Browsing by Author "Togun, NK"

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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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    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.