Order reduction of structural dynamic systems with static piecewise linear nonlinearities

Eric A. Butcher, Rongdong Lu

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


A technique for order reduction of dynamic systems in structural form with static piecewise linear nonlinearities is presented. By utilizing two methods which approximate the nonlinear normal mode (NNM) frequencies and mode shapes, reduced-order models are constructed which more accurately represent the dynamics of the full model than do reduced models obtained via standard linear transformations. One method builds a reduced-order model which is dependent on the amplitude (initial conditions) while the other method results in an amplitude-independent reduced model. The two techniques are first applied to reduce two-degree-of-freedom undamped systems with clearance, deadzone, bang-bang, and saturation stiffness nonlinearities to single-mode reduced models which are compared by direct numerical simulation with the full models. It is then shown via a damped four-degree-of-freedom system with two deadzone nonlinearities that one of the proposed techniques allows for reduction to multi-mode reduced models and can accommodate multiple nonsmooth static nonlinearities with several surfaces of discontinuity. The advantages of the proposed methods include obtaining a reduced-order model which is signal-independent (doesn't require direct integration of the full model), uses a subset of the original physical coordinates, retains the form of the nonsmooth nonlinearities, and closely tracks the actual NNMs of the full model.

Original languageEnglish (US)
Pages (from-to)375-399
Number of pages25
JournalNonlinear Dynamics
Issue number3
StatePublished - Aug 2007


  • Nonlinear normal modes
  • Order reduction
  • Piecewise linear nonlinearities

ASJC Scopus subject areas

  • Mechanical Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering
  • Control and Systems Engineering


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