Order Reduction of Large Scale Systems via Nonlinear Normal Modes

Abstract

By employing the piecewise modal method (PMM) and local equivalent linear stiffness method (LELSM) to estimate NNM frequencies and mode shapes, improved reduced order models were obtained for several types of nonsmooth nonlinearities. The resulting approximate frequencies and mode shapes were compared with the exact NNM frequencies and best-fit lines to the NNM manifolds obtained via least squares regression from the direct numerical integration of the full model. The technique was applied specifically to a system with a bilinear clearance-type nonlinearity, to systems with symmetric nonsmooth nonlinearities, and to systems with multiple surfaces of discontinuity. The two methods of approximation (PMM and LELSM) were each shown to work better than linear-based order reduction in all cases. It was found that the PMM method was preferable for bilinear clearance nonlinearities while the LELSM method was preferable for symmetric nonlinearities such as deadzone, saturation, and bang-bang. The PMM and LELSM methods were also used to help control a piecewise linear system by designing an active controller which forces the system to have certain assigned vibration frequencies and mode shapes.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2001
Accession Number
ADA430329

Entities

People

  • Eric Butcher
  • Subhash Sinha

Organizations

  • University of Alaska Fairbanks

Tags

Communities of Interest

  • Air Platforms
  • Autonomy
  • Human Systems

DTIC Thesaurus Topics

  • Autonomous Systems
  • Clearances
  • Differential Equations
  • Discontinuities
  • Dynamic Response
  • Engineering
  • Equations
  • Frequency
  • Linear Systems
  • Mechanical Engineering
  • Modal Analysis
  • Nonlinear Differential Equations
  • Nonlinear Dynamics
  • Nonlinear Systems
  • Numerical Integration
  • Stiffness
  • Vibration

Readers

  • Control Systems Engineering.
  • Regression Analysis.
  • Underwater engineering and Marine Technology.