Magneto-Aeroelastic Dynamic Buckling and Flutter of Rotating Conductive Annular Disks Under Air-Film Loading

This paper focuses on the magneto-aeroelastic dynamic buckling and flutter generated by traveling waves of rotating conductive disks under air-film loading. A distributed time-variable aerodynamic model is derived by using the Navier–Stokes (NS) equation and the lubrication theory. The electromagnetic force on the disk is modeled by using the electromagnetic theory. Based on Kirchhoff’s theory and considering the rotating centrifugal effect, the dynamic equations for magnetic-aeroelastic coupling are established by using the Hamiltonian principle. Bessel functions are assumed for the mode shapes, and the steady-state properties of the aerodynamic equations are presented that allow for the derivation and decoupling of the coupling differential equations in the Galerkin approach of Hilbert space. The effects of the magnetic field intensity, rotational speed, and aerodynamic parameters on the magneto-aeroelastic buckling instability and flutter characteristics generated by backward traveling wave instability are investigated, respectively. The numerical calculations show the damping effect of the magnetic field, which increases magnetic field intensity and suppresses buckling instability and flutter. Moreover, the sensitivity of the system with respect to magnetic field intensity demonstrated that, for high-order mode instability, a critical instability region (CIR) emerges with changes in the magnetic field intensity, whereby a distribution with a very small frequency may induce dynamical buckling instability of the system. Additionally, the rotational speed escalates to reach either the critical speed or flutter speed, the system may experience dynamic buckling or flutter instability characterized by divergent response or equal-amplitude vibration, respectively.