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Dynamic responses of unsaturated half-space soil to a moving harmonic rectangular load

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS 2018年第9期42卷 1057-1077页

作者： Lu, Zheng Fang, Ran Yao, Hailin Dong, Cheng Xian, Shaohua Chinese Acad Sci Inst Rock & Soil Mech State Key Lab Geomech & Geotech Engn Wuhan 430071 Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China Hunan Commun Res Inst Changsha 410015 Hunan Peoples R China

The problem of the dynamic responses of a semi-infinite unsaturated poroelastic medium subjected to a moving rectangular load is investigated analytical/numerically. The dynamic governing equations are obtained with consideration of the compressibility of solid grain and pore fluid, inertial coupling, and viscous drag as well as capillary pressure in the unsaturated soil, and they can be easily degraded to the complete Biot's theory. Using the Fourier transform, the general solution for the equations is derived in the transformed domain, and then a corresponding boundary value problem is formulated. By introducing fast Fourier transform algorithm, the unsaturated soil vertical displacements, effective stresses, and pore pressures induced by moving load are computed, and some of the calculated results are compared with those for the degenerated solution of saturated soils and confirmed. The influences of the saturation, the load speed, and excitation frequency on the response of the unsaturated half-space soil are investigated. The numerical results reveal that the effects of these parameters on the dynamic response of the unsaturated soil are significant.

关键词： dynamic response fft algorithm Fourier transform moving load saturation unsaturated soil

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Analysis and simulation of diffractive imaging field in thick film photoresist by using angular spectrum theory

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OPTICS COMMUNICATIONS 2005年第1-6期244卷 123-130页

作者： Tang, XG Gao, FH Guo, YK Du, JL Liu, SJ Gao, F Sichuan Univ Dept Phys Chengdu 610064 Peoples R China

The thick film photoresist lithography is a much more complicated process compared to the thin film photoresist lithography. In this paper, we have developed a new model for lithography of thick film photoresist by using the angular spectrum theory. The thick film photoresist is divided into many homogeneous layers, and the diffractive optical imaging distribution in photoresist is regarded as superposition of different spectrum plane waves. Propagation of each plane wave is determined by the optical transfer function, and the propagation direction, amplitude and phase are dominated by reflection and transmission between each interface of the sub-layers. The fast Fourier transform (fft) has been converted into a convolution calculation to keep the computation accurate and reduce computation cost. Numerical calculation results show that optical intensity in cross-sect of thick film resist is strongly affected by reflection, transmission on interface and variation of dielectric permittivity along direction of depth, and therefore these factors should be considered while analyzing diffractive imaging field in thick film photoresist. (C) 2004 Elsevier B.V. All rights reserved.

关键词： diffractive optics lithography angular spectrum theory optical transfer function thick film photoresist fft algorithm

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Improved scattering analysis of arbitrary-shaped cylinders in a focused beam system using Gabor representation

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IEE PROCEEDINGS-MICROWAVES ANTENNAS AND PROPAGATION 1999年第3期146卷 193-196页

作者： Shavit, R Ben Gurion Univ Negev Dept Elect & Comp Engn IL-84105 Beer Sheva Israel

Gabor expansion is used to reconstruct the scattering pattern and the induced field ratio (IFR) of an arbitrarily-shaped cylinder measured in a focused beam system. The fields of the transmitting and receiving antennas in the measurement system are described by equivalent fundamental Gaussian beams. The results obtained by the proposed method of analysis verify well with the scattering characteristics computed analytically or numerically by the method of moments (MoM), finite elements method (FEM) and by a previous method of analysis using an fft algorithm.

