Mathematical Modeling of a Moving Planar Payload Pendulum on Flexible Portal Framework

Abstract

Mathematical modeling of a moving planar payload pendulum on elastic portal framework is presented in this paper. The equations of motion of such a system are obtained by modeling the portal frame using finite element in conjunction with moving finite element method and moving planar payload pendulum by using Lagrange’s equations. The generated equations indicate the presence of nonlinear coupling between dynamics of portal framework and the payload pendulum. The combinational direct numerical integration technique, namely Newmarkand fourth-order Runge-Kutta method, is then proposed to solve the coupled equations of motion. Several numerical simulations are performed and the results are verified with several benchmarks. The results indicate that the amplitude and frequency of the payload pendulum swing angle are greatly affected by flexibility of structure and the cable in term of carriage speed.

Keywords

• payload pendulum
• portal framework
• moving finite element method
• lagrange’s equations