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2005 - 20072
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Yazar: Erbay, Hüsnü Ata × İndeks: Conference Proceedings Citation Index – Science (CPCI-S) ×

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  • Küçük Resim
    Yayın
    A numerical study of the long wave-short wave interaction equations
    (Elsevier B.V., 2007-03-07) Borluk, Handan; Muslu, Gülçin Mihriye; Erbay, Hüsnü Ata
    Two numerical methods are presented for the periodic initial-value problem of the long wave-short wave interaction equations describing the interaction between one long longitudinal wave and two short transverse waves propagating in a generalized elastic medium. The first one is the relaxation method, which is implicit with second-order accuracy in both space and time. The second one is the split-step Fourier method, which is of spectral-order accuracy in space. We consider the first-, second- and fourth-order versions of the split-step method, which are first-, second- and fourth-order accurate in time, respectively. The present split-step method profits from the existence of a simple analytical solution for the nonlinear subproblem. We numerically test both the relaxation method and the split-step schemes for a problem concerning the motion of a single solitary wave. We compare the accuracies of the split-step schemes with that of the relaxation method. Assessments of the efficiency of the schemes show that the fourth-order split-step Fourier scheme is the most efficient among the numerical schemes considered.
  • Küçük Resim
    Yayın
    Dynamic extension of a compressible nonlinearly elastic membrane tube
    (Oxford Univ Press, 2005-02) Erbay, Hüsnü Ata; Tüzel, Vasfiye Hande
    The dynamic response of an isotropic compressible hyperelastic membrane tube is considered when one end is fixed and the other is subjected to a suddenly applied dynamic extension. The equations governing dynamic axially symmetric deformations of the membrane tube are presented for a general form of compressible isotropic elastic strain-energy function. Numerical results, obtained using a Godunov-type finite volume method and valid up to the time at which reflections occur at the fixed end of the tube, are given for two specific forms of the strain-energy function that characterizes a class of compressible elastomers (the Blatz-Ko model). The question of how the numerical results are related to the exact solution obtained for a limiting case is discussed.