Search results for "Transfer-matrix method"

Multiple low-frequency broad band gaps generated by a phononic crystal of periodic circular cavity sandwich plates

2017

Abstract We propose a new type of phononic crystal (PnC) composed of a periodic alternation of circular cavity sandwich plates. In the low-frequency regime, the crystal can modulate the propagation of flexural waves. Governing equations are deduced basing on the classical theory of coupled extensional and flexural vibrations of plates. The dispersion relation of the infinite PnC is calculated by combining the transfer matrix method with Bloch theory. The dynamic response of the PnC with finite unit cells is further studied with finite element analysis. An experiment is carried out to demonstrate the performance of the PnC in vibration isolation. Numerical results and experimental results bo…

Acoustic characterization of Silica aerogel clamped plates for perfect absorption purpose

2017

International audience; Silica aerogel has been widely studied as bulk material for its extremely low density and thermal conductivity. Plates or membranes made of this extremely soft materials exhibits interesting properties for sound absorption. A novel signal processing method for the characterization of an acoustic metamaterial made of silica aerogel clamped plates is presented. The acoustic impedance of a silica aerogel clamped plate is derived from the elastic theory for the flexural waves, while the transfer matrix method is used to model reflection and transmission coefficients of a single plate. Experimental results are obtained by using an acoustic impedance tube. The difference b…

Transfer matrix method applied to the parallel assembly of sound absorbing materials

2013

International audience; The transfer matrix method (TMM) is used conventionally to predict the acoustic properties of laterally infinite homogeneous layers assembled in series to form a multilayer. In this work, a parallel assembly process of transfer matrices is used to model heterogeneous materials such as patchworks, acoustic mosaics, or a collection of acoustic elements in parallel. In this method, it is assumed that each parallel element can be modeled by a 2 × 2 transfer matrix, and no diffusion exists between elements. The resulting transfer matrix of the parallel assembly is also a 2 × 2 matrix that can be assembled in series with the classical TMM. The method is validated by compar…

Three-body approach to proton-hydrogen charge exchange and elastic scattering

1999

The impact-parameter Faddeev approach to atomic three-body collisions which has been developed for, and successfully applied to, ion-atom scattering processes, has now been developed further by including, instead of the Coulomb potentials, the full two-particle off-shell Coulomb {ital T} matrices in all {open_quotes}triangle{close_quotes} contributions to the effective potentials. Results of calculations of proton-hydrogen collisions with only the ground states of the hydrogen retained in both the direct and the rearrangement channels are presented. Total and differential electron transfer, as well as differential elastic scattering cross sections, are obtained simultaneously in very good a…

Acoustics of porous materials with partially opened porosity

2013

International audience; A theoretical and experimental study of the acoustic properties of porous materials containing dead-end (or partially opened) porosity was recently proposed by Dupont et al. The present article provides a description of partially opened porosity systems and their numerous potential applications in the general context of the study of porous materials, the classical models describing them, and the characterization techniques. It is shown that the dead-end pore effect can be treated independently and that the description of this effect can be associated with any acoustic model of porous media. Different theoretical developments describing the dead-end porosity effect ar…

Photonic band gaps in highly ionic medium: CuCl, CuBr, CuI

2003

Abstract Using the transfer-matrix-method, we have studied the propagation of electromagnetic waves through two-dimensional (2D) and three-dimensional (3D) dispersive photonic band gap (PBG) structures constructed from copper halides materials, especially from CuCl compounds. A special attention has been paid to the effect of the polariton gap on the PBG properties. This study reveals that “Twin gaps” and “Twin brothers” concepts and the flattened bands phenomena in both polarizations and for both structures (i.e. 2D and 3D) are all consequences of the strong photon–phonon coupling, particularly near the long wave length transverse optical phonon frequency. Furthermore, results for comparis…

One-Dimensional Magnetism: An Overview of the Models

2003

Teaching stable two-mirror resonators through the fractional Fourier transform

2009

We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation–lens–propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g parameters) and those of the equivalent FRFT systems (the FRFT order and scaling parameters). Expressions connecting Gaussian beam q-transformation with FRFT parameters are derived. In particular, we show that the beam waist of the resonator's mode is located at the plane leading to two FRFT subsystems with equal scaling parameter which, moreover, coincid…

A transfer matrix method for the analysis of fractal quantum potentials

2005

The scattering properties of quantum particles on fractal potentials at different stages of fractal growth are obtained by means of the transfer matrix method. This approach can be easily adopted for project assignments in introductory quantum mechanics for undergraduates. The reflection coefficients for both the fractal potential and the finite periodic potential are calculated and compared. It is shown that the reflection coefficient for the fractal has a self-similar structure associated with the fractal distribution of the potential.

Effect of amorphous sequences on the longitudinal acoustic modes in partially crystalline polymers. I. Transfer matrix method

1983

A novel theoretical scheme is developed which enables the determination of the LAM-like vibrations of polymer chains made up of crystalline and amorphous parts as they occur in partially crystalline structures. The boundary conditions effective at the junction points are formulated in terms of the compliances of the associated amorphous sequences. These compliances can be derived from their eigenfrequencies and eigenvectors in a disconnected state. The treatment uses a matrix formalism which can be extended to include bending and torsional motions in a general state of vibration of the crystalline stem. A first numerical example demonstrates that the LA mode of a crystalline stem can be str…