Transfer Matrix Method For Analysis Research Articles

Design of three layered step index fiber for femtosecond pulse delivery at 1550 nm wavelength

This paper presents the design and numerical analysis of a step index three-layered fiber optimized for singlemode operation at a wavelength of 1550 nm. The fiber exhibits an extraordinary mode area, measuring 2020 μm², enabling the delivery of ultra-short pulses without distortion. We have used the Transfer Matrix Method for analysis and the Split-Step Fourier Method to solve the nonlinear Schrödinger equation. The study also incorporates considerations for Raman scattering response and self-steepening phenomena in the analysis, enhancing the comprehensive understanding of the proposed step index three-layered fiber for single-mode operation. Demonstrating the propagation of 100-fs pulses with a peak power of 57.7 kW over a 3.4 m length, the fiber maintains a dispersion length-to-nonlinear length ratio of 1 to ensure pulse fidelity. This research offers insights into designing high-performance optical fibers for efficient and distortion-free pulse transmission in ultra-fast laser applications.

Experimental Research and Transfer Matrix Method for Analysis of Transmission Loss in Multilayer Constructions with Devulcanized Waste Rubber

According to circular economy principles, the recycling and reuse of tyre rubber waste are among the most advanced and ecological waste disposal technologies. Each year, about 19 million tons of tyres are produced, and this number increases every year. One of the most innovative ways to recycle rubber waste is devulcanization. There are many methods of rubber devulcanization, but the most popular is chemical devulcanization. Also, pre-process treatment is important before devulcanization. In this article, devulcanized rubber granules were used for the preparation of rubber samples. Two of the samples were obtained via the grinding method and one via chemical devulcanization. In total, 15 different rubber samples were produced for experimental measurements. Multilayer constructions, with two solid layers of plasterboard on both sides (GKB (a standard gypsum board) and GKFI (an enhanced-strength and surface-hardness gypsum board)) and the porous acoustic material of the rubber sample inside, were produced. Measurements were made in an impedance tube and compared with the results of a transfer matrix method (TMM) analysis. The same trends of resonant frequencies were determined. According to the results, the resonant frequencies depended on the thickness of the material, since transmission loss (TL) values depended on the mass of the construction. According to the test results of transmission loss, constructions with 50 mm thick rubber samples had results that were, on average, 3 dB better than those of structures with 25 mm thick samples and 5 dB better than those of structures with 12 mm thick rubber samples. In addition, it was found that higher-density plasterboards (GKFI) increased the overall transmission loss value of the structure by 5 dB. The same trends were determined using the TMM method. The test results showed that multilayered constructions with devulcanized waste rubber had high transmission loss results and could be used for sound-insulating structures.

Transfer matrix method for analysis of flow thermohydraulic characteristics with extremely nonlinear behavior of thermophysical properties using channel approach

The adaptation procedure of the transfer matrix method for the analysis of nonlinear thermohydraulic (TH) processes using the successful experience of the beam approximation approach is described. The basic principles of spatial and time discretization for the controlling equations system are formulated on the channel approach example. Introduced in the current study effective linearization concept based on “basic” and “corrective” values allowed to remove the restrictions on the medium state equations. The proposed efficient numerical algorithm considering the adaptation of the computational domain helps to solve one of the main problems – obtaining the convergent solution in the case of extremely nonlinear TH properties. Simple classic verification examples, for which theoretical solution exists, were used to test the correctness of applied method realization. The high stability of the suggested method is demonstrated when using implicit correlations for supercritical parameters. The proposed method for the elementary section does not impose restrictions on the type of boundary conditions, which is very important for the organization of branched pipeline systems calculation.

A Developed Transfer Matrix Method for Analysis of Elastic–Plastic Behavior of Structures

A Developed Transfer Matrix Method for Analysis of Elastic–Plastic Behavior of Structures

Modal Analyses of a Thin Shell with Constrained Layer Damping (CLD) Based on Rayleigh-Ritz Method

Foreign Object Debris (FOD) is debris or article alien, which may This paper presents analytical results of natural frequencies and loss factors of node-diameter and node-circumferential modes of a thin shell treated with constrained layer damping (CLD) based on Rayleigh-Ritz method. General differential equations of motion of the thin CLD shell are derived firstly by following the Donnell-Mushtari shell theory. By taking the beam characteristic functions as the admissible functions, the Rayleigh-Ritz method is employed to deduce the higher degree equations of natural frequencies of the thin CLD shell under different boundary conditions. It is confirmed that the present method is accurate and convenient so that it is applicable to the thin CLD shell compared with classic analytic method or transfer matrix method. Several examples are achieved and compared to illustrate the effects of the viscoelastic material (VEM) and constrain layer’s thickness ratios on the natural frequencies and modal loss factors, besides the effect of boundary conditions. The results show that the thickness ratio of VEM affects sensitively the modal frequencies and the total damping capacity of the thin CLD shell.

変位法に基づくWinklerばね上格子梁の解析法

Winkler model is widely used in the analysis of foundations. It is usually employed in the transfer matrix method for analysis of laterally loaded piles, but it is difficult to take account of the model in the stiffness matrix of the grid beam structures. On the other hand, since in the stiffness matrix the soil supporting beams is modeled by only concentrate springs, many elements are needed to obtain the correctness of calculated quantities. The authors present the convenient method transforming from the transfer matrix to the stiffness matrix for the analysis of the grid beam structure on the soil.

