Refinement of periodic solution obtained via describing function method

摘要

A solution of the periodic problem in a nonlinear system comprising a static symmetric nonlinearity and linear dynamics is presented. The solution is designed as an iterative algorithm of refinement of the approximate solution obtained via application of the describing function method. The algorithm is based upon the transformation of the original nonlinear system into an equivalent nonlinear system for which the filtering hypothesis is satisfied exactly, and for that reason the latter being suitable for application of the developed algorithm. It is also based upon the concept of the periodic signal mapping applied to the open-loop equivalent nonlinear system. The solution is sought for as a fixed point of the periodic signal mapping. The proposed approach is illustrated by examples of analysis of periodic motions in nonlinear systems. A good convergence and accuracy is demonstrated.