Free Vibration of Micro Cantilever Beam With Electromagnetic Actuators

Free vibration of cantilever beam with an electromagnetic actuator is studied. The governing equation of motion of the system is developed and the electromagnetic actuation part is added to the system. The system is modeled by 1DOF vibration mode. Three different analytical solution methods, namely, Krylov and Bogoliubov, Energy Balance and Modified Energy Balance are utilized to obtain the equations of motion and the frequency response of the system. Expression for the fundamental frequency is obtained using different types of analytical procedures. Frequency responses of the system are obtained using different numerical methods and the accuracy of the proposed approaches is studied. The influence of the initial conditions on the system performance is studied and the point where, the system starts to show an unstable behavior and quasi-periodic response is identified. Phase-plane trajectories are presented to elaborately analyze the dynamical behaviors of the system. Variations of the natural frequencies for different values of actuation parameter and the initial conditions are plotted to reveal the sensitivity of the objective system.