Browsing by Author "Özkaya E."
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Item Non-liner vibrations of a beam-mass system under different boundary conditions(Academic Press, 1997) Özkaya E.; Pakdemirli M.; Öz H.R.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 are solved for five different set of boundary conditions. Approximate solutions of the equations are obtained by using the method of multiple scales, a perturbation technique. The first terms of the perturbation series lead to the linear problem. Natural frequencies and mode shapes for the linear problem are calculated exactly for different end conditions. Second order non-linear terms of the perturbation series appear as corrections to the linear problem. Amplitude and phase modulation equations are obtained. Non-linear free and forced vibrations are investigated in detail. The effects of the position and magnitude of the mass, as well as effects of different end conditions on the vibrations, are determined. © 1997 Academic Press Limited.Item Non-linear vibrations of a slightly curved beam resting on anon-linear elastic foundation(Academic Press, 1998) Öz H.R.; Pakdemirli M.; Özkaya E.; Yilmaz M.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 non-linear elastic foundation. The immovable end supports result in the extension of the beam during the vibration and hence introduces further non-linear terms to the equations of motion. The integro-differential equations of motion are solved analytically by means of direct application of the method of multiple scales (a perturbation method). The amplitude and phase modulation equations are derived for the case of primary resonances. Both free and forced vibrations with damping are investigated. Effect of non-linear elastic foundation as well as the effect of curvature on the vibrations of the beam are examined. It is found that the effect of curvature is of softening type. For sufficiently high values of the coefficients, the elastic foundation may suppress the softening behaviour resulting in a hardening behaviour of the non-linearity. © 1998 Academic Press Limited.Item Vibrations of a beam-mass systems using artificial neural networks(Elsevier Ltd, 1998) Karlik B.; Özkaya E.; Aydin S.; Pakdemirli M.The nonlinear vibrations of an Euler-Bernoulli beam with a concentrated mass attached to it are investigated. Five different sets of boundary conditions are considered. The transcendental equations yielding the exact values of natural frequencies are presented. Using the Newton-Raphson method, natural frequencies are calculated for different boundary conditions, mass ratios and mass locations. The corresponding nonlinear correction coefficients are also calculated for the fundamental mode. The calculated natural frequencies and nonlinear corrections are used in training a multi-layer, feed-forward, backpropagation artificial neural network (ANN) algorithm. The algorithm produces results within 0.5 and 1.5% error limits for linear and nonlinear cases, respectively. By employing the ANN algorithm, computational time is drastically reduced compared with the conventional numerical techniques. © 1998 Published by Elsevier Science Ltd. All rights reserved.Item Non-linear vibrations of a beam-mass system with both ends clamped(Academic Press, 1999) Özkaya E.; Pakdemirli M.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] (Özkaya et al. 1997 Journal of Sound and Vibration 199, 679-696). In addition to five different end conditions considered in reference [1], the case of clamped-clamped edge conditions is treated in this work. Exact solutions for the mode shapes and frequencies are given for the linear part of the problem. For the non-linear problem, approximate solutions using perturbations are searched. Alternatively, the natural frequencies and non-linear corrections are used in training a multi-layer, feed-forward, back propagation artificial neural network (ANN) algorithm. Using the algorithm, the numerical calculations are drastically reduced for obtaining the natural frequencies and non-linear corrections corresponding to different input parameters. © 1999 Academic Press.Item Lie group theory and analytical solutions for the axially accelerating string problem(Academic Press Ltd, 2000) Özkaya E.; Pakdemirli M.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. From the symmetries of the partial differential equation, the method for deriving exact solutions for the arbitrary velocity case is shown. Special cases of interest such as constant velocity, constant acceleration, harmonically varying velocity and exponentially decaying velocity are investigated in detail. Finally, for a simply supported strip, approximate solutions are presented for the exponentially decaying and harmonically varying cases.Item Vibrations of an axially accelerating beam with small flexural stiffness(Academic Press Ltd, 2000) Özkaya E.; Pakdemirli M.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 model becomes a boundary layer type of problem. Approximate solutions are searched using the method of multiple scales and the method of matched asymptotic expansions. Results of both methods are contrasted with the outer solution.Item Linear transverse vibrations of a simply supported beam carrying concentrated masses(Association for Scientific Research, 2001) Özkaya E.Linear transverse vibrations of an Euler-Bernoulli beam are considered. The beam carries masses and is simply supported at both ends. The equations of motion are obtained and solved. Linear frequency equations are obtained. Natural frequencies are calculated for different number of masses, mass ratios, and mass locations.Item Non-linear transverse vibrations of a simply supported beam carrying concentrated masses(Academic Press, 2002) Özkaya E.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. Exact solutions for the natural frequencies are given for the linear problem. For the nonlinear problem, an approximate solution using a perturbation method is searched. Nonlinear terms of the perturbation series appear as corrections to the linear problem. Amplitude and phase modulation equations are obtained. Non-linear free and forced vibrations are investigated in detail. The effect of the positions, magnitudes and number of the masses are investigated.Item Group - Theoretic approach to axially accelerating beam problem(2002) Özkaya E.; Pakdemirli M.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. From the symmetries of the partial differential equation, the way of deriving exact solutions for the case of arbitrary velocity is shown. Special cases of interest such as constant velocity, harmonically varying velocity and exponentially decaying velocity are investigated in detail. Finally, for a simply supported beam, approximate solutions are presented for the exponentially decaying and harmonically varying cases.Item Natural frequencies of suspension bridges: An artificial neural network approach(Academic Press, 2002) Çevik M.; Özkaya E.; Pakdemirli M.