Transmissibility function analysis for the detection and localization of damage with nonlinear features in MDOF structural systems

Transmissibility function analysis refers to the evaluation of the ratio between the spectra of two different outputs of a system and has been widely used for the detection and localization of damage in linear structural systems. In this article, a new transmissibility function analysis methodology is proposed to detect and localize damage with nonlinear features in multi degree-of-freedom (MDOF) structural systems. The methodology assumes the MDOF systems are subject to a general input with only the frequency range known a priori so is applicable to address damage detection and location issues for a wide range of engineering structures and systems. This methodology is derived based on the concept of nonlinear output frequency response functions (NOFRFs) and the concept of transmissibility of nonlinear systems introduced based on the NOFRFs. The transmissibility function analysis over output frequencies contributed by system nonlinearities is exploited to detect and localize damage with nonlinear features in MDOF structural systems. Both numerical simulations and experimental studies on a cracked beam structure in the laboratory have been conducted. The results verify the effectiveness and demonstrate the potential applications of the proposed methodology in the detection and localization of damage in practical engineering structures.