Magnetic-thermoelastic coupling resonance and bifurcation behavior of a rotating functionally graded cylindrical shell induced by armature

Abstract

The magnetic-thermoelastic coupling resonance, bifurcation, and chaos of a rotating functionally graded cylindrical shell induced by armature are investigated in present work. The air-gap magnetic field is excited by armature, which induces the nonlinear magnetization of ferromagnetic materials. Meanwhile, a thermal field is set to be distributed nonlinearly along thickness. Based on the dual-nonlinear magneto-thermal effects, geometric nonlinear factors are introduced through Kirchhoff–Love theory. Combining thermoelasticity and magnetic-solid coupling theories, the magnetic-thermoelastic coupling dynamical model is established by Hamilton’s principle. The Galerkin truncation is used to obtain discrete equations, and the amplitude–frequency relationship and stability criterion are derived from Krylov–Bogoliubov–Mitropolski method and Lyapunov stability theory. Through numerical examples, the effects of electromagnetic parameters, temperature, rotational speed, excitation, and dimensions on coupling resonance behaviors are discussed. Results indicate that the resonance region is expanded by increasing the magnetic potential, and non-solution regions are discovered when the excitation position approaches constraints. The bifurcation and chaos exhibit high sensitivity to magnetic potential, rotational speed, and excitation. The response state can be transmitted from periodic to chaos through period-doubling and tangent bifurcation routes.