Linear vibration movements of the mid-supported micro beam
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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.