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Yayın Contributions of higher order terms to nonlinear waves in fluid-filled elastic tubes: strongly dispersive case(Pergamon-Elsevier Science, 2003-07) 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 modified reductive perturbation technique presented by us [15] the amplitude modulation of weakly nonlinear waves is examined. It is shown that the first order term in the perturbation expansion is governed by a nonlinear Schrodinger equation and the second order term is governed by the linearized Schrodinger equation with a nonhomogeneous term. In the longwave limit a travelling wave type of solution to these equations are also given.Yayın Interactions of nonlinear acoustic waves in a fluid-filled elastic tube(Pergamon-Elsevier Science, 2001-03) Akgün, Güler; Demiray, HilmiIn the present work, the nonlinear interactions of two acoustical waves propagating in a fluid-filled elastic tube with different wave numbers, frequencies and group velocities are examined. Employing the multiple-scale expansion method, expanding the field quantities into asymptotic series of the smallness parameter and solving the resulting differential equations of various orders of the same parameter, we obtained two coupled nonlinear Schrodinger equations. The nonlinear plane wave solutions to these equations are also given for some special cases.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 The boundary layer approximation and nonlinear waves in elastic tubes(Pergamon-Elsevier Science, 2000-09) Antar, Nalan; Demiray, HilmiIn the present work, employing the nonlinear equations of an incompressible, isotropic and elastic thin tube and approximate equations of an incompressible viscous fluid, the propagation of weakly nonlinear waves is examined. In order to include the geometrical and structural dispersion into analysis, the wall's inertial and shear deformation are taken into account in determining the inner pressure-inner cross sectional area relation. Using the reductive perturbation technique, the propagation of weakly nonlinear waves, in the long-wave approximation, are shown to be governed by the Korteweg-de Vries (KdV) and the Korteweg-de Vries-Burgers (KdVB), depending on the balance between the nonlinearity, dispersion and/or dissipation. In the case of small viscosity (or large Reynolds number), the behaviour of viscous fluid is quite close to that ideal fluid and viscous effects are confined to a very thin layer near the boundary. In this case, using the boundary layer approximation we obtain the viscous-Korteweg-de Vries and viscous-Burgers equations.Yayın Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations(Academic Press Inc Elsevier Science, 2011-02-01) Duruk, Nilay; Erbay, Hüsnü Ata; Erkip, AlbertWe study the initial-value problem for a general class of nonlinear nonlocal coupled wave equations. The problem involves convolution operators with kernel functions whose Fourier transforms are nonnegative. Some well-known examples of nonlinear wave equations, such as coupled Boussinesq-type equations arising in elasticity and in quasi-continuum approximation of dense lattices, follow from the present model for suitable choices of the kernel functions. We establish local existence and sufficient conditions for finite-time blow-up and as well as global existence of solutions of the problem.Yayın Reflection and transmission of nonlinear waves from arterial branching(Elsevier Ltd, 2006-10) Demiray, HilmiIn this work, treating the arteries as a prestressed thin walled elastic tube and the blood as an inviscid fluid, we have studied the reflection and transmission of nonlinear waves from arterial branching, through the use of reductive perturbation method. The reflected and the transmitted waves at the bifurcation point are calculated in terms of the incident wave. The numerical results indicate that the reflected wave is comparatively small whereas the transmitted waves in branches are comparable with the incident wave. This result is quite consistent with the experimental measurements [N. Sergiopulos, M. Spiridon, F. Pythoud, J.J. Meister, On wave transmission and reflection properties of stenosis, J. Biomechanics 26 (1996) 31-38].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 A Higher-order Boussinesq equation in locally non-linear theory of one-dimensional non-local elasticity(Oxford Univ Press, 2009-02) Duruk, Nilay; Erkip, Albert; Erbay, Hüsnü AtaIn one space dimension, a non-local elastic model is based on a single integral law, giving the stress when the strain is known at all spatial points. In this study, we first derive a higher-order Boussinesq equation using locally non-linear theory of 1D non-local elasticity and then we are able to show that under certain conditions the Cauchy problem is globally well-posed.Yayın Amplitude modulation of nonlinear waves in a fluid-filled tapered elastic tube(Elsevier Science Inc, 2004-07-15) Bakırtaş, İlkay; Demiray, HilmiIn the present work, treating the arteries as a tapered, thin walled, long and circularly conical prestressed elastic tube and using the reductive perturbation method, we have studied the amplitude modulation of nonlinear waves in such a fluid-filled elastic tube. By considering the blood as an incompressible inviscid fluid the evolution equation is obtained as the nonlinear Schrodinger equation with variable coefficients. It is shown that this type of equations admit a solitary wave type of solution with variable wave speed. It is observed that, the wave speed decreases with distance for tubes with descending radius while it increases for tubes with ascending radius.Yayın Eshelby tensors for a spherical inclusion in microstretch elastic fields(Elsevier Ltd, 2006-08) Kırış, Ahmet; İnan, EsinIn the present work, microelastic and macroelastic fields are presented for the case of spherical inclusions embedded in an infinite microstretch material using the concept of Green's functions. The Eshelby tensors are obtained for a spherical inclusion and it is shown that their forms for microelongated, micropolar and the classical cases are the proper limiting cases of the Eshelby tensors of microstretch materials.
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