Erdoğan Özkaya

• PhD
• Professor at Manisa Celal Bayar University

In this study, fluid conveying continuous media was considered as micro beam. Unlike the classical beam theory, the effects of shear stress on micro-structure's dynamic behavior not negligible. Therefore, modified couple stress theory (MCST) were used to see the effects of being micro-sized. By using Hamilton's principle, the nonlinear equations of...

In this study, multi-supported axially moving string is discussed. Supports located at the ends of the string are simple supports. A support located in the middle section owns the features of a spring. String speed is assumed to vary harmonically around an average rate. Hamilton's principle has been used to figure out the nonlinear equations of mot...

This study represents the transverse vibrations of an axially accelerating Euler–Bernoulli beam resting on multiple simple supports. This is one of the examples of a system experiencing Coriolis acceleration component that renders such systems gyroscopic. A small harmonic variation with a constant mean value for the axial velocity is assumed in the...

In this study, the transverse vibrations of an axially moving flexible beams resting on multiple supports are investigated. The time-dependent velocity is assumed to vary harmonically about a constant mean velocity. Simple-simple, fixed-fixed, simple-simple-simple and fixed-simple-fixed boundary conditions are considered. The equation of motion bec...

In this study, nonlinear vibrations of an axially moving multi-supported string have been investigated. The main difference of this study from the others is in that there are non-ideal supports allowing minimal deflections between ideal supports at both ends of the string. Nonlinear equations of the motion and boundary conditions have been obtained...

In this study, nonlinear vibrations of an axially moving string are investigated. The main difference of this study from other studies is that there is a nonideal support between the opposite sides, which allows small displacements. Nonlinear equations of motion and boundary conditions are derived using Hamilton’s principle. Equations of motion and...

The transverse vibrations of an axially accelerating Euler–Bernoulli beam resting on simple supports are investigated. The supports are at the ends, and there is a support in between. The axial velocity is a sinusoidal function of time varying about a constant mean speed. Since the supports are immovable, the beam neutral axis is stretched during t...

In this study, nonlinear transverse vibrations of a tensioned Euler-Bernoulli beam resting on multiple supports are investigated. The immovable end conditions due to simple supports cause stretching of neutral axis and introduce cubic nonlinearity to the equations of motion. Forcing and damping effects are included in the analysis. The general arbi...

In this study, a slightly curved Euler Bernoulli beam carrying a concentrated mass was handled. The beam was resting on an elastic foundation and simply supported at both ends. Effects of the concentrated mass on nonlinear vibrations were investigated. Sinusoidal and parabolic type functions were used as curvature functions. Equations of motion hav...

In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained by using Hamilton's principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Natural frequencies are calculated for different boundary conditions, stepped...

In this study, the vibrations of multiple stepped beams with cubic nonlinearities are considered. A three-to-one internal resonance case is investigated for the system. A general approximate solution to the problem is found using the method of multiple scales (a perturbation technique). The modulation equations of the amplitudes and the phases are...

In this study, nonlinear transverse vibrations of an Euler-Bernoulli beam with multiple supports are considered The beam is supported with immovable ends. The immovable end conditions cause stretching of neutral axis and introduce cubic nonlinear terms to the equations of motion. Forcing and damping effects are included in the problem. The general...

In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained using Hamilton's principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Forcing and damping terms were also included in the equations. The dimensionless...

Artificial neural networks (ANNs) are a new type of information processing system based on modeling the neural system of human brain. Effects of ageing conditions at various temperatures, load, sliding speed, abrasive grit diameter in 6351 aluminum alloy have been investigated by using artificial neural networks. The experimental results were train...

We consider an Euler-Bernoulli type beam carrying masses at different locations. Natural frequencies for transverse vibrations are investigated for different end conditions. Frequency equations are obtained for two and three mass cases, and analytical and numerical results are compared.

Transverse vibrations of curved beams are investigated. Different curvatures are considered. The beam is simply supported and resting on a nonlinear elastic foundation. The method of multiple scales is used in the analysis. A three-to-one internal resonance case is studied. It is possible when one of the mode numbers is three times the other mode....

Vibrations of a general continuous system with arbitrary quadratic nonlinearities are considered. The nonlinearities are expressed in terms of arbitrary quadratic operators. The two-to-one internal resonance case is considered. A general approximate solution is presented for the system. Amplitude and phase modulation equations are derived. Steady s...

