Browsing by Author "Yapanmis, BE"

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    Investigation of the non-linear vibration behaviour and 3:1 internal resonance of the multi supported nanobeam
    Yapanmis, BE; Bagdatli, SM
    In this present work, linear and non-linear vibration of multi-supported nanobeams, which are a fundamental part of the nano-electromechanical systems, is examined. To the best of the researchers' knowledge, there is no study performed into multi-supported nanobeam in the literature. The governing equations of the system are obtained by dint of the Hamilton principle and solved via the perturbation technique which is divided linear and non-linear parts of the main equations. The natural frequencies and mode shapes are calculated from the linear problem. The non-linear natural frequencies and amplitude-phase modulation graphs are obtained from the non-linear equation. All equations are written in generalized form, and 3, 4 and 5 supported nanobeams are investigated in detail. The nonlocal coefficient, support number and position and end condition types are focused on. The three to one internal resonance cases are also investigated. It is occurred that the clamped-end conditions shift right in the hardening behaviour graphs more than the simply supported condition. Moreover, it is shown that the supported numbers play a significant role in natural frequency.
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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.