The Experts below are selected from a list of 13989 Experts worldwide ranked by ideXlab platform
T. Zhong - One of the best experts on this subject based on the ideXlab platform.
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the structure of Weighting Coefficient matrices of harmonic differential quadrature and its applications
arXiv: Computational Engineering Finance and Science, 1999Co-Authors: Wen Chen, W Wang, T. ZhongAbstract:The structure of Weighting Coefficient matrices of Harmonic Differential Quadrature (HDQ) is found to be either centrosymmetric or skew centrosymmetric depending on the order of the corresponding derivatives. The properties of both matrices are briefly discussed in this paper. It is noted that the computational effort of the harmonic quadrature for some problems can be further reduced up to 75 per cent by using the properties of the above-mentioned matrices.
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The structure of Weighting Coefficient matrices of harmonic differential quadrature and its applications
Communications in Numerical Methods in Engineering, 1996Co-Authors: Xiaohua Wang, T. ZhongAbstract:SUMMARY The structure of Weighting Coefficient matrices of harmonic differential quadrature (HDQ) is found to be either centrosymmetric or skew centrosymmetric, depending on the order of the corresponding derivatives. The properties of both matrices are briefly discussed in the paper. It is noted that the computational effort of the harmonic quadrature for some problems can be further reduced by up to 75 per cent by using the properties of the above-mentioned matrices.
T C Fung - One of the best experts on this subject based on the ideXlab platform.
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generalized lagrange functions and Weighting Coefficient formulae for the harmonic differential quadrature method
International Journal for Numerical Methods in Engineering, 2003Co-Authors: T C FungAbstract:In the harmonic differential quadrature method, truncated Fourier series comprising the trigonometric functions are used to approximate the solutions. The generalized Lagrange functions composed of trigonometric functions are constructed as interpolation functions so that the unknowns are the function values, rather than the Fourier Coefficients. In the spirit of the differential quadrature method, the derivatives at a sampling grid point are expressed as weighted linear sums of function values at all the sampling grid points. It is shown that the corresponding Weighting Coefficients of higher order derivatives can be evaluated recursively and the general explicit formulae are given in this paper. The differential quadrature analog of the governing equations can then be established easily at the sampling grid points. For the periodic boundary value problems, the periodic boundary conditions are satisfied automatically and no other boundary conditions are required in general. It is also shown that the harmonic differential quadrature method is related to the trigonometric collocation method and the harmonic balance method. Numerical examples are given to illustrate the validity and efficiency of the present method. Copyright © 2003 John Wiley & Sons, Ltd.
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imposition of boundary conditions by modifying the Weighting Coefficient matrices in the differential quadrature method
International Journal for Numerical Methods in Engineering, 2003Co-Authors: T C FungAbstract:One of the important issues in the implementation of the differential quadrature method is the imposition of the given boundary conditions. There may be multiple boundary conditions involving higher-order derivatives at the boundary points. The boundary conditions can be imposed by modifying the Weighting Coefficient matrices directly. However, the existing method is not robust and is known to have many limitations. In this paper, a systematic procedure is proposed to construct the modified Weighting Coefficient matrices to overcome these limitations. The given boundary conditions are imposed exactly. Furthermore, it is found that the numerical results depend only on those sampling grid points where the differential quadrature analogous equations of the governing differential equations are established. The other sampling grid points with no associated boundary conditions are not essential. Copyright © 2002 John Wiley & Sons, Ltd.
Xiaohua Wang - One of the best experts on this subject based on the ideXlab platform.
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The structure of Weighting Coefficient matrices of harmonic differential quadrature and its applications
Communications in Numerical Methods in Engineering, 1996Co-Authors: Xiaohua Wang, T. ZhongAbstract:SUMMARY The structure of Weighting Coefficient matrices of harmonic differential quadrature (HDQ) is found to be either centrosymmetric or skew centrosymmetric, depending on the order of the corresponding derivatives. The properties of both matrices are briefly discussed in the paper. It is noted that the computational effort of the harmonic quadrature for some problems can be further reduced by up to 75 per cent by using the properties of the above-mentioned matrices.
C Shu - One of the best experts on this subject based on the ideXlab platform.
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implementation of clamped and simply supported boundary conditions in the gdq free vibration analysis of beams and plates
International Journal of Solids and Structures, 1997Co-Authors: C ShuAbstract:Abstract In this paper, a new methodology for implementing the clamped and simply supported boundary conditions is presented for the free vibration analysis of beams and plates using the generalized differential quadrature (GDQ) method. The proposed approach directly substitutes the boundary conditions into the governing equations and is referred to as SBCGE approach. The SBCGE approach is presented to overcome the drawbacks of previous approaches in treating the boundary conditions. A comparison of the SBCGE approach with the method of modifying Weighting Coefficient matrices (MWCM) is made by their application to the vibration analysis of beams and plates with combinations of simply supported and clamped boundary conditions. Some details of the GDQ method are also described in the paper.
Laurent Lablonde - One of the best experts on this subject based on the ideXlab platform.
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bending sensors based on fiber bragg gratings the key role of the mean effective index
EPL, 2017Co-Authors: Romain Guyard, J Beauce, Marc Douay, Julien Potet, Yann Lecieux, Dominique Leduc, Cyril Lupi, Laurent LablondeAbstract:In this article we show that the Bragg wavelength variation induced by a curvature in the fiber Bragg grating is related to both the variation of the effective index and the variation of the coupling Coefficient of counter-propagating modes. The Weighting Coefficient between the two variables is the mean effective index of the grating. The two effects act in opposition as proved both by our model and by our experimental observations. This work can be used to design strain sensors insensitive to bending, or, on the contrary, bending sensors insensitive to strain.
