2017 Volume 4 Issue 4 Pages 17-00030
Accurate modeling of a flexible body must take into account motion with large deformation, rotation and time-varying length. Numerical analysis, employing a variable-domain finite element model and the absolute nodal coordinate formulation, has been used to model such motion. Unfortunately, the calculation cost of this approach is very high due to the use of nonlinear finite elements with time-varying length. In order to the reduce calculation cost without sacrificing accuracy, we apply the multiple timescale method to the equation of motion. We define three timescales for the multiple timescale method, and refer to them as Cases 1, 2, and 3. Case 1 is based on longitudinal vibration, Case 2 is based on lateral vibration, and Case 3 is based on motion of the rigid pendulum. We compare these three sets of timescales and evaluate the analysis range for each of the sets. The numerical results show that Case 1 delivers the best accuracy when the velocity of the time-varying length is high, whereas Case 2 delivers the quickest calculation time.