Browsing by Author "Togun N."
Now showing 1 - 8 of 8
Results Per Page
Sort Options
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 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 LtdItem 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.Item 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.Item 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.Item Nonlinear vibration of microbeams subjected to a uniform magnetic field and rested on nonlinear elastic foundation(Walter de Gruyter GmbH, 2024) Baǧdatll S.M.; Togun N.; Yapanmlş B.E.; Akkoca S.This study investigates the nonlinear vibration motions of the Euler-Bernoulli microbeam on a nonlinear elastic foundation in a uniform magnetic field based on Modified Couple Stress Theory (MCST). The effect of size, foundation, and magnetic field on the nonlinear vibration motion of microbeam has been examined. The governing equations related to the nonlinear vibration motions of the microbeam are obtained by using Hamilton's Principle, and the Multiple Time Scale Method was used to obtain the solutions for the governing equations. The linear natural frequencies of microbeam are presented in the table according to nonlinear parameters and boundary conditions. The linear and nonlinear natural frequency ratio graphs are shown. The present study results are also compared with previous work for validation. It is observed that length scale parameters and magnetic force have a more significant effect on the natural frequency of microbeams. It is seen that when the linear elastic foundation coefficient, the Pasternak foundation and the magnetic force effects increase, the ratio of nonlinear and linear natural frequency decreases. © 2023 Walter de Gruyter GmbH, Berlin/Boston.Item Nonlinear vibration analysis of three supported nanobeam based on nonlocal elasticity theory; [Yerel olmayan elastisite teorisine göre üç mesnetli nano kirişin doğrusal olmayan titreşim davranışı](Gazi Universitesi, 2024) Yapanmış B.E.; Bağdatlı S.M.; Togun N.The importance of nanoscale devices is increasing day by day. Therefore, nanobeams, nanoplates, nanorods have been the focus of engineers in nanoelectromechanical structures. From that point of view, the nonlinear behaviour of three supported nanobeams is investigated in this paper numerically. Firstly, linear natural frequencies were calculated; and then, nonlinear natural frequencies were found thanks to nonlinear correction terms. Nonlinear natural frequencies versus amplitude and nonlinear frequency response curves are plotted to clarify the nonlinear behaviour. Nonlocal parameters, second support position and different modes effects are examined comprehensively. In addition, the different first and last support types are investigated. It is shown that nonlocal parameters and second support position have great importance for nanobeam. The glorious effect is obtained highest modes. © 2024 Gazi Universitesi. All rights reserved.