Dynamic response characteristics of axially moving plates subjected to moving load

In this paper, the dynamic response of axially moving geometric nonlinear plates carrying moving mass is investigated. Based on von Kármán plate theory, the time-varying dynamic equation of the axially moving plate under moving loads is obtained by using the extended Hamiltonian principle and discretized into a set of finite-dimensional ordinary differential nonlinear equations by the assumed mode method. The equation incorporates the additional mass, damping, and stiffness matrix resulting from the inertia force, centrifugal force, and Coriolis force of the moving mass. Comparing the axially moving of plate, dynamic response results of linear and nonlinear results show the necessity of considering geometric nonlinearity in the model. The effects of system load parameters, including the mass of the moving load, the speed of the axially moving plate, and the plate’s aspect ratio on the vibration characteristics of the plate, are discussed. The dynamic responses of the axially moving plates under three different moving load trajectories are contrasted. Numerical results show that increasing the moving load mass and the speed of the axially moving plate leads to greater instability of the system, and the aspect ratio and different moving trajectories also have effects on the transverse vibration of the plate.