Browsing by Author "Bağdatli S.M."

Now showing 1 - 7 of 7
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    Dynamics of axially accelerating beams with multiple supports
    (Kluwer Academic Publishers, 2013) Bağdatli S.M.; Özkaya E.; Öz H.R.
    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 problem. The immovable supports introduce nonlinear terms to the equations of motion due to stretching of neutral axis. The method of multiple scales is directly applied to the equations of motion obtained for the general case. Natural frequency equations are presented for multiple support case. Principal parametric resonances and combination resonances are discussed. Solvability conditions are presented for different cases. Stability analysis is conducted for the solutions; approximate stable and unstable regions are identified. Some numerical examples are presented to show the effects of axial speed, number of supports, and their locations. © 2013 The Author(s).
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    Nonlinear vibrations of spring-supported axially moving string
    (Kluwer Academic Publishers, 2015) Kesimli A.; Özkaya E.; Bağdatli S.M.
    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 motion and boundary conditions. These equations and boundary conditions are dimensionless. Considering the nonlinear effects caused by the string extensions, nonlinear equations of motion are obtained. By using multi-timescaled method, which is one of the perturbation methods, approximate solutions have been found. The first term in the perturbation series causes the linear problem. With the solution of the linear problem, exact natural frequencies have been calculated for different locations of the supports on the middle, various spring coefficients and, with the spring support in the middle of the different location, different spring coefficient and axial speed values. Nonlinear terms on second order add correction terms to the linear problem. Effect of nonlinear terms on the natural frequency has been calculated for various parameters. The cases when the changing frequency of speed is equal to zero, close to zero and close to two times of the natural frequency have been analyzed separately. For each case, the stable and unstable areas in the solutions have been identified by stability analysis. © 2015, Springer Science+Business Media Dordrecht.
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    Stability of fluid conveying nanobeam considering nonlocal elasticity
    (Elsevier Ltd, 2017) Bağdatli S.M.; Togun N.
    In this study, the nonlocal Euler–Bernoulli beam theory is employed in the vibration and stability analysis of a nanobeam conveying fluid. The nanobeam is assumed to be traveling with a constant mean velocity along with a small harmonic fluctuation. In the considered analysis, the effects of the small-scale of the nanobeam are incorporated into the equations. By utilizing Hamilton's principle, the nonlinear equations of motion including stretching of the neutral axis are derived. Damping effect is considered in the analysis. The closed form approximate solution of nonlinear equations is solved by using the multiple scale method, a perturbation technique. The effects of the different value of the nonlocal parameters, mean speed value and ratios of fluid mass to the total mass as well as effects of the simple–simple and clamped–clamped boundary conditions on the linear and nonlinear frequencies, stability, frequency–response curves and bifurcation point are presented numerically and graphically. The solvability conditions are obtained for the three distinct cases of velocity fluctuation frequency. For all cases, the stability areas of system are constructed analytically. © 2017 Elsevier Ltd
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    Investigation of linear vibration behavior of middle supported nanobeam; [Ortadan destekli nano kirişin doğrusal titreşim davranışının incelenmesi]
    (TUBITAK, 2020) Yapanmiş B.E.; Bağdatli S.M.; Togun N.
    In this study, linear vibration of middle supported nanobeam, which is commonly used in nano electro-mechanical systems, is analyzed. Eringen’s nonlocal elasticity theory is used to capture nanoscale effect. Equation of motion of nanobeam is derived with the Hamilton principle. Multiple scale methods, which is one of the perturbation techniques, is performed for solving the equation of motion. Support position and nonlocal effect are focused on the research. The results are presented with graphs and table. In conclusion, when the nonlocal parameter is getting a raise, more nanoscale structure is obtained. Highest rigidity and linear natural frequency are received with mid-position of the support. © 2020, TUBITAK. All rights reserved.
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    Investigation of nonlinear vibration behavior of the stepped nanobeam
    (Techno-Press, 2023) Nalbant M.O.; Bağdatli S.M.; Tekin A.
