Nonlinear magneto-thermoelastic natural vibrations of rotating ferromagnetic functionally graded cylindrical shells with geometric imperfections
摘要
Cylindrical shell structures commonly exhibit initial geometric imperfections under practical conditions due to manufacturing tolerances, transport damage, and operational disturbances. These imperfections can significantly affect the vibrational characteristics and dynamic stability of rotating shells. This study theoretically investigates the nonlinear natural vibrations of rotating cylindrical shells made of ferromagnetic metal-ceramic functionally graded materials. The shells contain initial geometric imperfections and are subjected to both magnetic and thermal fields. Material parameters along the shell thickness are characterized using a power-law Voigt model. Incorporating geometric nonlinearity and initial imperfections, the constitutive relations are derived based on the Kirchhoff–Love theory. Based on magnetoelastic interaction theory, the Lorentz and magnetization forces induced by a straight conductor and an improved Helmholtz coil are modeled. Hamilton’s principle and the Galerkin method are employed to formulate the magneto-thermoelastic differential governing equations. Under Volmir’s thin-shell kinematic assumption, approximate analytical expressions for the nonlinear natural frequencies are obtained. The analytical solutions are validated through literature comparisons and numerical simulations using the Runge–Kutta method. Systematic parametric analyses are conducted to investigate the effects of vibration modes, temperature, rotational speed, current intensity, and geometric imperfections on the frequencies. The results indicate that non-axisymmetric imperfections and rotational effects induce frequency splitting, while the magnetic field enables active tuning of this splitting through electromagnetic forces. The proposed model provides a theoretical basis for magnetic-thermal control analyses of composite structures with imperfections subjected to multi-physics fields.