Gözde Sarı

Boundary Layer Equations and Lie Group Analysis of a Sisko Fluid

Boundary layer equations are derived for the Sisko fluid. Using Lie group theory, a symmetry analysis of the equations is performed. A partial differential system is transferred to an ordinary differential system via symmetries. Resulting equations are numerically solved. Effects of non-Newtonian parameters on the solutions are discussed.

Vibrations of a Slightly Curved Microbeam Resting on an Elastic Foundation with Nonideal Boundary Conditions

An investigation into the dynamic behavior of a slightly curved resonant microbeam having nonideal boundary conditions is presented. The model accounts for midplane stretching, an applied axial load, and a small AC harmonic force. The ends of the curved microbeam are on immovable simple supports and the microbeam is resting on a nonlinear elastic foundation. The forced vibration response of curved microbeam due to the small AC load is obtained analytically by means of direct application of the method of multiple scales (a perturbation method). The effects of the nonlinear elastic foundation as well as the effect of curvature on the vibrations of the microbeam are examined. It is found that the effect of curvature is of softening type. For sufficiently high values of the coefficients, the elastic foundation and the axial load may suppress the softening behavior resulting in hardening behavior of the nonlinearity. The frequencies and mode shapes obtained are compared with the ideal boundary conditions case and the differences between them are contrasted on frequency-response curves. The frequency response and nonlinear frequency curves obtained may provide a reference for the choice of reasonable resonant conditions, design, and industrial applications of such systems. Results may be beneficial for future experimental and theoretical works on MEMS.

A comprehensive perturbation theorem for estimating magnitudes of roots of polynomials

A comprehensive new perturbation theorem is posed and proven to estimate the magnitudes of roots of polynomials. The theorem successfully determines the magnitudes of roots for arbitrary degree of polynomial equations with no restrictions on the coefficients. In the previous papers ‘Pakdemirli and Elmas, Appl. Math. Comput. 216 (2010) 1645–1651’ and ‘Pakdemirli and Yurtsever, Appl. Math. Comput. 188 (2007) 2025–2028’, the given theorems were valid only for some restricted coefficients. The given theorem in this work is a generalization and unification of the past theorems and valid for arbitrary coefficients. Numerical applications of the theorem are presented as examples. It is shown that the theorem produces good estimates for the magnitudes of roots of polynomial equations of arbitrary order and unrestricted coefficients.

Lie Group Analysis of Unsteady Flow and Heat Transfer over a Porous Surface for a Viscous Fluid

The problem of a two-dimensional, unsteady flow and a heat transfer of a viscous fluid past a surface in the presence of variable suction/injection is analyzed. The unsteadiness is due to the time dependent free stream flow. The governing equations are derived with the usual boundary layer approximation. Using Lie group theory, a group classification of the equations with respect to the variable free stream flow and suction/injection velocity is performed. Restrictions imposed by the boundary conditions on the symmetries are discussed. Adopting the obtained symmetry groups, governing partial differential equations are converted into ordinary differential equations and then solved numerically. Effects of the dimensionless problem parameters on the velocity and temperature profiles are outlined in the figures.

Numerical analysis of vibrating touch screen actuated by piezo elements

Audiovisual feedback generally is used on touch screens on portable electronic devices, which are frequently used in daily life. Tactile feedback is one of the issues that have recently gained importance in this technology. Tactile feedback occurs by stimulating the nerves at the fingertip by moving the touch screen. In this study, we have determined the vibration characteristics of touchscreens made from different materials used in the sector. The finite element method is employed to obtain the vibration modes of the screen. In addition to, the effects of the materials of piezo, applied voltage, the number of the piezo patches are investigated to produce the best vibration function and graphically are presented.

An experimental study of a piezoelectrically actuated touch screen

An audiovisual feedback is used on touch screens in portable electronic devices. When these devices are used in noisy and distracting environments, suitable available feedback methods is severely inadequate and the availability of the device severely reduced. For these reasons, touch screen technology has become a popular recently. These panels used in many sectors such as watches, cars, mobile devices, aerospace. Touch screens, which provide tactile feedback to the user, are activated using solenoid actuators, coil-type actuators or vibration motors. The use of evolving piezoelectric vibrators has attracted considerable attention in recent years to obtain high-resolution tactile feedback. Their higher bandwidth helps create more user-perceivable haptic effects. In this work, we experimented to observe the effect of the piezo vibrator on the screen. As a result, the various types of tactile feedback functions will be developed on the screen and compared. The best vibration functions depending on the settings are obtained through experiments.

Solution of a quadratic nonlinear problem with multiple scales Lindstedt-Poincare method

A recently developed perturbation algorithm namely the Multiple Scales Lindstedt-Poincare method (MSLP) is employed to solve an equation with quadratic nonlinearity. Approximate solutions are obtained with classical multiple scales Method (MS) and the MSLP method and they are compared with numerical solutions. It is shown that MSLP solutions are better than the MS solutions for the strongly nonlinear case.

Non-Newtonian fluid effects on surface reactions in a microfluidic flow cell

Mass transfer over a reactive surface in microfluidic flow cells plays a key role in understanding biomoleculer interactions and diagnosis of small molecules for biomedical and environmental applications. The effects of Non-Newtonian power law fluid on the binding reaction kinetic of immunoglobulin G in a flow cell are analyzed in this study. Governing equations for the fluid flow, mass transport and surface reaction are derived. The finite element method is employed to solve resulting equations. In addition, the effects of volumetric flow rate, fluid behavior index and reaction constants on the surface reaction are analyzed and presented graphically.