Investigation of stepped micro beam vibration motions according to modified couple stress theory

In this study, linear and nonlinear vibration movements of simply supported stepped micro beams placed in a magnetic field have been analyzed using Modified Stress Couple Theory. By taking into account the step radius ratio, step change position, and material size parameter, the equations of motion of the stepped micro beam are obtained using the Hamilton principle. The resulting equations of motion are nondimensionalized to eliminate dependence on material type and geometric structure. The approximate solution of the dimensionless equations of motion are calculated by the method of multiple scales, one of the perturbation methods. The solution stages of the study are divided into two separate parts as linear and nonlinear problems. Firstly, the linear problem of the stepped micro beam is addressed. By solving the linear problem, the natural frequencies of the system are obtained. Linear and nonlinear effects of step radius ratio, step change position, and micro beam coefficient are investigated and frequency-amplitude graphs are presented. The resonance state where forcing frequency is equal to natural frequency is examined and stability analysis has been made.