    Nonlinearity plays an important role in control systems and the application of design. For this reason, in addition to linear vibrations, nonlinear vibrations of the stepped nanobeam are also discussed in this manuscript. This study investigated the vibrations of stepped nanobeams according to Eringen’s nonlocal elasticity theory. Eringen’s nonlocal elasticity theory was used to capture the nanoscale effect. The nanoscale stepped Euler Bernoulli beam is considered. The equations of motion representing the motion of the beam are found by Hamilton’s principle. The equations were subjected to nondimensionalization to make them independent of the dimensions and physical structure of the material. The equations of motion were found using the multi-time scale method, which is one of the approximate solution methods, perturbation methods. The first section of the series obtained from the perturbation solution represents a linear problem. The linear problem’s natural frequencies are found for the simple-simple boundary condition. The second-order part of the perturbation solution is the nonlinear terms and is used as corrections to the linear problem. The system’s amplitude and phase modulation equations are found in the results part of the problem. Nonlinear frequency-amplitude, and external frequency-amplitude relationships are discussed. The location of the step, the radius ratios of the steps, and the changes of the small-scale parameter of the theory were investigated and their effects on nonlinear vibrations under simple-simple boundary conditions were observed by making comparisons. The results are presented via tables and graphs. The current beam model can assist in designing and fabricating integrated such as nano-sensors and nano-actuators. © 2023 Techno-Press, Ltd.
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    Nonlinear Vibrations of a Nanobeams Rested on Nonlinear Elastic Foundation Under Primary Resonance Excitation
    (Springer Nature, 2024) Bağdatli S.M.; Togun N.
    In this paper, a comprehensive analysis of the nonlinear vibrations of nanobeams on nonlinear foundations under primary resonance excitation is presented. By utilizing advanced theories and highlighting the distinctions from previous work, we provide valuable insights into the behavior of these structures and their interaction with the supporting foundation. The results contribute to advancing the understanding and design of micro/nanoscale systems in a wide range of applications. The nanobeam is modeled in this paper as a Euler–Bernoulli beam with size-dependent properties. The material length scale parameter in this non-classical nanobeam model accounts for size effects at the nanoscale. For the nanobeam, two boundary conditions are taken into account: simply supported and clamped–clamped. The system's governing equation of motion is derived using the modified couple stress theory, and the accompanying boundary conditions are obtained by applying Hamilton's principle. This hypothesis enhances the analysis's precision by accounting for size effects. To arrive at an approximative analytical solution, the study employs an analytical method called the multiple-scale method. To manage primary resonance excitation in nonlinear systems, this technique is frequently used. The analysis takes into account a number of parameters, including the nonlinear foundation parameter (KNL), Winkler parameter (KL), Pasternak parameter (KP), and material length scale parameter (l/h). These variables have a significant impact on how the nanobeam behaves on the nonlinear foundation. The study includes numerical results in graphical and tabular formats that show how the linear fundamental frequency, nonlinear frequency ratio, and vibration amplitude are affected by the material length scale parameter and stiffness coefficients of the nonlinear foundation. The research includes a comparison study with prior literature on related issues to verify the accuracy of the results acquired. © The Author(s), under exclusive licence to Shiraz University 2023.
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    Application of Modified Couple-Stress Theory to Nonlinear Vibration Analysis of Nanobeam with Different Boundary Conditions
    (Springer, 2024) Togun N.; Bağdatli S.M.
    Purpose: In the present study, the nonlinear vibration analysis of a nanoscale beam with different boundary conditions named as simply supported, clamped-clamped, clamped-simple and clamped-free are investigated numerically. Methods: Nanoscale beam is considered as Euler-Bernoulli beam model having size-dependent. This non-classical nanobeam model has a size dependent incorporated with the material length scale parameter. The equation of motion of the system and the related boundary conditions are derived using the modified couple stress theory and employing Hamilton’s principle. Multiple scale method is used to obtain the approximate analytical solution. Result: Numerical results by considering the effect of the ratio of beam height to the internal material length scale parameter, h/l and with and without the Poisson effect, υ are graphically presented and tabulated. Conclusion: We remark that small size effect and poisson effect have a considerable effect on the linear fundamental frequency and the vibration amplitude. In order to show the accuracy of the results obtained, comparison study is also performed with existing studies in the literature. © The Author(s) 2024.