An efficient mode-based alternative to principal orthogonal modes in the order reduction of structural dynamic systems with grounded nonlinearities

Eric Butcher, Mohammad A. Al-Shudeifat

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

An alternative order reduction technique, based on the local equivalent linear stiffness method (LELSM), is suggested in this paper and compared with the principal orthogonal decomposition (POD) and the linear-based order reductions of structural dynamic systems with grounded cubic and dead-zone nonlinearities. It is shown that the updated LELSM modes approximate the principal orthogonal modes (POMs) of these systems with high accuracy especially at initial conditions corresponding to the linear modes of these systems. The use of the POMs for order reduction of nonlinear structural dynamic systems, while previously shown to be effective, requires that the solution response matrix in space and time should be obtained a priori while the alternative LELSM technique in this paper has no such requirement. The methods are applied to illustrative 2-dof (two degree-of-freedom) and 40-dof springmass systems with cubic and dead-zone nonlinearities. The reduced models of these systems in physical coordinates, obtained via updated LELSM modes, have been found nearly equivalent to POD modal-based reduced models and more accurate than the linear-based reduced models. Like POD modal-based order reduction, LELSM modal-based order reduction gives in-phase time histories with the exact numerical solution of the full model for long time periods of simulation. As a result, the updated LELSM modes are proposed as an alternative to POMs in order reduction of structural dynamic systems with grounded nonlinearities.

Original languageEnglish (US)
Pages (from-to)1527-1549
Number of pages23
JournalMechanical Systems and Signal Processing
Volume25
Issue number5
DOIs
StatePublished - Jul 2011
Externally publishedYes

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Structural dynamics
Dynamical systems
Stiffness
Decomposition

Keywords

  • Grounded nonlinearity
  • Local equivalent linear stiffness
  • Model order reduction
  • Principal orthogonal decomposition

ASJC Scopus subject areas

  • Mechanical Engineering
  • Civil and Structural Engineering
  • Aerospace Engineering
  • Control and Systems Engineering
  • Computer Science Applications
  • Signal Processing

Cite this

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abstract = "An alternative order reduction technique, based on the local equivalent linear stiffness method (LELSM), is suggested in this paper and compared with the principal orthogonal decomposition (POD) and the linear-based order reductions of structural dynamic systems with grounded cubic and dead-zone nonlinearities. It is shown that the updated LELSM modes approximate the principal orthogonal modes (POMs) of these systems with high accuracy especially at initial conditions corresponding to the linear modes of these systems. The use of the POMs for order reduction of nonlinear structural dynamic systems, while previously shown to be effective, requires that the solution response matrix in space and time should be obtained a priori while the alternative LELSM technique in this paper has no such requirement. The methods are applied to illustrative 2-dof (two degree-of-freedom) and 40-dof springmass systems with cubic and dead-zone nonlinearities. The reduced models of these systems in physical coordinates, obtained via updated LELSM modes, have been found nearly equivalent to POD modal-based reduced models and more accurate than the linear-based reduced models. Like POD modal-based order reduction, LELSM modal-based order reduction gives in-phase time histories with the exact numerical solution of the full model for long time periods of simulation. As a result, the updated LELSM modes are proposed as an alternative to POMs in order reduction of structural dynamic systems with grounded nonlinearities.",
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N2 - An alternative order reduction technique, based on the local equivalent linear stiffness method (LELSM), is suggested in this paper and compared with the principal orthogonal decomposition (POD) and the linear-based order reductions of structural dynamic systems with grounded cubic and dead-zone nonlinearities. It is shown that the updated LELSM modes approximate the principal orthogonal modes (POMs) of these systems with high accuracy especially at initial conditions corresponding to the linear modes of these systems. The use of the POMs for order reduction of nonlinear structural dynamic systems, while previously shown to be effective, requires that the solution response matrix in space and time should be obtained a priori while the alternative LELSM technique in this paper has no such requirement. The methods are applied to illustrative 2-dof (two degree-of-freedom) and 40-dof springmass systems with cubic and dead-zone nonlinearities. The reduced models of these systems in physical coordinates, obtained via updated LELSM modes, have been found nearly equivalent to POD modal-based reduced models and more accurate than the linear-based reduced models. Like POD modal-based order reduction, LELSM modal-based order reduction gives in-phase time histories with the exact numerical solution of the full model for long time periods of simulation. As a result, the updated LELSM modes are proposed as an alternative to POMs in order reduction of structural dynamic systems with grounded nonlinearities.

AB - An alternative order reduction technique, based on the local equivalent linear stiffness method (LELSM), is suggested in this paper and compared with the principal orthogonal decomposition (POD) and the linear-based order reductions of structural dynamic systems with grounded cubic and dead-zone nonlinearities. It is shown that the updated LELSM modes approximate the principal orthogonal modes (POMs) of these systems with high accuracy especially at initial conditions corresponding to the linear modes of these systems. The use of the POMs for order reduction of nonlinear structural dynamic systems, while previously shown to be effective, requires that the solution response matrix in space and time should be obtained a priori while the alternative LELSM technique in this paper has no such requirement. The methods are applied to illustrative 2-dof (two degree-of-freedom) and 40-dof springmass systems with cubic and dead-zone nonlinearities. The reduced models of these systems in physical coordinates, obtained via updated LELSM modes, have been found nearly equivalent to POD modal-based reduced models and more accurate than the linear-based reduced models. Like POD modal-based order reduction, LELSM modal-based order reduction gives in-phase time histories with the exact numerical solution of the full model for long time periods of simulation. As a result, the updated LELSM modes are proposed as an alternative to POMs in order reduction of structural dynamic systems with grounded nonlinearities.

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