Numerical Integration Method to Determine Periodic Solutions of Nonlinear Systems

A new method to obtain periodic solution of nonlinear systems is proposed by combining secant method with numerical integration. This method can be applied to nonlinear systems with discontinuous characteristics without special treatment. To check the validity of the proposed method, we applied this method to nonlinear systems with discontinuous characteristics, such as piecewise linear spring system, system with Coulomb’s friction and impact damper system. Comparing the results by the proposed method with the results by simple numerical integration or experimental results, the validity of the proposed method is confirmed.