Parametric instability of a cantilever beam subjected to two electromagnetic excitations: Experiments and analytical validation

An electromagnetic device, acting like a spring with alternating stiffness, has been designed to parametrically excite the cantilever beam. However, only one parametric excitation (induced by one electromagnetic device) was considered in current research, and the effects of the design parameters of the device upon the instability were studied inadequately. Actually, multiple parametric excitations with various phases and amplitudes would bring significant impacts to the system instability. The electromagnetic device with various design parameters could cause the unstable regions to change evidently. Thus, the parametric instability of a cantilever beam subjected to two electromagnetic excitations is studied experimentally and analytically in the paper. The governing equations for the beam system are established utilizing the assumed mode method, and then verified through a DC current test. Based upon these, the instability experiments for the cantilever beam with one or two electromagnetic excitations are conducted in detail. Two design parameters of the device (magnet spacing and device location) are investigated, respectively, for their effects upon the instability regions. When two electromagnetic devices operate together to bring two parametric stiffness excitations with various phases and amplitudes to the cantilever beam, the variations of both simple and combination instability regions with coil current are observed and discussed. The above experimental results are all found to agree well with the analytical ones.