Chapter18 How Linear Is a Linear System? D. Roettgen, B. Pacini, and B. Moldenhauer Abstract Often, when testing structures, engineers assume the experimental system only exhibits linear behavior. This linear assumption means that the modal frequency and damping of the structure do not change with response level. In many assembled structures, components are connected through bolted joints. These systems behave in a weakly nonlinear fashion due to frictional contact at these interfaces, but often these structures are still treated linearly at low excitation levels. This work contains a case study where an assumed linear system exhibits nonlinear behavior. Because of this nonlinearity, if the force applied to the structure duringlinear testing is not sufficiently low then the test may capture a nonlinear frequency or damping instead of the true linear parameters. The errors associated with this linearization causes inaccuracy when simulating a system response. In particular, a linear substructuring problem is presented in which true linear frequencies and damping ratios are compared to slightly nonlinear counterparts to observe the error caused in the assembled response. This paper documents lessons learned and heuristics to be considered when capturing true linear parameters from a weakly nonlinear structure. Keywords Linear modal analysis · Nonlinear systems · Structural dynamics · Heuristics · Best practices 18.1 Introduction Traditional experimental modal analysis transforms a set of measured responses into single degree-of-freedom (DOF) modal responses. Linear modal analysis is a useful tool for updating finite element models, performing low excitation level system predictions, and obtaining modal information about a mechanical system (i.e., natural frequencies and mode shapes). Many industries manufacture mechanical systems assembled using bolted joints. The frictional interfaces that occur due to these joints often introduce nonlinearity into an otherwise linear system. This type of weakly nonlinear response is often observed experimentally as a small change in frequency and a large change in damping [1–3]. Often this nonlinearity is overlooked when predicting system response which can lead to erroneous results. This work shows the errors that can arise when one assumes linearity of a weakly nonlinear system. This is shown through an experimental-analytical substructuring when the wrong linear parameters are identified due to a weak nonlinearity. The assembly of interest contains multiple bolted joints which add nonlinearity to the system. This system was previously tested to assess the nonlinear response in [3–5] where in [5] the authors completed nonlinear substructuring on the same structure of interest. In [5] the linear substructuring errors for the system were significantly lower than previous works using similar techniques. This study documents the methods used to minimize these substructuring errors through the use of nonlinear theory and testing, providing heuristics and tools to ensure an experimentalist is obtaining the linear dynamics of abreak system. Sandia National Laboratories is a multisession 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. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. D. Roettgen ( ) · B. Pacini Department of Structural Dynamics, Sandia National Laboratories, Livermore, CA, USA B. Moldenhauer Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI, USA © Society for Experimental Mechanics, Inc. 2020 M. L. Mains, B. J. Dilworth (eds.), Topics in Modal Analysis & Testing, Volume 8, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-12684-1_18 185
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