Non-linear System Identification Using Frequency Domain Measurement Data

In this paper, an efficient method for identifying non-linear element positions and their physical parameters within a multiple degree of system or structure is presented. The local non-linear stiffness and damping restoring forces are first modeled with polynomial series functions of the relative displacements and velocities, respectively. Second, an iterative equation between excitation and response signals and the general frequency response function are derived. Then, in the frequency domain, the non-linear degree of freedom can be extracted from the general system. Thus, when two different levels of excitation forces are imposed on a testing system, the frequency domain measurement data is used to detect the nonlinear element positions. In addition, an approach for non-linear physical parameter identification is developed, which can be used to obtaining all the polynomial coefficients of the non-linear stiffness and damping forces The effectiveness of the method is demonstrated by numerical examples, and the results are found to be quite encouraging for application to practical structures with multiple degree offreedom.