MODELLING OF VIBRATING SYSTEMS USING TIME-DOMAIN FINITE ELEMENT METHOD

In this paper, several dynamic systems are modelled using the time-domain finite element method. Galerkinʹs weak principle is used to model the general second order mechanical system, and is applied to the dynamics of the simple pendulum. Problems that arise during the approximation of the final momentum are also investigated. Furthermore, additional dynamic analysis methods are suggested for hybrid co-ordinate systems that have both slew and flexible modes. The proposed methods are based on both extended Hamiltonʹs principle and Galerkinʹs weak principle. The matrix wave equation is propagated in a space domain, satisfying the geometric/natural boundary conditions. As a result, the flexible motion can be obtained, and this was compatible with the applied control input. A numerical example is used to demonstrate the effectiveness of the proposed modelling methods for the hybrid co-ordinate systems.