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The primary resonance behavior of a rotating ferromagnetic functional gradient cylindrical shell in a magnetic field, temperature field, and excitation force is investigated. Based on the physical neutral surface deformation theory and the Donnell theory, considering the effect of geometric nonlinearity, expressions of strain energy and kinetic energy of the shell and the work of forces are given, respectively. Applying the Hamilton principle, the magneto–thermo–elastic equation of a functional gradient cylindrical shell is derived by considering the magnetization effect of ferromagnetic metal. The question is discretized by Galerkin method and solved by the multi-scale method to obtain the amplitude–frequency response equation. The stability of the solution is discriminated by using the Lyapunov theory. Through numerical examples, the response curves of the system under different parameters are plotted, and the parameter ranges corresponding to multi-valued solution regions and single-valued solution regions are determined. The effects of parameter changes on the dynamic response and stability of system are analyzed. The results show that a coupling mechanism between temperature field, magnetic field, and excitation force affects the response and stability of the system, and the change of parameters have a significant effect on the vibration characteristics and stability. The dynamics model established in this paper is a theoretical reference for investigation on the multi-physics field coupling dynamic behaviors of structures.

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