Investigation of multi support micro beam vibration movements according to modified couple stress theory

In this study, vibration movements of multisupport micro-beams placed in an electrically smooth area are analyzed. It has been assumed that the potential voltage that creates the electrical field strength varies harmonically. The most general nonlinear (NL) motion equations for multi-support micro-beams have been obtained by taking into account the material size parameter, the number of support and support positions, damping effect, axial stresses, electrical field strength and NL effects resulting from elongations. The NL equations of motion are obtained according to the Hamilton method using the Modified Couple Stress Theory (MCST). The resulting equations of motion are nondimensionalized. In this way, the mathematical model has been made independent from the type and geometric structure of the material. Approximate solutions of the obtained dimensionless motion equation are obtained by the multiscale method, which is one of the perturbation methods. The solution method has been applied directly to the problem. In the study, the solution steps are divided into two separate parts. Firstly, the linear problem of the multisupport micro-beam is discussed. After the determination of linear natural frequencies from this problem, the solution of the NL problem of vibration motion was started. The effects of the support number and position, stress coefficient, micro-beam coefficient and electric field strength parameters on linear and NL natural frequency and bifurcation points were examined and frequency-response graphs were drawn. Forcing frequency; The dominant resonance state where the natural frequency is approximately equal to twice the natural frequency, the resonance state where it is equal to the natural frequency and the state where it is zero are examined and stability analysis has been made. The results obtained with the MCST method were compared with the classical beam theory and other micro-beam studies analyzed with MCST in the literature, and the effect of material size properties on the vibration character was shown and the accuracy of the study was demonstrated.