Investigation on tunneling in optoelectronic devices with consideration of subwaves

Since novel optoelectronic devices based on the peculiar behaviors of the tunneling probability, e.g., resonant tunneling devices (RTD) and band-pass filter, are steadily proposed, the analytic transfer matrix (ATM) method is extended to study these devices. For several examples, we explore the effect of the scattered subwaves on tunneling; it is shown that the resonant or band-pass structures in tunneling probability are determined by the phase shift results from the scattered subwaves.

A transfer-matrix method for analysis of multicomponent diffusion with any number of components

A transfer-matrix method (TMM) is presented for the development of concentration and flux profiles in multicomponent diffusion involving any numbern of components. From interdiffusion fluxes or concentration gradients available at an initial positionx s, the authors derive expressions for the transfer matrix and its integral so that the concentrations or interdiffusion fluxes of the components can be obtained at any coordinatex. The TMM requires data for interdiffusion coefficients, which are obtained as average values over selected regions by the method of moments developed by Dayananda. Expressions for the concentrations are also obtained from initial conditions on the fluxes or the concentration gradients. The method is also applicable to the case when all the concentrations are known at two ends of a region over which the diffusion coefficients are considered constant. The integration of the fluxes over time, or over the coordinatex, can be evaluated using the transfer-matrix approach, provided the value of the interdiffusion flux is given at a given coordinate. The TMM is applicable to any number of components and can be regarded as a compact generalization of the solutions available for ternary diffusion couples with constant interdiffusion coefficients. An application of the method is illustrated with the experimental data for a ternary Cu-Ni-Zn diffusion couple, and the results are compared with those based on the Fujita-Gosting solution.

Determination of Field Configuration and Eigenvalues of PlanarOptical Waveguides with Arbitrary Index Profiles

We extend the analytic transfer matrix (ATM) method to solve thefield configuration of planar optical waveguides with arbitraryindex profiles including several turning points. The results arecompared with the predictions obtained from the finite element methodand the Wentzel–Kramer–Brillouin approximationtechnique. It is shown that the ATM method not only can produceaccurate eigenvalues, but also reach correct and meaningful fieldconfiguration for any type of optical planar waveguides.

Determination of Optical Waveguide Refractive-Index Profiles with the Inverse Analytic Transfer Matrix Method

In this paper, we present an inverse analytic transfer matrix (IATM) method to predict the refractive index profiles from the measurement of mode indices based on the analytic transfer matrix (ATM) method, which can exactly determine the modal characteristics of a planar optical waveguide with arbitrary index profiles. IATM method has been proved to be universally reliable not only in slowly changing profiles but also the profiles changing rapidly in which inverse WKB method would find difficult through numerical analysis for several typical refractive index profiles.

Analysis of planar waveguides with index discontinuity or index slope discontinuity

In this paper, we propose a novel analytic transfer matrix method (ATMM) to the analysis of planar waveguides with index discontinuity or index slope discontinuity, for the cases when the conventional WKB method is no longer valid. We also analyze the physical insight of the approximations in WKB theory, and according to our research, the phase shift at the turning point is not π/2, but exactly π. Test calculations are done for an index profile with a known solution and the comparison shows that our method gives extremely accurate propagation constant.

Shape optimization of satellite tanks for minimum weight and maximum storage capacity

The aim of structural design is to determine the dimensions and the shape of a system that fulfils certain requirements in an optimal way. Although this problem is not at all new, the application of mathematical algorithms together with multicriteria and shape optimization techniques as strategies for achieving an optimum are still very rarely used in practice. The efficiency of the optimization procedure SAPOP is demonstrated through the shape optimization of ultra light shell structures (e.g. satellite tanks) for which bending effects as well as the influence of large deformations in the shell theory are taken into account. After establishing a corresponding transfer matrix method for analysis, the meridional shape can be determined by using special shape functions (modified ellipsoids) and a “direct” shape optimization strategy. In addition, simultaneous optimization of shape and wall thickness distribution is introduced.

Steady state response of an internally damped spherical shell translationally or rotationally driven at an edge

The steady state response of an internally damped spherical shell translationally or rotationally driven at an edge is determined by the transfer matrix analysis method. For this purpose, the applicability of the thin shell theory is assumed and the governing equations of vibration of the shell are written as a coupled set of first order differential equations by using the transfer matrix of the shell. Once the transfer matrix has been determined by quadrature of the equations, the steady state response is calculated numerically together with the natural frequencies in terms of the elements of the transfer matrix of the shell under any combination of boundary conditions. By the application of the method, the dynamic responses and the resonant frequencies are calculated numerically for shells driven by sinusoidally varying axial, transverse deflection, or angular rotation at an edge.

Steady-state response of an internally damped spherical shell translationally or rotationally driven at an edge.

The steady-state response of an internally damped spherical shell translationally or rotationally driven at an edge is determined by the transfer matrix analysis method. For this purpose, the applicability of the thin shell theory is assumed and the governing equations of vibration of the shell are written as a coupled set of first order differential equations by using the transfer matrix of the shell. Once the transfer matrix has been determined by quadrature of the equations, the steady-state response is calculated numerically together with the natural frequencies in terms of the elements of the transfer matrix of the shell under any combination of boundary conditions. By the application of the method, the dynamic response and the resonant frequencies are calculated numerically for the shells driven by sinusoidally varying axial, transverse deflection, or angular rotation at an edge.