Analysis of multi-physics interaction effects in a coupled dynamical electro-magneto-mechanical (2+2×1/2)DOF system

•The hierarchy of the models describing dynamics of the multi-physical electro-magneto-mechanical system is considered.•The multiple scales method is applied to study a nonlinear behaviour of these models.•Three operation regimes are identified.•Possible application of the system for adaptive-passive control is discussed.

The operation of electro-magneto-mechanical systems involves the interaction of these three physical domains. In the paper, this interaction is analysed for a lumped parameter model, which consists of a two degrees of freedom (2DOF) linear mechanical system coupled via a nonlinear electro-magnetic field with two electrical circuits, contributing with 1/2DOF each. Dynamics of this multi-physical model is considered both in the nonlinear and in the linearised problem formulations. In the former case, the method of multiple scales is used to describe softening and modal interaction phenomena. The 2−1 (super-harmonic) internal resonance is investigated, where stability and jump phenomena are analysed. The regimes of uni- and bi-modal responses are identified and a parametric study performed. The mathematical description of nonlinearities, introduced by multi-physical coupling, is compared with the classical formulation of nonlinear stiffness of a spring. For the linearised problem, the equivalent stiffness and the damping, as functions of the parameters of electro-magnetic elements, are assessed. The ranges of these parameters, when the nonlinear multi-physics interaction effects are suppressed by the dissipation effects of the same origin, are identified. The analytical predictions are verified by the numerical simulations. The relevance of the reported results to the operation of electro-magnetic adaptive passive control systems, capable to alter a natural frequency and add damping, is discussed.