Non-linear vibration analysis of an elastic plate subjected to heavy fluid loading in magnetic field

In the present study, the non-linear vibration of an elastic plate subjected to heavy fluid loading in an inclined magnetic field is investigated. The structural non-linearity, fluid non-linearity, and the effects of magnetic field are all incorporated in the formulations to derive the governing equation of the plate. The method of multiple scales is adopted to determine the eigenvalues and mode shapes of the linear vibration, and then the amplitude of the non-linear vibration response of the plate is calculated. Based on the assumptions of ordering and formulations of multiple scales, it can be concluded that the linear dynamic behavior of the plate under heavy fluid loading but weak near-resonant loading is influenced by the effects of the fluid loading, linear structural rigidity and linear magnetic field, furthermore, the non-linear dynamic behavior of the plate under heavy fluid loading but weak near-resonant loading is dominated and controlled by the effects of the fluid loading, non-linear structural rigidity and non-linear magnetic field. Both thick and thin plates are investigated; the contributions due to the structural non-linearity and acoustic linear radiation damping are of the same order for a rather thick plate. For a thin plate, the structural non-linearity completely controls the behavior of the plate, which implies that in this case the effect of fluid loading is considerably negligible. In general, it can be concluded that both the effects of magnetic field and structural non-linearity play important roles only on the first few modes of the plate.