impulse response functions for. Wave propagation in periodic structures electric filters and crystal lattices first edition. These are quasi periodic waves, propagating in one direction, the displacement profiles of which change with time, but repeat after the wave has traversed a complete cell of the material. These are quasi periodic waves, propagating in one direction, the displacement profiles of which change with time, but repeat after the wave has traversed. Jul 28, 2006 the propagation of waves through nonhomogeneous elastic material, with a periodic structure of elastic constants and density variation, can be conveniently treated in terms of floquet waves. First order approximate analytical expressions for the space harmonics are obtained. Nonreciprocal elastic wave propagation in timespace periodic structures k. Classic treatment of wave propagation covers a broad variety of problems with a common mathematical background, from solid state physics to propagation along electric lines, xrays. The source of the structure waves is unspecified so one of the arbitrary amplitudes an is used as a reference. Wave propagation in coupled periodic lattices and application. Vibration response and wave propagation in periodic structures. We analyzed the dispersion relations and studied the properties of the bloch waves in timespace periodic beams.
Nonreciprocal wave propagation in onedimensional nonlinear. Wave propagation in periodic structures electric filters and crystal. Kochmann 1graduate aerospace laboratories, california institute of technology, pasadena, california 91125, usa 2department of mechanical and process engineering, eth zurich, zurich. The electromagnetic wave propagation in an asymmetric dielectric waveguide with a periodically perturbed surface is analyzed in terms of a floquet mode solution. Propagation and confinement of electric field waves along one.
Wave propagation in periodic metallic structures with equilateral triangular holes article pdf available in applied sciences 105. In each case, however, a structure contains the same repeated spatial segments, which, in turn are composed of curved and straight pipe elements. The photonic energy band structure of periodic composite materials, consisting of regular spherical arrays or scaffoldings of one kind of dielectric material in a different background material, are studied using the plane wave expansion method in order. Wave propagation and instabilities in monolithic and periodically structured elastomeric materials undergoing large deformations k. Wave propagation in threecoupled periodic structures wave propagation in threecoupled periodic structures romeo, francesco. I the performance of the pml improves as the damping strength.
Summary this chapter analyzes wave propagation in periodic network materials, which shows higher. It is shown that an exhaustive description of the propagation domains requires spaces that. Propagation and confinement of electric field waves along. Firstly, an integral equation approach is developed to analyze the twodimensional 2d scattering from multilayered periodic array. In order to understand the basic wave propagation phenomena associated with a periodic structure, let us use the simplest structure, namely fig. Nonreciprocal elastic wave propagation in spatiotemporal. Elastic wave scattering by periodic structures of spherical. Electromagnetic wave propagation in periodic structures.
A perturbation approach for predicting wave propagation in onedimensional nonlinear periodic structures j. The photonic bandgap property of pcs makes them the electromagnetic analog of electronic semiconductor crystals. Wave propagation in a plate with periodic structure. Customers who bought this item also bought these digital items. This shopping feature will continue to load items when the enter key is pressed. Wave propagation for a periodic structure is commonly ana lyzed by representing. Wave propagation and instabilities in monolithic and. Oct 09, 2012 provides an analytic approach to describing the operation of photonic crystals and related periodic structures. Elastic wave propagation in highrise buildings is studied using a timoshenko beam model with rigid floor slabs, with the objective of gaining insight into the effects of their repeatable arrangement. Nov, 20 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. New york antenna and wave propagation antennas and wave propagation antennas and wave propagation by j d kraus antennas and wave propagation by gsn raju pdf antenna and wave propagation by kd prasad pdf kd prasad antenna and wave propagation pdf fundamental of electromagnetic wave propagation antenna and wave propagation by kd prasad antennas and wave propagation by gsn raju g.
Wave propagation in periodic metallic structures with. Vibration control in periodic structures dtu orbit. In finite periodic structures the wave components are reflected at the end supports thereby producing standing waves. 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. This book focuses on basic and advanced concepts of wave propagation in diverse material systems and structures. Acoust june, 2010 a dispersive nonlocal model for inplane wave propagation in laminated composites with periodic structures. New york wave propagation in periodic structures wave propagation in periodic structures brillouin pdf periodic tablez periodic function pdf periodic table periodic table pdf periodic table of elements getting to know the periodic table answers getting to know the periodic table worksheet mendeleev periodic table periodic properties notes by p. Integral equation analysis of electromagnetic wave. Ebgs have the goal of creating high quality, low loss, periodic, dielectric structures. Dec 15, 2003 buy wave propagation in periodic structures dover phoenix editions on free shipping on qualified orders.
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