Analytical solutions for the magneto-fluid-structure interaction dynamics with two degrees of freedom

The study focuses on the interaction between fluid and structure under an external magnetic field. The system consists of two rigid cylinders, with the inner cylinder having either translating vibrating or rotating vibrating freedoms. The solutions describing the coupling characteristics among the multi-physics fields are derived, using the zero- and first-order complex modified Bessel functions. The study analyzes the effects of the magnetic field on flow fields, electrical potential distributions, and cylinder vibration characteristics. It also reveals the physical mechanisms behind the coupled effects among fluid flow, cylinder vibration, and the electrical potential field. The study finds that for initial tangential rotating vibration, the magnetic field can stabilize both the flow field and cylinder vibration. Additionally, an increasing magnetic field can transform the cylinder vibration from underdamping to overdamping. On the other hand, for initial translating vibration, the magnetic field can induce instability in the system, with larger magnetic fields leading to divergent, negatively damped vibration. The critical magnetic fields for both rotating and translating vibrations are determined using phase maps. The study also shows that the combined effects of rotating and translating vibrations lead to asymmetry in the flow field. While translating vibration plays a dominant role in the combined vibration, it nonlinearly and non-monotonously influences the system dynamics.