How Linear Is a Linear System?

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 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.

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.