Adaptive, Parallel Discretization of Periodic Systems

Periodic systems arise in rotorcraft analysis as well as many other technical areas. Solutions to the periodic response based on time integration of the equations of motion have certain advantages at the potential cost of considerable computational expense and lack of certainty in obtaining a periodic response. Enforced-periodicity methods such as harmonic balance and time discretization guarantee a periodic solution without the need for time integration over an indefinite interval. Time discretization offers the possibility of computational efficiency through tuning the temporal mesh to match features in the response. An adaptive time-discretization method for solving the response of periodic systems was implemented using an object-oriented scripting language. The time elements may be refined based on computed error measures. The method is demonstrated for two simple test cases.