Analysis of Locally Nonlinear MDOF Systems Using Nonlinear Output Frequency Response Functions

The analysis of multidegree-of-freedom (MDOF) nonlinear systems is studied using the concept of nonlinear output frequency response functions (NOFRFs), which are a series of one-dimensional functions of frequency recently proposed by the authors to facilitate the analysis of nonlinear systems in the frequency domain. By inspecting the relationships between the NOFRFs of two consecutive masses in the locally nonlinear MDOF systems, a series of properties about the NOFRFs of the nonlinear systems are obtained. These properties clearly reveal how the system linear characteristic parameters govern the distribution of nonlinear effects induced by the system nonlinear component within the whole systems. The results obtained in the present work are of significance to the frequency response analysis for nonlinear systems. One important potential application of these results is the detection and location of damages in engineering structures, which make the structures behave nonlinearly.