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A comparison of different versions of the method of multiple scales for partial differential equations
(Academic Press, 1997) Boyaci H.; Pakdemirli M.
Applications of the methods of multiple scales (a perturbation method) to partial differential systems arising in non-linear vibrations of continuous systems are considered. Two different versions of the method of multiple scales are applied to two general non-linear models. In one of the models, the small parameter (ε) multiplies an arbitrary non-linear cubic operator whereas in the other model, arbitrary quadratic and cubic non-linearities exist. The linear parts of both models are represented by arbitrary operators. General solutions are found by applying different versions of the method of multiple scales. Results of the first version (reconstitution method) and the second version (proposed by Rahman and Burton [8]) are compared for both models. From the comparisons of both methods, it is found that the second version yields better results. Applications of the general models to specific problems are also presented. A final recommendation is to use the second version of the method of multiple scales combined with the direct-perturbation method in finding steady state solutions of partial differential equations. © 1997 Academic Press Limited.
Stability analysis of an axially accelerating string
(Academic Press, 1997) Pakdemirli M.; Ulsoy A.G.
The dynamic response of an axially accelerating string is investigated. The time dependent velocity is assumed to vary harmonically about a constant mean velocity. Approximate analytical solutions are sought using two different approaches. In the first approach, the equations are discretized first and then the method of multiple scales is applied to the resulting equations. In the second approach, the method of multiple scales is applied directly to the partial differential system. Principal parametric resonances and combination resonances are investigated in detail. Stability boundaries are determined analytically. It is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies. When the velocity variation frequency is close to zero or to the difference of two natural frequencies, however, no instabilities are detected up to the first order of perturbation. Numerical results are presented for a band-saw and a threadline problem.
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.
The direct-perturbation method versus the discretization-perturbation method: Linear systems
(Academic Press, 1997) Pakdemirli M.; Boyaci H.
[No abstract available]
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.
Vibrations of an axially moving beam with time-dependent velocity
(Academic Press, 1999) Öz H.R.; Pakdemirli M.
The dynamic response of an axially accelerating, elastic, tensioned beam is investigated. The time-dependent velocity is assumed to vary harmonically about a constant mean velocity. These systems experience a coriolis acceleration component which renders such systems gyroscopic. The equation of motion is solved by using perturbation analysis. Principal parametric resonances and combination resonances are investigated in detail. Stability boundaries are determined analytically. It is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies. When the velocity variation frequency is close to zero or to the difference of two natural frequencies, however, no instabilities are detected up to the first order of perturbation. Numerical results are presented for different flexural stiffness values and for the first two modes. © 1999 Academic Press.
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.
Vibrations of continuous systems with a general operator notation suitable for perturbative calculations
(Academic Press, 2001) Pakdemirli M.
The operator notation previously developed to analyze vibrations of continuous systems has been further generalized to model a system with an arbitrary number of coupled differential equations. Linear parts of the equations are expressed with an arbitrary linear differential and/or integral operators, and non-linear parts are expressed with arbitrary quadratic and cubic operators. Equations of motion are solved in their general form using the method of multiple scales, a perturbation technique. The case of primary resonances of the external excitation and one-to-one internal resonances between the natural frequencies of the equations is considered. The algorithm developed is applied to a non-linear cable vibration problem having small sag-to-span ratios. © 2001 Academic Press.
On the vibrations of an axially travelling beam on fixed supports with variable velocity
(Academic Press, 2001) Öz H.R.
[No abstract available]
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.
Natural frequencies of suspension bridges: An artificial neural network approach
(Academic Press, 2002) Çevik M.; Özkaya E.; Pakdemirli M.
[No abstract available]
Effect of non-ideal boundary conditions on the vibrations of continuous systems
(Academic Press, 2002) Pakdemirli M.; Boyaci H.
[No abstract available]
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]
Comparison of higher order versions of the method of multiple scales for an odd non-linearity problem
(Academic Press, 2003) Pakdemirli M.
[No abstract available]
Non-linear vibrations of a simple-simple beam with a non-ideal support in between
(Academic Press, 2003) Pakdemirli M.; Boyaci H.
A simply supported Euler-Bernoulli beam with an intermediate support is considered. Non-linear terms due to immovable end conditions leading to stretching of the beam are included in the equations of motion. The concept of non-ideal boundary conditions is applied to the beam problem. In accordance, the intermediate support is assumed to allow small deflections. An approximate analytical solution of the problem is found using the method of multiple scales, a perturbation technique. Ideal and non-ideal frequencies as well as frequency-response curves are contrasted.
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.
Infinite mode analysis and truncation to resonant modes of axially accelerated beam vibrations
(Academic Press, 2008) Pakdemirli M.; Öz H.R.
The transverse vibrations of simply supported axially moving Euler-Bernoulli beams are investigated. The beam has a time-varying axial velocity with viscous damping. Traveling beam eigenfunctions with infinite number of modes are considered. Approximate analytical solutions are sought using the method of Multiple Scales, a perturbation technique. A detailed analysis of the resonances in which upto four modes of vibration involved are performed. Stability analysis is treated for each type of resonance. Approximate stability borders are given for the resonances involving only two modes. For higher number of modes involved in a resonance, sample numerical examples are presented for stabilities. © 2007 Elsevier Ltd. All rights reserved.
Immune and inflammatory role of hydroxyethyl starch 130/0.4 and fluid gelatin in patients undergoing coronary surgery
(Academic Press, 2015) Öztürk T.; Onur E.; Cerrahoğlu M.; Çalgan M.; Nizamoglu F.; Çivi M.
