Nonlinear resonance of a rotating ferromagnetic functionally graded cylindrical shell in harmonic magnetic and thermal fields

This paper is concerned with the nonlinear resonance response and dynamic stability of a rotating ferromagnetic functionally graded (FG) cylindrical shell in harmonic magnetic and thermal fields. Considering spatial graded and temperature-dependent characteristics of physical parameters, nonlinear constitutive equations are determined by adopting Donnell’s nonlinear shell theory. According to the magnetoelasticity theory, models for Lorentz force and magnetizing force are established. Hamilton’s principle and Galerkin’s method are employed for the derivation and discretization of nonlinear governing equations. The analytical solutions and stability discriminations of the primary resonance response are obtained by utilizing the Krylov–Bogoliubov–Mitropolski (KBM) method and Lyapunov stability theory. Subsequently, bifurcation topologies of analytical solutions are analyzed via singularity theory, revealing static bifurcation characteristics in different parameter regions based on transition sets. Finally, detailed numerical analyses are performed to investigate the effects of different parameters on vibration response and dynamical stability for the nonlinear system. Results indicate significant effects from the magnetic field strength, temperature, mechanical load, and rotational speed on the vibration mechanism. The sensitivity of the ferromagnetic FG cylindrical shell to external physical fields relies on the nonuniform variation of its constituent materials.