Most actual mechanical systems are composed of many parts connected to one another by various type of joints, even if the dynamical model of each part is fairly accurately known, the whole system dynamic motion will becomes erroneous if the accurate joint properties are not known because quite often the whole system motion is closely related to the joint properties. Especially when a joint has nonlinear characteristics, the local nonlinear joint changes the whole system to be nonlinear, even though all the remaining subsystems are quite linear, and results in dynamic analysis of the whole system being complicated. Also it is important to judge whether a linear model for a system or structure analysis is adequate or not. If it is thought that a linear model is not acceptable, a nonlinear model should be considered for more accurate analysis even it is more complicate and difficult to handle.
Firstly, in this work, the inverse Fourier transform of FRF (frequency response function) method is adopted to identify and quantify nonlinearity. NPR (noncausal power ratio) value is defined as the ratio of noncausal power to the total FRF power. Those values are calculated from the time domain data of the inverse Fourier trasformed FRF. It is conceptually explained that a nonlinear system shows some noncausal power within its inverse Fourier transform of systems FRFs. Then this mehod is tested out not only with single degree of freedom systems having different types of nonlinearity but also with multi degree of freedom system. NPR values are compared as varying excitaiton force level of a single degree of freedom having different kinds of nonlinear type. It was found that NPR value grows with increasing nonlinearities.
Secondly, a method is suggested to identify nonlinear joint properties. This method is characterized in that the joint forces, whether they are linear or nonlinear, are treated as external forces and can be fitted using the substructure's FRFs and the joint responses in the frequency domain. In that sense, this method extends the force-state mapping technique, which fits the joint forces with the joint degree response data in the time domain, into the frequency domain manipulations. The force-state mapping method has some limitations when applying to complex real structures because it uses a time domain lumped parameter model. On the other hand, the frequency domain method is easily applicable to a complex real structure having nonlinear joints since it uses each substructure's FRFs. The validity of the proposed method was tested numerically with a 3 dofdos system having nonlinear joints and experimentally with a suspension system and a beam structure having Coulomb friction. From the numerical and experimental results it was verified that the frequency domain method has some advantages over the classical force-state mapping technique such as the less number of data points needed in curve fit and the flexibility to select better quality data points from the used FRFs. Furthermore this method is very useful to identify the nonlinear parameters of a structure having arbitrary nonlinear boundaries.
