Karhunen-Loeve decomposition for reducing the order and monitoring the dynamics of coupled oscillators

Xianghong Ma, Alexander F. Vakakis, Lawrence Bergman

Research output: Contribution to conferencePaper

Abstract

Karhunen-Loeve - KL modes are used to discretize the dynamics of a four-bay linear truss. This is achieved by defining global KL modal amplitudes and employing the orthogonality relations between KL modes that are inherent in the KL decomposition. It is found that the KL-based low-order models can capture satisfactory the transient dynamics of the truss, even when only a limited number of them is used for the order reduction. A comparison between the exact and low-order dynamics in the frequency domain reveals that the low-order models capture the leading resonances of the truss. A series of experiments with a practical three-bay truss is then performed to validate the theoretical KL decomposition. A comparison between theory and experiment indicates agreement between the predicted and realized dominant KL mode shapes, but less so in the higher order modes. The reasons for this discrepancy between theory and experiment are discussed, and possible applications of the KL-based order reduction to passive and active control of practical large-scale flexible systems are outlined.

Original languageEnglish (US)
Pages873-882
Number of pages10
StatePublished - Dec 1 2001
Event18th Biennial Conference on Mechanical Vibration and Noise - Pittsburgh, PA, United States
Duration: Sep 9 2001Sep 12 2001

Other

Other18th Biennial Conference on Mechanical Vibration and Noise
CountryUnited States
CityPittsburgh, PA
Period9/9/019/12/01

ASJC Scopus subject areas

  • Modeling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

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    Ma, X., Vakakis, A. F., & Bergman, L. (2001). Karhunen-Loeve decomposition for reducing the order and monitoring the dynamics of coupled oscillators. 873-882. Paper presented at 18th Biennial Conference on Mechanical Vibration and Noise, Pittsburgh, PA, United States.