Sensitivity of NL-RDM to Errors in Parameters Used From the Underlying Linear System

The Non-linear Resonant Decay method (NL-RDM) addresses the identification of multiple degree of freedom non-linear dynamic systems. This method offers a practical approach to the identification of lumped parameter and continuous systems by producing a non-linear extension of the classical linear modal model. The method is introduced, its potential as a practical identification approach explained and some basic examples presented for a two degree of freedom system with a cubic stiffness non-linearity. Since the method makes use of modal parameters obtained at a low level of excitation to provide an estimated underlying linear model, its sensitivity to inaccuracy in these parameters, namely imperfect mode shapes, force vectors and natural frequency is considered using simulations of a two degree of freedom system. For each type of imperfection, the possible reasons for such errors occurring are firstly considered and the potential impact of the errors discussed in conceptual terms. The impact of the imperfections is then explored using simulation. Before applying the NL-RDM method to assess the effect of errors, the relevant inaccuracies are generated and introduced into the system under consideration. The effects of these inaccuracies are then evaluated and compared with perfect simulation results. Knowing the errors present in the identified parameters will help in understanding the influence of these factors on the method. Thus, knowledge of this behaviour could allow better control of levels of inaccuracies in the identification approach. The simulation results are presented later in this paper.