A Systematic Approach to Modal Testing of Nonlinear Structures

The application of experimental modal analysis methods to nonlinear structures (sometimes referred to as "nonlinear modal testing" - NLMT) is not a new field, but only in the past few years has it become mature enough to be approached in a systematic way. Many methods have been developed over the years for dealing with nonlinearities in structural dynamics, but nonlinearity is an extremely complex phenomenon with so many aspects and consequences that is not possible to have a single method capable to deal with all of them. Rather than taking a holistic approach, it is perhaps useful for the engineer to have a set of mathematical tools to analyse separate subsets of the whole problem, i.e. one being within the scope of each individual investigation. The main objective of this paper is to provide a modular framework from which the engineer can choose the most appropriate method to retrieve information about an examined nonlinearity, based on the type of information needed and the available data set. This is achieved by performing a breakdown of the nonlinear modal analysis process into four main stages: detection, localisation, characterisation and quantification - each of these providing a different level of insight into the problem. A review of currently-available algorithms applicable for these four categories is presented, as well as their application to two simple case studies.