Order reduction of nonlinear systems subjected to an external periodic excitation

Sangram Redkar, S. C. Sinha

Research output: Contribution to conferencePaper

Abstract

In this work, the basic problem of order reduction nonlinear systems subjected to an external periodic excitation is considered. This problem deserves attention because the modes that interact (linearly or nonlinearly) with the external excitation dominate the response. A linear approach like the Guyan reduction does not always guarantee accurate results, particularly when nonlinear interactions are strong. In order to overcome limitations of the linear approach, a nonlinear order reduction methodology through a generalization of the invariant manifold technique is proposed. Traditionally, the invariant manifold techniques for unforced problems are extended to the forced problems by 'augmenting' the state space, i.e., forcing is treated as an additional degree of freedom and an invariant manifold is constructed. However, in the approach suggested here a nonlinear time-dependent relationship between the dominant and the non-dominant states is assumed and the dimension of the state space remains the same. This methodology not only yields accurate reduced order models but also explains the consequences of various 'primary' and 'secondary resonances' present in the system. Following this approach, various 'reducibility conditions' are obtained that show interactions among the eigenvalues, the nonlinearities and the external excitation. One can also recover all 'resonance conditions' commonly obtained via perturbation or averaging techniques. These methodologies are applied to some typical problems and results for large-scale and reduced order models are compared. It is anticipated that these techniques will provide a useful tool in the analysis and control of large-scale externally excited nonlinear systems.

Original languageEnglish (US)
Pages1169-1175
Number of pages7
DOIs
StatePublished - Jan 1 2005
Externally publishedYes
Event2005 ASME International Mechanical Engineering Congress and Exposition, IMECE 2005 - Orlando, FL, United States
Duration: Nov 5 2005Nov 11 2005

Other

Other2005 ASME International Mechanical Engineering Congress and Exposition, IMECE 2005
CountryUnited States
CityOrlando, FL
Period11/5/0511/11/05

Keywords

  • Nonlinear systems
  • Order reduction

ASJC Scopus subject areas

  • Control and Systems Engineering

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    Redkar, S., & Sinha, S. C. (2005). Order reduction of nonlinear systems subjected to an external periodic excitation. 1169-1175. Paper presented at 2005 ASME International Mechanical Engineering Congress and Exposition, IMECE 2005, Orlando, FL, United States. https://doi.org/10.1115/IMECE2005-82354