Search results for "Matrix method"
showing 10 items of 32 documents
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…
A numerical study of atmospheric signals in the Earth-ionosphere electromagnetic cavity with the Transmission Line Matrix method
2006
[1] The effect of the Earth-ionosphere electromagnetic cavity on the spectrum of an atmospheric signal generated by a broadband electrical current source is analyzed numerically by means of the Transmission Line Matrix (TLM) method. Two new TLM meshes are developed, one with transmission lines connected in parallel and the other with connections in series. The equations describing propagation through these parallel or series meshes are equivalent to the Maxwell equations for TEr or TMr modes in the spherical Earth-ionosphere cavity, respectively. The numerical algorithm obtains Schumann resonance frequencies very close to the experimental ones, confirming that this methodology is a valid nu…
Determination of the effective permittivity of dielectric mixtures with the transmission line matrix methodDetermination of the effective permittivit…
2007
In this article, the effective permittivity of two-phase dielectric mixtures is calculated by applying the transmission line matrix (TLM) method. Two slightly different TLM algorithms are considered: a hybrid approach, which combines the TLM method with a subgriding technique based on dual capacitor circuits, to allow a refined description of the material, and a standard or pure TLM approach, which uses a mesh size smaller than the typical dimension of insertions in order to appropriately describe details of the geometry. A study of the statistical distribution of permittivity for insertions in random positions is also presented, showing that the effective permittivity of the mixture tends …
Fractional Fourier transforms, symmetrical lens systems, and their cardinal planes
2007
We study the relation between optical lens systems that perform a fractional Fourier transform (FRFT) with the geometrical cardinal planes. We demonstrate that lens systems symmetrical with respect to the central plane provide an exact FRFT link between the input and output planes. Moreover, we show that the fractional order of the transform has real values between 0 and 2 when light propagation is produced between principal planes and antiprincipal planes, respectively. Finally, we use this new point of view to design an optical lens system that provides FRFTs with variable fractional order in the range (0,2) without moving the input and output planes.
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…
Vibration of damaged beams under a moving mass: theory and experimental validation
2004
Abstract A theoretical and experimental study of the response of a damaged Euler–Bernoulli beam traversed by a moving mass is presented. Damage is modelled through rotational springs whose compliance is evaluated using linear elastic fracture mechanics. The analytical solution is based on the series expansion of the unknown deflection in a basis of the beam eigenfunctions. The latter are calculated using the transfer matrix method, taking into account the effective mass distribution of the beam. The convective acceleration terms, often omitted in similar studies, are considered here for a correct evaluation of the beam–moving mass interaction force. The analytical solution is then validated…
FDTD simulation for electromagnetic radiated emissions in 42 V vehicle electrical systems
2005
In this paper a full 3D approach, based on finite difference time domain method, is used to predict the electromagnetic radiated emissions from 42 V vehicle electrical loads. An experimental set-up has been arranged on purpose. A comparative analysis among measured and computed results is performed. The good agreement obtained among simulated and measured data enables to validate the numerical scheme. The proposed methodology contributes to predict electromagnetic emissions in the automotive environment since the design stage. Moreover, the proposed numerical tool can be used to define, for new vehicle electrical architectures, low cost test methods for electromagnetic compatibility and sui…
Wideband modeling of cascaded H-plane waveguide junctions using the generalised impedance matrix representation
2009
A strong interest in H-plane waveguide components composed of a large number of cascaded planar junctions is recently renewed. Therefore, the more efficient development of full-wave analysis tools of such devices is again receiving consideration, specially for its potential use within modern design tools. A novel technique for providing the wideband generalised impedance matrix representation of the inductive devices in the form of pole expansions, thus extracting the most expensive computations from the frequency loop is proposed. For such purpose, the whole device is first decomposed into simpler building blocks, i.e. planar junctions and uniform waveguides, which are modelled in terms of…