Objectives: Compare the effects on inflammatory (TNF-α, IL-6, IL-8 and IL-10) and immunologic (CD3+, CD4+, CD8+, CD11b+, CD16+/56+ T cells and total lymphocyte concentration) variables of hydroxyethyl starch 130/0.4, 4% modified fluid gelatin, or crystalloid when used as volume replacement fluids for acute normovolemic hemodilution (a blood conservation technique) in coronary artery bypass graft patients. Methods: Thirty patients undergoing coronary artery bypass graft surgery were randomized to receive Isolyte S® (Group ISO), 6% hydroxyethyl starch 130/0.4 (Group HES) or 4% modified gelatin solution (Group GEL) for acute normovolemic hemodilution. Blood samples were taken immediately after induction of anaesthesia (T0), and 2h (T1), 12h (T2), 24h (T3), and 48h (T4) after separation from cardiopulmonary bypass. TNF-α, IL-6, IL-8 and IL-10 levels were determined with commercially available ELISA kits. CD3+ (mature T cells), CD4+ (T helper cells), CD8+ (suppressor cytotoxic T cells), CD16+/56+ (natural killer lymphocytes), and CD11b+ (Mac-1, adhesion receptor) levels were measured using flow-cytometry reagents. The CD4+:CD8+ ratio was calculated. Results: Between-group comparisons showed significantly higher levels of TNF-α at T1 (2h after weaning from cardiopulmonary bypass) in Group HES compared to Group ISO (p=0.003). IL-8 was significantly lower in Group HES than Group GEL at T1 (p=0.0005). IL-10 was significantly higher in Group HES than in Group GEL at T1 (p=0.0001). The CD4+:CD8+ ratio in Group ISO was significantly lower than that in Group HES at T2 (p=0.003). CD11b+ levels in Group HES were also higher than those in Group GEL and group ISO at T2, but not significantly. CD16/56+ levels in Group HES were higher than those in Group GEL at T2 (p<0.003). No excessive hemorrhage occurred in any patient. Mediastinal drainage during the first 24h after surgery in Group HES (347±207mL) was not significantly different from that of Group GEL (272±177mL) or Group ISO (247±109) (p>0.05). Conclusion: Hydroxyethyl starch 130/0.4 reduced pro-inflammatory responses and increased anti-inflammatory responses to a greater degree than gelatin solution and isolyte S®. The use of hydroxyethyl starch, compared to gelatin solution and isolyte S®, resulted in less decrease in the CD4+:CD8+ ratio, suggesting less immunosuppression. © 2014 Elsevier Ltd.
Determination and modeling of contact angle of Canola oil and olive oil on a PTFE surface at elevated temperatures using air or steam as surrounding media
(Academic Press, 2016) Aydar A.Y.; Rodriguez-Martinez V.; Farkas B.E.
Contact angles (CAs) of unused Canola and olive oils on polytetrafluoroethylene (PTFE) were measured, and the effect of oil type, surrounding media, and temperature evaluated. CAs were compared to values predicted by Girifalco-Good-Fowkes-Young (GGFY) equation, and GGFY combined with the Eötvös equation (GGFY-E). Finally, a relationship between the CA and interfacial tension for each oil type was obtained. CAs were measured by the sessile drop method (ramé-hart instrument co.). For oil-air systems, measurements were performed at 23 ± 1 °C, 40 °C, and then every 20 °C until reaching the oils' smoke point (olive oil: 180 °C, Canola oil: 200 °C). The same procedure was followed for oil-steam systems with first and second temperatures of 110 and 120 °C, respectively. Temperature and oil type had a significant effect (P < 0.05) on CAs, while no significant effect of surrounding media was observed. CAs decreased linearly as temperature increased (approximately 0.2°/°C). Error (E%) values were less than 10% for the majority of Canola oil systems and olive oil-air predicted CAs. Using Zisman plots, PTFE's surface tension estimates were determined using Canola and olive oil air systems (16.0 and 18.2 mN/m respectively); both systems showed a linear correlation (r2 = 0.99) between interfacial tension and CA. © 2015 Elsevier Ltd.
Effect of olive mill waste addition on the properties of porous fired clay bricks using Taguchi method
(Academic Press, 2016) Sutcu M.; Ozturk S.; Yalamac E.; Gencel O.
Production of porous clay bricks lightened by adding olive mill waste as a pore making additive was investigated. Factors influencing the brick manufacturing process were analyzed by an experimental design, Taguchi method, to find out the most favorable conditions for the production of bricks. The optimum process conditions for brick preparation were investigated by studying the effects of mixture ratios (0, 5 and 10 wt%) and firing temperatures (850, 950 and 1050 °C) on the physical, thermal and mechanical properties of the bricks. Apparent density, bulk density, apparent porosity, water absorption, compressive strength, thermal conductivity, microstructure and crystalline phase formations of the fired brick samples were measured. It was found that the use of 10% waste addition reduced the bulk density of the samples up to 1.45 g/cm3. As the porosities increased from 30.8 to 47.0%, the compressive strengths decreased from 36.9 to 10.26 MPa at firing temperature of 950 °C. The thermal conductivities of samples fired at the same temperature showed a decrease of 31% from 0.638 to 0.436 W/mK, which is hopeful for heat insulation in the buildings. Increasing of the firing temperature also affected their mechanical and physical properties. This study showed that the olive mill waste could be used as a pore maker in brick production. © 2016 Elsevier Ltd

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