Nonlinear vibration of finitely-electroconductive plate strips in an axial magnetic field

The vibrational behavior of geometrically nonlinear, finitely electroconductive, isotropic elastic plate strips immersed in an axial magnetic field is investigated. Kirchhoff hypothesis in conjunction with von-Kármán's concept of strain is used to model the mechanical part, while the assumptions proposed by Ambartsumyan et al. are adopted to model the distribution of electric and magnetic disturbances through the plate-strip thickness. A system of nonlinear singular integro-differential equations are obtained, and by applying the Galerkin's method, a third order nonlinear ordinary differential equation is derived. The influence of the magnetic field and electroconductivity on the plate-strip vibration is investigated and analytical solutions of the nonlinear fundamental frequency are obtained via the Method of Multiple Scales for two special cases, consisting of weak magnetic field and high electroconductivity. Finally, some pertinent conclusions are provided.