Non-linear effects in performance of 2+2x1/2DOF electro-magnetic dampeners

The idea to use electromagnetic devices to reduce vibration levels of mechanical systems has been discussed in variety of publications. Some authors use a linearized problem formulation, however, due to the action of an electromagnetic force, the electro-magneto-mechanical system is inherently non-linear and so it should be investigated accordingly. In the paper, using a lumped parameter modelling approach, we consider a 2DOF structure, coupled to a pair of electromagnetic elements. Due to its physical nature, each element contributes with 1/2DOF. Thus the coupled electro-magneto-mechanical system can be described as the one with 2+2x1/2 degrees of freedom. The non-linear vibration problem is solved by means of the classical multiple scales method, where the forced response and stability of alternative regimes at primary resonances and internal resonances are addressed. Furthermore, the role of the damping introduced by coupling between electromagnets and the mechanical system is analysed and parameters of electromagnets are tailored to match limitations of the vibration levels