Nonlinear Dynamical Modeling and Free Vibration of Functionally Graded Cylindrical Shell in Air-gap Magnetic and Thermal Fields

Abstract

Nonlinear dynamical modeling and free vibration of ferromagnetic functionally graded (FG) cylindrical shell in air-gap magnetic and thermal fields are investigated in this work. The shell is surrounded by an armature, and the air-gap layer generated by physical isolation exists between the two structures. The air-gap magnetic field in this space is generated by the armature, which induces the nonlinear magnetization of ferromagnetic materials. The nonlinear heat conduction characteristics along the shell thickness are considered. Under the theory framework for dual-nonlinear magneto-thermal effect, the magneto-thermoelastic dynamical model is established using Hamilton principle. The discrete governing equations and the natural frequency expression separately are derived by Galerkin and Krylov-Bogoliubov-Mitropolski (KBM) methods. Subsequently, the natural frequency characteristics under different parameter conditions are systematically analyzed. The results indicate that magnetic potential, initial air-gap thickness, and volume fraction index have a significant impact on natural frequencies. Temperature has a complex effect on natural frequencies corresponding to different circumferential wave numbers.