On the inversion of describing functions in nonlinear system analysis

Nonlinear mechanical vibrations are widely found in engineering structures. Traditional linear analysis methods are failing to meet the growing requirements of analysis accuracy. Because of the complexity of nonlinear system, there is no general method for nonlinear system analysis. Based on the describing function method, a polynomial inversion method may be used in nonlinear system identification. Using this method, the measured DF can be inverted into the form of force which has a clearer physical meaning and is easier to use for parameter fit. A MDOF system with two types of nonlinearities at the same location is studied to demonstrate this method.