Browsing by Author "Togun, N"

Now showing 1 - 9 of 9
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    Stability of fluid conveying nanobeam considering nonlocal elasticity
    Bagdatli, SM; 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. (C) 2017 Elsevier Ltd. All rights reserved.
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    Free vibrations analysis of fluid conveying nanobeam based on nonlocal elasticity theory
    Bagdatli, SM; Togun, N
    In this study, linear vibration analysis of a nanobeam conveying fluid is investigated under simple-simple and clamped-clamped boundary conditions. Eringen's nonlocal elasticity theory is applied to Euler-Bernoulli beam model. Nonlocal elasticity theory is a popular growing technique for the mechanical analyses of MEMS and NEMS structures. The Hamilton's principle is employed to derive the governing equations and boundary conditions. Non-dimensional form of equations is obtained. The obtained equations of motion and boundary conditions are independent from material and geometric structure. It is assumed that fluid velocity is harmonically changed about a constant average speed. Approximate solutions were obtained using the Method of Multiple Scales, a perturbation method. The first term in perturbation series composes linear problem. Natural frequencies and mode shapes are calculated by solving the linear problem for different boundary conditions. For both boundary conditions, the natural frequencies are decreased by increasing the nonlocal parameter (gamma)and the fluid velocity (nu(0)). The results are presented and interpreted by graphics.
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    THE VIBRATION OF NANOBEAM RESTING ON ELASTIC FOUNDATION USING MODIFIED COUPLE STRESS THEORY
    Togun, N; Bagdatli, SM
    In this paper, the vibration of nanobeams resting on the Winkler foundation is proposed using the modified couple stress theory. Hamilton's principle is utilized to construct the governing equations. The size effect of the nanobeam cannot be captured by using classical Euler-Bernoulli beam theory, but the modified couple stress theory model can capture it because it includes material length scale parameter that a newly developed model has. Once the material length scale parameter is assumed to be zero, the classical Euler-Bernoulli beam theory equation is obtained. Multiple scale method is employed to obtain the result. Simply supported boundary condition is used to study natural frequencies. The influence of material length scale parameter and the Winkler elastic foundation parameter on the fundamental frequencies of the nanobeam is investigated and tabulated. Also, in the present study, Poisson's ratio is taken as constant. Nanobeam resting on the Winkler foundation which is simply supported is analyzed to illustrate the size effects on the free vibration. Numerical results for the simply supported nanobeam indicate that the first fundamental frequency calculated by the presented model is higher than the classical one. Moreover, it is obtained that the size influence is more substantial for higher vibration modes. The results indicate that the significant importance of the size influences the analysis of nanobeams. The vibration of nanobeam exhibits a hardening spring behavior, and the newly developed models are the beams stiffer than according to the classical beam theory. Modified couple stress theory tends to be more helpful in describing the size-dependent mechanical properties of nanoelectromechanical systems (NEMS).
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    Application of Modified Couple-Stress Theory to Nonlinear Vibration Analysis of Nanobeam with Different Boundary Conditions
    Togun, N; Bagdatli, SM
    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, upsilon 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.
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    Nonlinear vibration of microbeams subjected to a uniform magnetic field and rested on nonlinear elastic foundation
    Bagdatli, SM; Togun, N; Yapanmis, BE; 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.
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    Nonlinear vibration analysis of three supported nanobeam based on nonlocal elasticity theory
    Yapanmis, BE; Bagdatli, SM; 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.
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    Magnetic field effect on nonlinear vibration of nonlocal nanobeam embedded in nonlinear elastic foundation
    Yapanmi, BE; Togun, N; Bagdatli, SM; Akkoca, S
    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.
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    Nonlinear Vibrations of a Nanobeams Rested on Nonlinear Elastic Foundation Under Primary Resonance Excitation
    Bagdatli, SM; 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.
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    Size dependent nonlinear vibration of the tensioned nanobeam based on the modified couple stress theory
    Togun, N; Bagdatli, SM
    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. (C) 2016 Elsevier Ltd. All rights reserved.