Implementing the restoring force surface method to fit experimentally measured modal coupling effects

Abstract

In complex structures, particularly those with jointed interfaces, the dynamic response of individual modes can behave nonlinearly. To simplify analyzing and modeling this response, it is typically assumed that modes are uncoupled, in that each responds independently of the excitation level of other modes. This assumption is derived from the belief that, while modal coupling generally exists in physical structures, its effects are relatively small and negligible. This practice is reinforced by the fact that the actual causes of modal coupling are poorly understood and difficult to model. To that end, this work attempts to isolate and fit a model to the effects of modal coupling in experimental data from a nonlinear structure. After performing a low-level test to determine the linear natural frequencies and damping ratios of several modes, sine beat testing is used to individually excite each mode and record its nonlinear dynamic response. The Restoring Force Surface (RFS) method is then implemented to fit a nonlinear model to each isolated modal response. Sine beats are then done on multiple modes simultaneously, in which the response is assumed to be a combination of the nonlinear models of each isolated mode and some coupling term between them. As the terms modeling the individual modes are known, the only unknown is the coupling term. This procedure is performed on several mode pairs and excitation levels to evaluate the effectiveness of all proposed coupling models and gauge the significance of modal coupling in the structure.