Browsing by Author "Baǧdatli S.M."
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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 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.Item Non-linear transverse vibrations and 3:1 internal resonances of a tensioned beam on multiple supports(2011) Baǧdatli S.M.; Öz H.R.; Özkaya E.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 arbitrary number of support case is investigated and 3, 4, and 5 support cases analyzed in detail. A perturbation technique (the method of multiple scales) is applied to the equations of motion to obtain approximate analytical solutions. 3:1 internal resonance case is also considered. Natural frequencies and mode shapes for the linear problem are found for the tensioned beam. Nonlinear frequencies are calculated; amplitude and phase modulation figures are presented for different forcing and damping cases. Frequency-response and force-response curves are drawn. Different internal resonance cases between modes are investigated. © Association for Scientific Research.Item Size dependent nonlinear vibration of the tensioned nanobeam based on the modified couple stress theory(Elsevier Ltd, 2016) Togun N.; Baǧdatli S.M.This paper presents a nonlinear vibration analysis of the tensioned nanobeams with simple-simple and clamped-clamped boundary conditions. The size dependent Euler-Bernoulli beam model is applied to tensioned nanobeam. Governing differential equation of motion of the system is obtain by using modified couple stress theory and Hamilton's principle. The small size effect can be obtained by a material length scale parameter. The nonlinear equations of motion including stretching of the neutral axis are derived. Damping and forcing effects are considered in the analysis. The closed form approximate solution of nonlinear equations is solved by using the multiple scale method, a perturbation technique. The frequency-response curves of the system are constructed. Moreover, the effect of different system parameters on the vibration of the system are determined and presented numerically and graphically. The size effect is significant for very thin beams whose height is at the nanoscale. The vibration frequency predicted by the modified couple stress theory is larger than that by the classical beam theory. Comparison studies are also performed to verify the present formulation and solutions. © 2016 Elsevier Ltd.Item Nonlinear vibration of a nanobeam on a pasternak elastic foundation based on non-local euler-bernoulli beam theory(MDPI AG, 2016) Togun N.; Baǧdatli S.M.In this study, the non-local Euler-Bernoulli beam theory was employed in the nonlinear free and forced vibration analysis of a nanobeam resting on an elastic foundation of the Pasternak type. The analysis considered the effects of the small-scale of the nanobeam on the frequency. By utilizing Hamilton's principle, the nonlinear equations of motion, including stretching of the neutral axis, are derived. Forcing and damping effects are considered in the analysis. The linear part of the problem is solved by using the first equation of the perturbation series to obtain the natural frequencies. The multiple scale method, a perturbation technique, is applied in order to obtain the approximate closed solution of the nonlinear governing equation. The effects of the various non-local parameters, Winkler and Pasternak parameters, as well as effects of the simple-simple and clamped-clamped boundary conditions on the vibrations, are determined and presented numerically and graphically. The non-local parameter alters the frequency of the nanobeam. Frequency-response curves are drawn. © 2016 by the authors; licensee MDPI, Basel, Switzerland.Item Free vibrations of fluid conveying microbeams under non-ideal boundary conditions(Techno Press, 2017) Atci D.; Baǧdatli S.M.In this study, vibration analysis of fluid conveying microbeams under non-ideal boundary conditions (BCs) is performed. The objective of the present paper is to describe the effects of non-ideal BCs on linear vibrations of fluid conveying microbeams. Non-ideal BCs are modeled as a linear combination of ideal clamped and ideal simply supported boundary conditions by using the weighting factor (k). Non-ideal clamped and non-ideal simply supported beams are both considered to show the effects of BCs. Equations of motion of the beam under the effect of moving fluid are obtained by using Hamilton principle. Method of multiple scales which is one of the perturbation techniques is applied to the governing linear equation of motion. Approximate solutions of the linear equation are obtained and the effects of system parameters and non-ideal BCs on natural frequencies are presented. Results indicate that, natural frequencies of fluid conveying microbeam changed significantly by varying the weighting factor k. This change is more remarkable for clamped microbeams rather than simply supported ones. Copyright © 2017 Techno-Press, Ltd.Item Magnetic field effect on nonlinear vibration of nonlocal nanobeam embedded in nonlinear elastic foundation(Techno-Press, 2021) Yapanmiş B.E.; Toǧun N.; Baǧdatli S.M.; Akkoca Ş.The history of modern humanity is developing towards making the technological equipment used as small as possible to facilitate human life. From this perspective, it is expected that electromechanical systems should be reduced to a size suitable for the requirements of the era. Therefore, dimensionless motion analysis of beams on the devices such as electronics, optics, etc., is of great significance. In this study, the linear and nonlinear vibration of nanobeams, which are frequently used in nanostructures, are focused on. Scenarios have been created about the vibration of nanobeams on the magnetic field and elastic foundation. In addition to these, the boundary conditions (BC) of nanobeams having clamped-clamped and simple-simple support situations are investigated. Nonlinear and linear natural frequencies of nanobeams are found, and the results are presented in tables and graphs. When the results are examined, decreases the vibration amplitudes with the increase of magnetic field and the elastic foundation coefficient. Higher frequency values and correction terms were obtained in clamped-clamped support conditions due to the structure's stiffening. © 2021 Techno-Press, Ltd.Item Linear vibration movements of the mid-supported micro beam; [Ortadan mesnetli mikro kirişin doǧrusal titreşim hareketleri](Gazi Universitesi, 2021) Akkoca S.; Baǧdatli S.M.; Toǧun N.K.In this study, the vibration behavior of the center supported micro beam is analyzed. The microbeam has a ceramic property and placed inside the electric field, and the vibrational characters are examined by changing the positions of the supports. The equations of motion are obtained by using the modified couple stress theory and Hamilton principle. The equation of motion is solved by using the method of multiple scales time that one of the perturbation methods. Natural frequencies and mode shapes were obtained depending on the dimensionless parameters like support position, coefficient of stress and coefficient of microbeam. As a result of the data obtained in the study, an increase was observed in the 1st mode natural frequency values of the micro beam with the movement of the support position towards the midpoint of the beam, while an increasing and decreasing wavy situation was encountered in the 2nd and 3rd mode natural frequency values. If the micro-beam coefficient value was increased, the frequency values increased at the same stress coefficient and mode value, except for the position ç = 0.1. It has been observed that the dimensional effect gives a distinctive feature to the vibration action of the micro beam at this location of the support. However, it has been observed that increasing the stress coefficient value does not have a great effect on the micro beam natural frequency. © 2021 Gazi Universitesi Muhendislik-Mimarlik. All rights reserved.Item Nonlinear Vibration Movements of the Mid-Supported Micro-Beam(World Scientific, 2022) Akkoca S.; Baǧdatli S.M.; Kara Toǧun N.This study analyzes the vibration movements of multi-support micro beams placed in an electrically smooth area using the modified couple stress theory. It has been assumed that the potential voltage that creates the electrical field strength varies harmonically. Large number of experiments in recent years have indicated that classical continuum theory is unable to predict the mechanical behavior of microstructure with small size. However, nonclassical continuum theory should be used to accurately design and analyze the microstructures. Modified couple stress theory models the micro and nanomechanical systems with higher accuracy because they employ additional material parameters to the equation considering size dependent behavior. The most general nonlinear motion equations for multi-support microbeams have been obtained by considering the material size parameter, the number of support and support positions, damping effect, axial stresses, electrical field strength, and nonlinear effects resulting from elongations. The nonlinear equations of motion are obtained according to the Hamilton method using the modified couple stress theory (MCST). The resulting equations of motion are nondimensionalized. In this way, the mathematical model has been made independent of the type and geometric structure of the material. Approximate solutions of the obtained dimensionless motion equation are obtained by the multi-scale method, which is one of the perturbation methods. As a result, an increase occurs in the first mode frequencies (ω1) and nonlinear correction effect parameters (λ(ω1)) with the progress of the center support position gradually towards η=0.5 and the increase of the microbeam elasticity coefficient (α2). © 2022 World Scientific Publishing Company.Item Three-to-one internal resonances of stepped nanobeam of nonlinearity(Walter de Gruyter GmbH, 2024) Nalbant M.O.; Baǧdatli S.M.; Tekin A.In this study, vibrations of stepped nanobeams were investigated according to Eringen's nonlocal elasticity theory. Multi-time scale method, which is one of the perturbation methods, has been applied to solve dimensionless state equations. The solution is considered in two steps. First-order terms obtained from the perturbation expansion formed the linear problem in the first step. In the second step, the solution of the second order of the perturbation expansion was made and nonlinear terms emerged as corrections to the linear problem from this solution. The main issue that the study wants to emphasize is the examination of the mechanical effects of the steps, which are discontinuities encountered at the nanoscale, on the system. For this purpose, while the findings of the research were obtained, various nonlocal parameter values were obtained to capture the nano-scale effect, and frequency-response and nonlinear frequency-amplitude curves corresponding to the 1st Mode values of the beam for different step ratios and step locations were obtained to capture the step effect. One of the important features of the nonlinear system is the formation of internal resonance between the modes of the system. How this situation affects the characteristics of the system has also been examined and results have been given by graphs. The obtained data show that taking into account the nanoscale step is essential for the accuracy and sensitivity of many nanostructures such as sensors, actuators, biostructures, switches, etc. that are likely to be produced at the nanoscale in practice. © 2023 Walter de Gruyter GmbH, Berlin/Boston.