Browsing by Author "Akkoca, S"

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    Nonlinear Vibration Movements of the Mid-Supported Micro-Beam
    Akkoca, S; Bagdatli, SM; Togun, NK
    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 non-dimensionalized. 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 (omega(1)) and nonlinear correction effect parameters (lambda(omega(1))) with the progress of the center support position gradually towards eta = 0.5 and the increase of the microbeam elasticity coefficient (alpha(2)).
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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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    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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    Linear vibration movements of the mid-supported micro beam
    Akkoca, S; Bagdatli, SM; Togun, NK
    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 eta = 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.