Numerical analysis of cracked beams using nonlinear output frequency response functions

Nonlinear output frequency response functions (NOFRFs) are a new concept recently developed for the analysis of nonlinear systems in the frequency domain. Based on this concept, the output frequency behaviors of nonlinear systems can be expressed using a number of one-dimensional functions similar to the approach used in the traditional frequency response analysis of linear systems. In this paper, the NOFRFs are first employed to analyze a typical representation for cracked structures, a single degree of freedom system (SDOF) bilinear model, to explain the occurrence of the nonlinear phenomena when a cracked structure is subjected to sinusoidal excitations, including the generation of super-harmonic components and sub-resonances. Then the NOFRF concept is used to analyze the crack induced nonlinear response of a beam represented by a finite model. The results show that higher order NOFRFs are extremely sensitive to the appearance of cracks in the beam, and can therefore be used as crack damage indicators to indicate the existences and the sizes of cracks. This research study establishes an important basis for the application of the NOFRF concept in fault diagnosis of mechanical structures.