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Yayın Nonlinear wave modulation in a prestressed thin elastic tube filled with an inviscid fluid(Wit Press, 2002) Bakırtaş, İlkay; Demiray, HilmiIn the present work, employing the nonlinear equations of an incompressible, isotropic and elastic thin tube and the approximate equations of an incompressible inviscid fluid and then utilizing the reductive perturbation technique, the amplitude modulation of weakly nonlinear waves is examined. It is shown that, the amplitude modulation of these waves is governed by a nonlinear Schrödinger (NLS) equation. The result is compared with some previous works on the same subject. The modulational instability of the monochromatic wave solution is discussed for some elastic materials and initial deformations. It is shown that the amplitude modulation of weakly nonlinear waves near the marginal state is governed by the Generalized Nonlinear Schrödinger equation (GNLS).Yayın 3-D Vibration analysis of microstretch plates(Springer, 2008) İnan, Esin; Kiriş, AhmetIn the present work, rectangular plates with various boundary conditions are Studied, which are modeled by the rnicrostretch theory. Wave propagation problem is investigated and new waves are observed which do not appear in the classical theory of elasticity. Ritz method is used for this investigation. Triplicate Chebyshev series, multiplied by boundary functions, are used as admissible functions and the frequency equations of the micro-stretch plate are obtained by the use of Chebyshev-Ritz method. The additional frequencies due to the microstructure of the plate are observed among the values of the frequencies obtained from the classical theory of elasticity. We observed that these additional frequencies disappear while the all microstretch constants are taken as zero.Yayın On travelling wave solutions of a generalized Davey-Stewartson system(Oxford Univ Press, 2005-02) Eden, Osman Alp; Erbay, SaadetThe generalized Davey-Stewartson (GDS) equations, as derived by Babaoglu & Erbay (2004, Int. J. Non-Linear Mech., 39, 941-949), is a system of three coupled equations in (2 + 1) dimensions modelling wave propagation in an infinite elastic medium. The physical parameters (gamma, m(1), m(2), lambda and n) of the system allow one to classify the equations as elliptic-elliptic-elliptic (EEE), elliptic-elliptic-hyperbolic (EEH), elliptic-hyperbolic-hyperbolic (EHH), hyperbolic-elliptic-elliptic (HEE), hyperbolic-hyperbolic-hyperbolic (HHH) and hyperbolic-elliptic-hyperbolic (HEH) (Babaoglu et al., 2004, preprint). In this note, we only consider the EEE and HEE cases and seek travelling wave solutions to GDS systems. By deriving Pohozaev-type identities we establish some necessary conditions on the parameters for the existence of travelling waves, when solutions satisfy some integrability conditions. Using the explicit solutions given in Babaoglu & Erbay (2004) we also show that the parameter constraints must be weaker in the absence of such integrability conditions.Yayın Dynamic extension of a compressible nonlinearly elastic membrane tube(Oxford Univ Press, 2005-02) Erbay, Hüsnü Ata; Tüzel, Vasfiye HandeThe 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.
