Modeling And Numerical Method Of Non-smooth Multibody System Based On LCP

Non-smooth dynamics of multi-body system focus on the multi-body systems with non-smooth factors such as friction and collision. Being discontinuous, non-linear structure of the variable topology, the system dynamics needs new mathematical frameworks and new numerical algorithms. The research of new mathematical frameworks and new algorithms is very important and challenging.Firstly, the DAEs(Differential Algebra Equations) of multi-body system with complex constraints including friction and collision is modeled by the means of variable topology structure. Then, the coulomb’s friction law and the law of collision are described by set-valued function and complementary relationship, and the LCP model of system is established. The algorithm of LCP is embedded in the numerical integration process of DAEs, and the non-smooth algorithms including Event-Driven scheme and TimeStepping scheme are given.Finally, the theory and algorithm is applied to specific problems to show their correctness and effectiveness. The characteristics of convex set about coulomb’s friction law are analyzed by the theory of convex analysis. The influences of the coulomb’s friction on mechanical vibration, especially the influence on the resonance are analyzed and some characteristics of vibration with coulomb friction are found with the help of numerical calculation. Event-Driven scheme has been carried out in an example of frog hammer with a single point contact and Time-Stepping scheme has been applied to an example of woodpecker toy with multiple contacts. The result of numerical simulation show our method is effective. Figure 28; Table 0; Reference 57...