A general continuous system with an arbitrary cubic non-linearity is considered. The non-linearity is expressed in terms of an arbitrary cubic operator. Three-to-one internal resonance case is considered. A general approximate solution is presented for the system. Amplitude and phase modulation equations are derived. Steady state solutions and thei...

An Euler-Bernoulli beam carrying concentrated masses is considered to be a beam-mass system. The beam is simply supported at both ends. The non-linear equations of motion are derived including stretching due to immovable end conditions. The stretching introduces cubic non-linearities into the equations. Forcing and damping terms are also included....

The calculation of the natural frequencies of suspension bridges and the parameters affecting the frequencies are studied. The exact values of the frequencies are calculated by the Newton-Raphson method. For each group of parameters, numerical analysis should be repeated, a lengthy process which requires the convergence of iterations. When the init...

An Euler–Bernoulli beam carrying concentrated masses is considered to be a beam–mass system. The beam is simply supported at both ends. The non-linear equations of motion are derived including stretching due to immovable end conditions. The stretching introduces cubic non-linearities into the equations. Forcing and damping terms are also included....

In this study, it was proposed that the residual stresses within steel bars after quenching in water from 600 °C could be calculated by using the finite element method (FEM) and an artificial neural network (ANN) algorithm. Three modelled cylindrical specimens of AISI 1020 steel were heated and then quenched in water. Using FEM, temperature distrib...

Transverse vibrations of a beam moving with time dependent axial velocity have been investigated. Analytical solutions of the problem are found using the systematic approach of Lie group theory. Group classification with respect to the arbitrary velocity function has been performed using a newly developed technique of equivalence transformations. F...

Transverse vibrations of an axially moving beam are considered. The axial velocity is harmonically varying about a mean velocity. The equation of motion is expressed in terms of dimensionless quantities. The beam effects are assumed to be small. Since, in this case, the fourth order spatial derivative multiplies a small parameter, the mathematical...

Transverse vibrations of a string moving with time-dependent velocity v (t) have been investigated. Analytical solutions of the problem are found using the systematic approach of Lie group theory. Group classification with respect to the arbitrary velocity function has been performed using a newly developed technique of equivalence transformations....

A clamped–clamped beam–mass system is considered. The non-linear equations of motion including stretching due to immovable end conditions were derived previously [1] (Özkayaet al. 1997Journal of Sound and Vibration199, 679–696). In addition to five different end conditions considered in reference [1], the case of clamped–clamped edge conditions is...

An approximate analytical expression for the natural frequency is given for the problem. For velocity profiles harmonically varying about a mean velocity, stability borders are determined analytically for fluctuation frequency versus amplitudes. Beam effects cause the stability boundaries to shift to higher frequency values

We study transverse vibrations of a simply supported beam moving with constant velocity, taking into account the transition from string to beam effects. In this model, the fourth-order spatial derivative multiplies a small parameter, and hence there arises a boundary layer. The problem is solved approximately using the method of multiple scales.

In this study, non-linear vibrations of slightly curved beams are investigated. The curvature is taken as an arbitrary function of the spatial variable. The initial displacement is not due to buckling of the beam, but is due to the geometry of the beam itself. The ends of the curved beam are on immovable simple supports and the beam is resting on a...

An Euler-Bernoulli beam and a concentrated mass on this beam are considered as a beam-mass system. The beam is supported by immovable end conditions, thus leading to stretching during the vibrations. This stretching produces cubic non-linearities in the equations. Forcing and damping terms are added into the equations. The dimensionless equations a...

In this study, the nonlinear vibrations of Euler-Bernoulli multiple-stepped beam are investigated. The beam is simply supported at both ends. The equations of motions are obtained using Hamilton's principle and made non-dimensional. The stretching effect induced non-linear terms to the equations. Forcing and damping terms are also included in the e...

Nonlinear vibrations of a multi-stepped Euler-Bernoulli beam with n different steps at arbitrary points are investigated. The beam is clamped at both ends. The equations of motion and boundary conditions are obtained using Hamilton’s principle. The equations of motion are made non-dimensional. So, the dependence of solution is eliminated from the m...

ZET Bu çalışmada dairesel kesitli bir kiriş ve bu kiriş üzerinde keyfi noktalarda n tane kademeye sahip bir kiriş sistemi ele alınmıştır. Her iki ucundan basit olarak mesnetlendiği kabul edilen kiriş için titreşim analizi yapılmıştır. Hamilton prensibi kullanılarak hareket denklemleri elde edilmiş ve denklemler boyutsuzlaştırılmıştır. Elde edilen k...