Wave Localization in Multi-Coupled Periodic Structures: Application to Truss Beams

1996 ◽  
Vol 49 (2) ◽  
pp. 65-86 ◽  
Author(s):  
Christophe Pierre ◽  
Matthew P. Castanier ◽  
Wan Joe Chen
Keyword(s):  
Lyapunov Exponents ◽  
Transfer Matrix ◽  
Periodic Structures ◽  
Wave Localization ◽  
Matrix Formulation ◽  
Wave Type ◽  
Recent Developments ◽  
Propagation Of Waves ◽  
Dynamics Problems ◽  
Localized Waves

A tutorial and a review of recent developments in the area of localization in linear structural dynamics problems are presented. Particular emphasis is placed on multi-coupled nearly periodic structures, which carry more than one wave type. First, background on perfectly periodic structures is provided, including both the wave and modal descriptions of the dynamics. A wave transfer matrix formulation for disordered periodic structures is then presented, which is well suited to the analysis of localized dynamics. Next, stochastic analysis tools are introduced that allow one to quantify the degree of localization in an asymptotic sense. Means of calculating these localization factors as the Lyapunov exponents of the system wave transfer matrix are discussed. Finally, the general theory is illustrated on an example multi-coupled structure - a planar truss beam which carries four pairs of waves. The propagation of waves in the disordered structure is examined, and Lyapunov exponents are calculated. In addition to the localization of the incident wave, significant mixing of the various wave types occurs, causing the leakage of energy to the least localized waves, and enabling sustainment of motion according to the smallest Lyapunov exponent.

Multimodal Transfer Matrix Method Applied to 3-D Periodic Structures

2021 ◽  
Author(s):  
Federico Giusti ◽  
Francisco Mesa ◽  
Qiao Chen ◽  
Guido Valerio ◽  
Oscar Quevedo-Teruel
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Periodic Structures

scholarly journals Gradient index phononic crystals and metamaterials

Nanophotonics ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 685-701 ◽  
Author(s):  
Yabin Jin ◽  
Bahram Djafari-Rouhani ◽  
Daniel Torrent
Keyword(s):  
Refractive Index ◽  
Wave Propagation ◽  
Acoustic Waves ◽  
Effective Properties ◽  
Periodic Structures ◽  
Phononic Crystals ◽  
Ray Theory ◽  
Acoustic Metamaterials ◽  
Propagation Of Waves ◽  
At Will

AbstractPhononic crystals and acoustic metamaterials are periodic structures whose effective properties can be tailored at will to achieve extreme control on wave propagation. Their refractive index is obtained from the homogenization of the infinite periodic system, but it is possible to locally change the properties of a finite crystal in such a way that it results in an effective gradient of the refractive index. In such case the propagation of waves can be accurately described by means of ray theory, and different refractive devices can be designed in the framework of wave propagation in inhomogeneous media. In this paper we review the different devices that have been studied for the control of both bulk and guided acoustic waves based on graded phononic crystals.

A transfer matrix formulation of an electromechanical Helmholtz resonator

2005 ◽  
Vol 118 (3) ◽  
pp. 1944-1944 ◽  
Author(s):  
Fei Liu ◽  
Lou Cattafesta ◽  
Mark Sheplak ◽  
Stephen Horowitz ◽  
Toshi Nishida
Keyword(s):  
Transfer Matrix ◽  
Helmholtz Resonator ◽  
Matrix Formulation

Wave Propagation in Periodic Stiffened Shells: Spectral Finite Element Modeling and Experiments

2003 ◽  
Vol 9 (9) ◽  
pp. 1057-1081 ◽  
Author(s):  
G. Solaroli ◽  
Z. Gu ◽  
A. Baz ◽  
M. Ruzzene
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Periodic Structures ◽  
Dynamic Stiffness ◽  
Geometrical Parameters ◽  
Pass Band ◽  
Matrix Formulation ◽  
Stiffened Shell ◽  
Stiffened Shells ◽  
Spectral Finite Element

The capability of periodic structures to act as filters for propagating waves is used to control the propagation of waves in thin shells. The shells are stiffened by periodically placed rings in order to generate periodic discontinuities in the stiffness and inertial spatial distribution along the longitudinal axes of these shells. Such discontinuities result in attenuation of the wave propagation over certain frequency bands called stop bands. A distributed-parameter approach is used to derive a spectral finite element model of the periodically stiffened shell. The model accurately describes the dynamic behavior of the shell using a small number of elements. The stiffening rings, modeled using the curved beam theory, are considered as lumped elements whose mass and stiffness matrices are combined with those of the shell. The resulting dynamic stiffness matrix of the ring-stiffened shell element is used to predict the wave propagation dynamics in the structure. In particular, the shell propagation constants are determined by solving a polynomial eigenvalue problem, as a numerically robust alternative to the traditional transfer matrix formulation. The study of the propagation constants shows that the discontinuity introduced by the stiffeners generates the typical stop/pass band pattern of periodic structures. The location and width of the stop bands depend on the spacing and geometrical parameters of the rings. The existence of the stop bands, as predicted from the analysis of the propagation constants, is verified experimentally. Excellent agreement between theoretical predictions and experimental results is achieved. The presented theoretical and experimental techniques provide viable means for designing periodically stiffened shells with desired attenuation and filtering characteristics.

