Magneto-thermo-elastic coupling vibration and bifurcation characteristics of functionally graded rotating cylindrical shell

The magneto-thermo-elastic coupling vibration of rotating ferromagnetic functionally graded cylindrical shell is investigated in this paper. Based on the physical neutral surface theory and Donnell's theory, the expressions of kinetic energy and strain energy are obtained by introducing geometric nonlinearity. The magneto-thermo-elastic vibration equations of the rotating ferromagnetic functionally graded cylindrical shell in multi-physical field are derived via the Hamilton's principle. Considering the magnetization effect of ferromagnetic shell in magnetic field, the expression of magnetization force is obtained according to the nonlinear magnetic constitutive relation. For simply supported boundary conditions, Galerkin's method is used to obtain the discretized ordinary differential equations, and the static deflection of the shell under static load is solved. The steady-state response of the system during primary resonance and the stability of solutions are given by the multi-scale method and the Lyapunov stability theory. Through numerical examples, the characteristic curves and surfaces of amplitude are plotted, and the parameter ranges corresponding to regions of multi-valued solutions and stable solutions are determined. The system dynamics laws describing the coupling effect between multiple parameters such as force, magnetism, heat, and rotational speed are evaluated. The Global bifurcation diagrams and the maximum Lyapunov exponent spectrums under different control parameters are plotted to analyze the effect of parameter changes on the dynamic response of system. The results show that the vibration characteristics of the system are significantly influenced by the external physical fields, in addition to the shell size and material volume fraction. Slight changes in parameters can lead to violent changes in the dynamic response of the system, exhibiting intermittent, jumping, and chaotic characteristics.