Effective algorithm for two-dimensional frictional system involving arbitrary impacting boundaries. (1st February 2020) - Wang, Xiaosun; Zhao, Deng; Wu, Shijing; Li, Xiaofeng; Yuan, Hao; Li, Qiaoquan
Highlights: We can precisely predict the impacting location, time and rebound velocity for a two-dimensional frictional system involving impacting by using analytical solutions. We propose a new numerical algorithm for the numerical solution of a two-dimensional frictional system involving impacting. We select several representative scenarios to evaluate and verify the accuracy and robustness of the new algorithm in a two-dimensional frictional system with boundaries. The relative errors of impacting locations are insensitive to the boundary complexity by utilizing our proposed algorithm. Our new algorithm is better than two conventional methods in calculating impacting location and time with high accuracy. Graphical abstract: Abstract: Impacting and friction are always encountered in the mechanical system and make the system experience nonlinearities in both force-position and force-velocity characteristics. In this paper, we propose one effective numerical algorithm for a two-dimensional frictional system involving the impacting by employing the closed form solution to yield the slip responses and extend the closed form solutions for curve length to predict the impacting location and time with high accuracy. By performing the accuracy analysis and robustness analysis through several representative scenarios, we reveal that, (1) the impacting dynamic responses can be predicted through our new algorithm with high accuracy, (2) the accumulative errors of dynamic responses are insensitive to the complex boundary, (3) the new algorithm can keep better robustness when involving repeated impacting.