İlkay Bakırtaş

The problem of a rigid punch on a non-homogeneous elastic half space

Abstract The elastostatic problem of a rigid punch on an elastic half space is considered. The medium is assumed to exhibit a non-homogeneity varying with depth. Using the Fourier Transform Technique, the mixed boundary value problem is reduced to a singular integral equation which is solved numerically. The effect of non-homogeneity on the stress distribution under the punch and on the stress singularity is studied. The influence of Poissons ratio on the results is also considered.

The contact problem of an orthotropic non-homogeneous elastic half space

Abstract The problem of a rigid punch on an elastic half plane with orthotropic and non-homogeneous material is considered. The axes of orthotropy are chosen to coincide with the Cartesian coordinate system in which one axis is parallel to the edge of the half plane and the other is perpendicular to it. Non-homogeneity is introduced in both directions of orthotropy as continuous functions along these directions. Using the Fourier Transform Technique, the mixed boundary value problem is reduced to a singular integral equation which is solved numerically. The formulation of the problem is obtained for a rigid punch with arbitrary shape.

Amplitude modulation of nonlinear waves in a fluid-filled tapered elastic tube

In 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.

Evolution equations for nonlinear waves in a tapered elastic tube filled with a viscous fluid

Abstract In this work, employing the reductive perturbation method and treating the arteries as a tapered, thin walled, long and circularly conical prestressed elastic tube, the propagation of weakly nonlinear waves is investigated in such a fluid-filled elastic tube. By considering the blood as an incompressible viscous fluid, depending on the viscosity and perturbation parameters we obtained various evolution equations as the extended Korteweg–de Vries (KdV), extended KdV Burgers and extended perturbed KdV equations. Progressive wave solutions to these evolution equations are obtained and it is observed that the wave speeds increase with the distance for negative tapering while they decrease for positive tapering.

Pulse shaping mechanism in mode-locked lasers

A pulse shaping mechanism applied to mode-locked lasers is proposed. By adding a linear (forcing) term in the power energy saturation model, we are able to control the resulting pulses in both energy and shape. In fact, this term also provides a focusing effect keeping most of the pulses energy confined within the width of the forcing. The appropriate condition for which mode-locking occurs is also derived and links the physical parameters of the system (gain, loss, filtering) to those of the pulse (amplitude, width, energy). Thus, given the desired pulse one only needs to fix the lasers parameters accordingly, so as to obey this condition, and mode-locking will occur.

Modulation of nonlinear waves near the marginal state of instability in fluid-filled elastic tubes

Using the nonlinear differential equations governing the motion of a fluid-filled and prestressed long thin elastic tube, the propagation of nonlinear waves near the marginal state is examined through the use of reductive perturbation method. It is shown that the amplitude modulation near the marginal state is governed by a generalized nonlinear Schrodinger (GNLS) equation. Some exact solutions, including oscillatory and solitary waves of the GNLS equation are presented.

Amplitude Modulation of Nonlinear Waves in Fluid-Filled Tapered Tubes

We study the modulation of nonlinear waves in fluid-filled prestressed tapered tubes. For this, we obtain the nonlinear dynamical equations of motion of a prestressed tapered tube filled with an incompressible inviscid fluid. Assuming that the tapering angle is small and using the reductive perturbation method, we study the amplitude modulation of nonlinear waves and obtain the nonlinear Schrödinger equation with variable coefficients as the evolution equation. A traveling-wave type of solution of such a nonlinear equation with variable coefficients is obtained, and we observe that in contrast to the case of a constant tube radius, the speed of the wave is variable. Namely, the wave speed increases with distance for narrowing tubes and decreases for expanding tubes.