关键词： broadcasting METHOD OF MOMENTS Cylinders Receiving antennas chemical methods of analysis nodal analysis Scattering Scattering characteristics fft algorithm induction field Cylinders beam system instrument flight rules focused beam

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ADAPTIVE FILTER FOR 2-DIMENSIONAL GABOR TRANSFORMATION AND ITS IMPLEMENTATION

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IEE PROCEEDINGS-I COMMUNICATIONS SPEECH AND VISION 1993年第1期140卷 2-6页

作者： TEUNER, A HOSTICKA, BJ Fraunhofer Institute of Microelectronic Circuits and Systems Duisburg Germany

An adaptive filter that enables coefficient computation of the Gabor expansion while employing the least mean-squared algorithm for complex signals is described. A significant simplification of the filter structure and the use of fft algorithms contribute to a fast and efficient determination of the coefficients when compared with known algorithms for Gabor computation. Based on these results, we propose a hardware realisation using a CORDIC processor. Computer simulations indicate that sufficient precision and a fast convergence of the coefficients can be obtained.

关键词： ADAPTIVE FILTERS fft algorithm IMAGE COMPRESSION

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THE RECEPTANCE-BASED PERTURBATIVE MULTIHARMONIC BALANCE METHOD FOR THE CALCULATION OF THE APERIODIC STEADY-STATE RESPONSE OF NONLINEAR-SYSTEMS

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JOURNAL OF SOUND AND VIBRATION 1995年第2期181卷 331-339页

作者： REN, Y School of Mechanical and Production Engineering Nanyang Technological University Singapore Republic of Singapore 2263

A receptance-based perturbative multi-harmonic balance (RPMHB) method has been developed recently [1]. The method can be applied to systems containing almost any type of non-linear element. It is computationally efficient, particularly when the number of the non-linear elements is small. This method has been successfully applied to calculate the periodic steady state response of localized non-linear systems. In this paper, the RPMHB method is generalized to calculate the aperiodic steady state response of systems containing localized non-linear elements. When the response is not periodic, the commonly used fft algorithm is not applicable. To overcome this problem, a direct fit algorithm is suggested to calculate the coefficients of the frequency components. Numerical examples are presented to illustrate the features of this method.

关键词： nonlinear device steady state response Steady state fft algorithm

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Stable desmearing of slit-collimated SAXS patterns by adequate numerical conditioning

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Acta Crystallographica, Section A: Foundations of Crystallography 1998年第pt 5期54卷 675-675页

作者： Soliman, M. Jungnickel, B.-J. Meister, E. Deutsches Kunststoff Inst Darmstadt Germany Tech Univ Darmstadt Fachbereich Math D-64287 Darmstadt Germany

Small-angle X-ray scattering (SAXS) patterns from slit cameras ('Kratkycameras') require a subsequent desmearing procedure in order to obtain the pinhole scattering curvethat is suitable for subsequent structure analysis. Since the corresponding integral equationcontains a singularity, its solutions are usually unstable and fail if large noise is present. It isdemonstrated how analytical stability can be achieved by physically reliable conditioning of theexperimental data, introduction of the Moore-Penrose pseudoinverse of the equation's discretizedintegral operator and solving the equation by a fft algorithm. This ensures the consistency of thesolution as well as its stability, and hence its convergence. This solution can account forarbitrarily nonsymmetrical primary-beam profiles. The algorithm does not require antecedentsmoothing of the scattering curve. It allows on the contrary low-pass filter smoothing duringdesmearing but remains stable despite large noise contributions.

关键词： Small angle X ray scattering Singularity structured analysis slit camera Conditioning DESMEARING fft algorithm Integral equations smoothing

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ON THE USE OF FOURIER-SERIES fftS AS GLOBAL BASIS FUNCTIONS IN THE SOLUTION OF BOUNDARY INTEGRAL-EQUATIONS FOR EM SCATTERING

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 1994年第9期42卷 1309-1316页

作者： JAMES, RM WA USA

Current methods for the solution of the surface integral equations of interest to practical electromagnetic scattering appear to have reached an impasse. Plagued by disputes concerning the suitability and performance of various competing choices for piecewise basis functions and facing horribly complicated piecewise quadratures for the construction of influence matrix elements, it has become quite commonplace for these methods to be matrix-build-time limited rather than matrix-solve-time limited. An extremely simple alternative to all this is described below and demonstrated, in an introductory sense, on some 2-D problems. In this procedure, the fft method, the basis functions are all global Fourier series in a suitably chosen parameter, and one attempts to estimate the coefficients describing the unknown surface current directly from the integral equation. This format circumvents all of the shortcomings discussed above-there are no singular integrals to evaluate. Furthermore, since the fft algorithm is used throughout, the computation is extremely efficient The results shown below suggest that, so far, this approach is very effective.

