How Linear Is a Linear System?

  • D. Roettgen
  • B. Pacini
  • B. Moldenhauer
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


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 during linear 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.


Linear modal analysis Nonlinear systems Structural dynamics Heuristics Best practices 



This manuscript has been authored by National Technology and Engineering Solutions of Sandia, LLC. under Contract No. DE-NA0003525 with the U.S. Department of Energy/National Nuclear Security Administration. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.


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Copyright information

© Society for Experimental Mechanics, Inc. 2020

Authors and Affiliations

  • D. Roettgen
    • 1
  • B. Pacini
    • 1
  • B. Moldenhauer
    • 2
  1. 1.Department of Structural DynamicsSandia National LaboratoriesLivermoreUSA
  2. 2.Department of Engineering PhysicsUniversity of Wisconsin-MadisonMadisonUSA

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