Nonlinear vibration analysis of an isotropic rectangular plate subjected to a moving mass

In this paper, nonlinear dynamics of an isotropic rectangular plate under influence of a moving mass is considered. The governing nonlinear coupled partial differential equations of motionis derived by energy method using Hamilton’s principle based on the large deflection theory in conjuncture with the Von-Karman strain-displacement relations. Then theGalerkin’s method is used to transform the equations of motion into the three coupled ordinarydifferential equations and then the numerical integration method is applied to compute the dynamic responses of the plate under the travelling mass. To verify the validity of the obtainedresults, some special case of this study is compared to other researcher’s study. A parametricstudy on the effect of moving mass or its equivalent concentrated force and the velocity of the moving mass or load has been investigated. Furthermore, the dynamic magnificationfactor and normalized time histories of the central point of the plate are discussed for various load velocity ratios and compared to the linear solution results.

Keywords:

Nonlinear vibration , isotropic rectangular plate , moving mass , Galerkin's method