An Overview and Recent Developments of Distinct Lattice Spring Model on Dynamic Fracturing of Rock

2014 ◽  
Vol 553 ◽  
pp. 507-512
Author(s):  
Gao Feng Zhao ◽  
Nasser Khalili
Keyword(s):  
Element Model ◽  
Discrete Element Model ◽  
Spring Model ◽  
Basic Principles ◽  
Lattice Spring Model ◽  
Recent Developments ◽  
Distinct Lattice Spring Model ◽  
Dynamic Fracturing ◽  
Dynamics Problems ◽  
Macroscopic Parameters

This paper presents some recent developments of the Distinct Lattice Spring Model (DLSM) on dynamic fracturing of rock. The DLSM is a micromechanics based discrete numerical model for rock dynamics problems. It provides an alternative tool for rock mechanics study. Compared with the classical Discrete Element Model (DEM), the DLSM can directly use macroscopic parameters without any requirement for calibration process. Another significant advantage is that the DLSM uses only half of the degree of freedoms, and therefore, is more computational efficient. Because of these advantages, it has been used in a number of fields, e.g., dynamic fracturing, wave propagation, and nuclear waste disposition. In this work, the basic principles of the DLSM and its latest developments will be outlined.

Dynamic Simulation of Compressor Station Operation Including Centrifugal Compressor and Gas Turbine

1991 ◽  
Vol 113 (2) ◽  
pp. 300-311 ◽  
Author(s):  
K. K. Botros ◽  
P. J. Campbell ◽  
D. B. Mah
Keyword(s):  
Dynamic Simulation ◽  
Transfer Matrix ◽  
Numerical Technique ◽  
Nonlinear Partial Differential Equations ◽  
Field Measurements ◽  
Compressor Station ◽  
Algebraic Equations ◽  
Gas Dynamics Equations ◽  
Matrix Formulation ◽  
Simulation Results

Dynamic simulation of the operation of a compressor station requires mathematical modeling of the dynamic behavior of the compressor unit and various piping elements. Such models consist of large systems of nonlinear partial differential equations describing the pipe flow together with nonlinear algebraic equations describing the quasi-steady flow through various valves, constrictions, and compressors. In addition, the models also include mathematical descriptions of the control system, which consists of mixed algebraic and ordinary differential (mad) equations with some inequalities representing controllers’ limits. In this paper a numerical technique for the solution of the gas dynamics equations is described, based on the transfer matrix formulation relating the state vector time difference at one side of an element to that on the other side. This approach facilitates incorporation of all element transfer matrices into an overall transfer matrix according to the system geometric connectivity. The paper also presents simulation results and comparison with actual field measurements of three case histories: (1) simulation of a compressor surge protection control process; (2) unit startup; and (3) slow transient of a compressor station responding to changes in the discharge pressure set point. Good agreement between simulation results and field measurements is demonstrated.

Radiative Properties of Pattered Wafers With Linewidth Below 100 nm

2005 ◽  
Author(s):  
Y.-B. Chen ◽  
Z. M. Zhang ◽  
P. J. Timans
Keyword(s):  
Periodic Structures ◽  
Numerical Study ◽  
Radiative Properties ◽  
Angle Of Incidence ◽  
Patterned Wafers ◽  
Rigorous Coupled Wave Analysis ◽  
Recent Developments ◽  
Effective Medium Approach ◽  
Rigorous Coupled Wave ◽  
Very High

Temperature nonuniformity is a critical problem in rapid thermal processing (RTP) of wafers because it leads to uneven diffusion of implanted dopants and introduces thermal stress that can produce defects. One cause of the problem is nonuniform absorption of thermal radiation, especially in patterned wafers, where the optical properties vary across the surface of the wafer. Recent developments in RTP have lead to the use of millisecond-duration heating cycles, where light with very high power density is used to heat the surface of the wafer. Pattern effects are especially important here, because there is very little time for thermal diffusion to even out temperature distributions during the heating cycle. There have been very few studies on the radiative properties of patterned wafers, especially for the structures expected to be used on advanced semiconductor devices. The feature size is already below 100 nm and is comparable or smaller than the wavelengths of radiation (200–1000 nm) emitted by the flash-lamps typically used for millisecond processing. Hence, this work is devoted to a parametric numerical study of the radiative properties of patterned wafers with the smallest dimension down to 30 nm. The effects of wavelength, wave polarization, and angle of incidence on selected periodically patterned wafers are presented. The methods include the rigorous coupled wave analysis (RCWA) and the effective medium approach (EMA). RCWA is used to obtain exact solutions of Maxwell’s equations, and EMA is used to approximate the periodic structures as a planar multilayer structure with an effective dielectric function. This study provides an assessment of the applicability of EMA for simulations of radiative properties of patterned wafers.

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