Influences of Modal Coupling on Experimentally Extracted Nonlinear Modal Models
Research has shown that mechanical structures can be modeled as a combination of weakly nonlinear uncoupled modal models. These modal models can take many forms such as a basic cubic stiffness and damping force model, or a modal Iwan model. This method relies on two assumptions: (1) the mode shapes of the structure are not amplitude dependent, and (2) the modes of the structure do not couple or interact in the amplitude range of interest. Recently, a hypothesis was proposed that when multiple modes are excited that exercise the same nonlinear joint, the modes begin to couple. This hypothesis is tested on a physical system using a series of narrow-band excitation techniques via a modal shaker and broad-band excitation from a modal hammer. The resulting amplitude dependent stiffness and damping from the various excitation types are used to characterize the degree of modal coupling. Significant modal coupling is observed between three of the low order modes of a cylindrical structure with a beam connected to a plate on its end, which exhibits nonlinearity due to micro-slip in bolted joints.
KeywordsModal coupling Nonlinear modal model Iwan model Nonlinear simulation Hilbert analysis Nonlinear reduced order models
This research was conducted at the 2018 Nonlinear Mechanics and Dynamics (NOMAD) Research Institute supported by Sandia National Laboratories. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525. The authors would also like to thank Bill Flynn from Siemens Industry Software NV for supplying the data acquisition and testing systems used to collect the experimental measurements presented throughout this work.
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