[No abstract available]Item Determination of natural frequencies and stability regions of axially moving beams using artificial neural networks method [3](Academic Press, 2002) Özkaya E.; Öz H.R.[No abstract available]Item Three-to-one internal resonances in a general cubic non-linear continuous system(Academic Press, 2003) Pakdemirli M.; Özkaya E.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 their stability are discussed in the general sense. The sufficiency condition for such resonances to occur is derived. Finally the algorithm is applied to a beam resting on a non-linear elastic foundation.Item Two-to-one internal resonances in continuous systems with arbitrary quadratic nonlinearities(King Fahd University of Petroleum and Minerals, 2004) Pakdemirli M.; Özkaya E.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 state solutions and their stability are discussed in the general sense. The sufficiency condition for such resonances to occur is derived. Finally the algorithm is applied to a specific problem.Item Natural frequencies of beam-mass systems in transverse motion for different end conditions(Association for Scientific Research, 2005) Öz H.R.; Özkaya E.In this study, an Euler-Bernoulli type beam carrying masses at different locations is considered. Natural frequencies for transverse vibrations are investigated for different end conditions. Frequency equations are obtained for two and three mass cases. Analytical and numerical results are compared with each other. © Association for Scientific Research.Item The use of neural networks for the prediction of wear loss and surface roughness of AA 6351 aluminium alloy(Elsevier Ltd, 2006) Durmuş H.K.; Özkaya E.; Meriç C.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 trained in an ANNs program and the results were compared with experimental values. It is observed that the experimental results coincided with ANNs results. © 2004 Elsevier Ltd. All rights reserved.Item Non linear vibrations of stepped beam system under different boundary conditions(Techno-Press, 2007) Özkaya E.; Tekin A.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 equations were solved for six different set of boundary conditions. A perturbation method was applied to the equations of motions. The first terms of the perturbation series lead to the linear problem. Natural frequencies for the linear problem were calculated exactly for different boundary conditions. Second order non-linear terms of the perturbation series behave as corrections to the linear problem. Amplitude and phase modulation equations were obtained. Non-linear free and forced vibrations were investigated in detail. The effects of the position and magnitude of the step, as well as effects of different boundary conditions on the vibrations, were determined.Item Nonlinear transverse vibrations and 3:1 internal resonances of a beam with multiple supports(American Society of Mechanical Engineers(ASME), 2008) Özkaya E.; Baǧdatli S.M.; Öz H.R.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 arbitrary number of support case is considered at first, and then 3-, 4-, and 5-support cases are investigated The method of multiple scales is directly applied to the partial differential equations. Natural frequencies and mode shapes for the linear problem are found. The correction terms are obtained from the last order of expansion. Nonlinear frequencies are calculated and then amplitude and phase modulation figures are presented for different forcing and damping cases. The 3:1 internal resonances are investigated. External excitation frequency is applied to the first mode and responses are calculated for the first or second mode. Frequency-response and force-response curves are drawn. Copyright © 2008 by ASME.Item Three-to-one internal resonance in multiple stepped beam systems(Springer Netherlands, 2009) Tekin A.; Özkaya E.; Bağdatlı S.M.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 derived for two modes. These equations are utilized to determine steady state solutions and their stabilities. It is assumed that the external forcing frequency is close to the lower frequency. For the numeric part of the study, the three-to-one ratio in natural frequencies is investigated. These values are observed to be between the first and second natural frequencies in the cases of the clamped-clamped and clamped-pinned supports, and between the second and third natural frequencies in the case of the pinned-pinned support. Finally, a numeric algorithm is used to solve the three-to-one internal resonance. The first mode is externally excited for the clamped-clamped and clamped-pinned supports, and the second mode is externally excited for the pinned-pinned support. Then, the amplitudes of the first and second modes are investigated when the first mode is externally excited. The amplitudes of the second and third modes are investigated when the second mode is externally excited. The force-response, damping-response, and frequency-response curves are plotted for the internal resonance modes of vibrations. The stability analysis is carried out for these plots. © 2009 Shanghai University and Springer Berlin Heidelberg.Item Nonlinear transverse vibrations of a slightly curved beam carrying a concentrated mass(2009) Özkaya E.; Sarigül M.; Boyaci H.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 have cubic nonlinearities because of elongations during vibrations. Damping and harmonic excitation terms were added to the equations of motion. Method of multiple scales, a perturbation technique, was used for solving integro-differential equation analytically. Natural frequencies were calculated exactly for different mass ratios, mass locations, curvature functions, and linear elastic foundation coefficients. Amplitude-phase modulation equations were found by considering primary resonance case. Effects of nonlinear terms on natural frequencies were calculated. Frequency-amplitude and frequency-response graphs were plotted. Finally effects of concentrated mass and chosen curvature function on nonlinear vibrations were investigated. © 2009 The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH.Item Non linear vibrations of stepped beam systems using artificial neural networks(Techno-Press, 2009) Baǧdatli S.M.; Özkaya E.; Özyiǧit H.A.; Tekin A.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 ratios and stepped locations by Newton-Raphson Method. The corresponding nonlinear correction coefficients are also calculated for the fundamental mode. At the second part, an alternative method is produced for the analysis. The calculated natural frequencies and nonlinear corrections are used for training an artificial neural network (ANN) program which has a multi-layer, feed-forward, back-propagation algorithm. The results of the algorithm produce errors less than 2.5% for linear case and 10.12% for nonlinear case. The errors are much lower for most cases except clamped-clamped end condition. By employing the ANN algorithm, the natural frequencies and nonlinear corrections are easily calculated by little errors, and the computational time is drastically reduced compared with the conventional numerical techniques.