The combined resonance of superharmonic resonance and 1∶3 internal resonance of a rectangu-lar thin plate in transverse magnetic field is studied.For the rectangular thin plate with one side fixed and three sides simply supported,the two degree of freedom nonlinear vibration differential equations are ob-tained by the Galerkin method.Then the multiple-scale method is employed to solve equations,and ampli-tude frequency response equations of the first two modes are obtained.Through calculation examples,the relationship between the first two order response amplitudes and parameters when superharmonic internal resonance occurs in system is obtained,in which the influence of parameters e.g.,external excitation am-plitude and magnetic field intensity on the vibration of system is discussed.The results show that the high-order modes are indirectly excited when internal resonance is considered,and there is energy exchange in the system,and the resonance of system can be controlled by changing the magnetic field intensity.
magneto-elasticrectangular thin platesuperharmonic resonanceinternal resonancethe method of multiple scales
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