Magneto-thermoelastic coupled resonance characteristics of a rotating functionally graded ferromagnetic cylindrical shell under double harmonic line loads

The magneto-thermoelastic coupled resonance of a rotating functionally graded (FG) ferromagnetic cylindrical shell subjected to double harmonic line loads in magnetic and temperature fields is investigated. In accordance with Donnell's thin shell theory on the physical neutral surface, the nonlinear geometric equations are determined. Utilizing the thermoelastic constitutive relationships, combining with the gradient characteristics and temperature dependence of physical parameters, the governing equations of kinetic energy and strain energy are given. Based on the magnetoelasticity theory, and considering the nonlinear magnetization of ferromagnetic metal, the calculation formulas of Lorentz force and magnetizing force acting on the shell are deduced. The magneto-thermoelastic coupled dynamic equations are derived by applying Hamilton principle and discretized by Galerkin method. Subsequently, considering the different resonance forms, the multiple scales method and Lyapunov stability theory are employed to obtain the theoretical solutions and stability discriminants. Numerical examples are carried out to plot the characteristic diagrams with different parameters, which are used to analyze the characteristics of nonlinear coupled resonance. Furthermore, the primary resonance and combination resonance are selected to analyze the bifurcation and chaotic behavior. Results show that the variation of different parameters affects obviously the resonance amplitude and stability. The changes of amplitude and position of hard excitation can lead to resonance region drift. Amplitude, frequency, and position of excitation have significant effects on bifurcation and chaos. The motion state of cylindrical shell is transmitted from periodic response to chaotic response through the accumulation of period -doubling bifurcation.