Nonlinear Vibration Analysis of a Fluid-Loaded Plate in Magnetic Field

Abstract

In the present study, we perform the non-linear vibration analysis of an elastic plate subjected to weak fluid loading in an inclined magnetic field. The structural nonlinearity, fluid nonlinearity, 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 nonlinear vibration response of the plate is calculated. Based on the assumptions of ordering and formulations of multiple scales, it can be concluded that the non-linear dynamics in weak fluid loading conditions is totally dominated and controlled only by the structural nonlinearity and linear effect of the magnetic field. Both thick and thin plates are investigated; the contributions due to the structural nonlinearity and acoustic linear radiation damping are of the same order for a rather thick plate. For a thin plate, the structural nonlinearity 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 nonlinearity play important roles only on the first few modes of the plate.