Principal and internal resonance of rectangular conductive thin plate in transverse magnetic field

摘要

The principle and 1:3 internal resonance of a rectangular thin plate in a transverse magnetic field is investigated. Based on the magneto-elastic vibration equation and electromagnetic force expressions of the thin plates, the nonlinear magneto-elastic vibration differential equations of rectangular plates under external excitation in a transverse magnetic field are derived. For a rectangular plate with one side fixed and three other sides simply supported, the two-degree-of-freedom nonlinear Duffing vibration differen-tial equations are proposed by the method of Galerkin. The method of multiple scales is adopted to solve the model equations and obtain four first-order ordinary differential equations governing modulation of the amplitudes and phase angles involved via the first-order or the second-order primary-internal reso-nances. With a numerical example, the amplitude frequency response curves, time history responses, phase portraits and Poincare maps of the first two order vibration modes via principle-internal resonance are respectively captured. And the effects of external excitation amplitudes, magnetic field intensities and thicknesses on the vibration of system are discussed. The results show that the response is dominated by the low mode when principle-internal resonance occurs. The internal resonance provides a mechanism for transferring energy from a high mode to a low mode.