Nonlinear Dynamic Behavior of Rectangular Plate Dueto an Accelerated Travelling Mass

In this paper, nonlinear dynamics of an isotropic rectangular plate under influence of a movingaccelerated mass is considered. The governing nonlinear coupled partial differential equationsof motion is derived by energy method using Hamilton’s principle based on the largedeflection theory in conjuncture with the Von-Karman strain-displacement relations. Thenthe Galerkin’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 computethe dynamic responses of the plate under the accelerated travelling mass. To verify the validityof the obtained results, some special case of this study is compared to other researcher’sstudy. The appropriate parametric study by taking into account the effect of the velocity ofthe traveling mass with a constant acceleration/deceleration is carried out. It was seen that theexistence of quadratic-cubic nonlinear terms in the governing coupled PDEs of motion rendershardening/stiffening behavior on the dynamic responses of the plate when traversed by amoving mass. In addition, the obtained nonlinear results are compared with those from the linear analysis.

Keywords:

Nonlinear dynamics , rectangular plate , moving mass , Galerkin's method