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  • Open Access


    Highly Accurate Golden Section Search Algorithms and Fictitious Time Integration Method for Solving Nonlinear Eigenvalue Problems

    Chein-Shan Liu1, Jian-Hung Shen2, Chung-Lun Kuo1, Yung-Wei Chen2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.2, pp. 1317-1335, 2024, DOI:10.32604/cmes.2023.030618

    Abstract This study sets up two new merit functions, which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems. For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less, where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector. 1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues. Simultaneously, the real… More >

  • Open Access


    Solving Fully Fuzzy Nonlinear Eigenvalue Problems of Damped Spring-Mass Structural Systems Using Novel Fuzzy-Affine Approach

    S. Rout1, S. Chakraverty1,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.121, No.3, pp. 947-980, 2019, DOI:10.32604/cmes.2019.08036

    Abstract The dynamic analysis of damped structural system by using finite element method leads to nonlinear eigenvalue problem (NEP) (particularly, quadratic eigenvalue problem). In general, the parameters of NEP are considered as exact values. But in actual practice because of different errors and incomplete information, the parameters may have uncertain or vague values and such uncertain values may be considered in terms of fuzzy numbers. This article proposes an efficient fuzzy-affine approach to solve fully fuzzy nonlinear eigenvalue problems (FNEPs) where involved parameters are fuzzy numbers viz. triangular and trapezoidal. Based on the parametric form, fuzzy numbers have been transformed into… More >

  • Open Access


    Vibration Analysis of Arbitrarily Shaped Membranes

    S.Yu. Reutskiy1

    CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.2, pp. 115-142, 2009, DOI:10.3970/cmes.2009.051.115

    Abstract In this paper a new numerical technique for problems of free vibrations of arbitrary shaped non-homogeneous membranes:∇2w + k2q(x)w = 0, x∈ Ω⊂R2, B[w] = 0, x∈∂Ω is presented. Homogeneous membranes of a complex form are considered as a particular case. The method is based on mathematically modeling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the resonant frequencies. Applying the method, one gets a sequence of boundary value problems (BVPs) depending on the spectral parameter k. The eigenvalues are sought as positions of the maxima of… More >

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