Weakly nonlinear systems: Modeling and experimental methods

The prior chapter presented rigorous theory and methods for nonlinear systems, which is necessary in general because many nonlinear systems exhibit strong modal coupling due to the nonlinearity; this is commonly the case for the geometrically nonlinear structures that were the focus of that chapter. However, one of the most common sources of nonlinearity in built-up structures is the joints, and in many cases, these introduce only a weak stiffness nonlinearity together with a significant damping nonlinearity. In this case, and in many others that are relevant to industry, one can obtain good estimates of the response of the structure using a weakly nonlinear model in which the linear modes of the structure are presumed to be preserved and coupling between modes is neglected. This chapter provides a brief introduction to these concepts.—Chapter Authors: Randall Mayes and Matt Allen.