关键词： boundary-elements methods electromagnetic wave polarisation electromagnetic wave scattering fast Fourier transforms integral equations series (mathematics) 2-D problems EM scattering fft algorithm Fourier series TM polarisation boundary integral equation Fourier series boundary integral equations electromagnetic wave polarisation basis functions Boundary element methods fft algorithm Electromagnetic wave scattering Integral equations Fast Fourier transform

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NUMERICAL IMPLEMENTATION OF THE GABOR REPRESENTATION

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ELECTRONICS LETTERS 1988年第13期24卷 810-811页

作者： EINZIGER, PD Dept. of Electr. Eng. Technion Israel Inst. of Technol. Haipa

Gabor's expansion of an electromagnetic field in a discrete two-dimensional superposition of elementary beams is an extended spectral representation having relevance to wave propagation problems. The computational implications of the expansion scheme are investigated within the context of aperture theory leading to an efficient Gabor's expansion numerical processor

关键词： fft algorithm Gabor representation aperture theory discrete two-dimensional superposition electromagnetic field electromagnetic field theory electromagnetic wave propagation electromagnetic waves elementary beams expansion scheme fast Fourier transform fast Fourier transforms numerical processor wave propagation

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Evaluation of radiation loading on finite cylindrical shells using the fast Fourier transform: A comparison with direct numerical integration

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JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2018年第3期143卷 EL160-EL166页

作者： Liu, S. X. Zou, M. S. China Ship Sci Res Ctr Wuxi 214082 Peoples R China State Key Lab Deep Sea Manned Vehicles Wuxi 214082 Peoples R China

The radiation loading on a vibratory finite cylindrical shell is conventionally evaluated through the direct numerical integration (DNI) method. An alternative strategy via the fast Fourier transform algorithm is put forward in this work based on the general expression of radiation impedance. To check the feasibility and efficiency of the proposed method, a comparison with DNI is presented through numerical cases. The results obtained using the present method agree well with those calculated by DNI. More importantly, the proposed calculating strategy can significantly save the time cost compared with the conventional approach of straightforward numerical integration. (C) 2018 Acoustical Society of America

关键词： Numerical integration cylindrical shells fft algorithm Fast Fourier transform Radiation DNI

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Efficient simulation of two-spatial dimensional turbulent wind fields based on the factorization of random functions

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JOURNAL OF WIND ENGINEERING AND INDUSTRIAL AERODYNAMICS 2024年 247卷

作者： Liu, Yun Wang, Hao Xu, Zidong Zhao, Kaiyong Southeast Univ Key Lab C &PC Struct Minist Educ Nanjing 211189 Peoples R China Southeast Univ Sch Civil Engn Nanjing 211189 Peoples R China

Refined modelling of turbulence in two-spatial dimensions is necessary for reliability assessment of large-size structures such as wind turbines. Stochastic wave-based spectral representation (SWSR) method is a widelyused tool. However, the correlation of turbulent components is usually neglected in it. Based on the SWSR, a multi-dimension (n-D) multi-variable (n-V) continuous temporal-spatial field model is thus proposed in this study. The low efficiency exist in this model, which are also unavoidable in others when simulating turbulence in multi-spatial dimensions. One reason is the large number of sample functions in the Monte Carlo (MC)-based method. The other is the n-D matrix-based Fast Fourier Transform (fft) algorithm in single sample generation. Therefore, an efficient method is given to improve efficiency in both two aspects. The former improvement is realized through defining multi-index dimension reduction (DR) expressions in the proposed model. The latter is based on the 1-D vector-based fft algorithm, the key to which are the decoupling of n-D matrices and factorization of multi-index DR expressions. A numerical simulation of a stochastic wind field in two-spatial dimensions is designed to demonstrate the validity of the proposed method. Results show its improvement of efficiency in both views of sample sets and single sample generation.

关键词： Turbulence simulation Stochastic wave Spectral representation method Dimension reduction fft algorithm

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