Feasibility of Describing Joint Nonlinearity in Exhaust Components With Modal Iwan Models

Segalman recently proposed a model for joint nonlinearity in a built up structure in which each mode is treated independently (orthogonality is assumed to be preserved) and with an Iwan model added to each modal degree of freedom to capture the nonlinearity of all of the joints that are active in that mode. Recent works have shown that this type of model can faithfully describe the nonlinearity in simple laboratory structures and in simulations of structures with several Iwan joints in the micro-slip regime. This work explores the validity of these concepts for more complicated structures, each of which is part of a production automotive exhaust system. Where possible, factory gaskets were used and the bolted joints were tightened per the manufacturer’s specifications. Tests were performed on different subassemblies of the exhaust using a modal hammer to excite the structure and accelerometers to measure its response. Mayes & Allen’s ZEFFT algorithm was used to determine which modes were behaving nonlinearly. Then an algorithm based on the Hilbert transform was used to extract the instantaneous frequency and damping for the modes of interest and to fit the behavior to a modal Iwan model. The results show several modes that exhibit small frequency shifts and damping that changes by as much as a factor of two over the range of forces that were employed.