UNIFICATION of POINCARÉ and FLOQUET THEORY for TIME PERIODIC SYSTEMS

Susheelkumar C. Subramanian, Sangram Redkar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

As per Floquet theory, a transformation matrix (Lyapunov Floquet transformation matrix) converts a linear time periodic system to a linear time-invariant one. Though a closed form expression for such a matrix was missing in the literature, this method has been widely used for studying the dynamical stability of a time periodic system. In this paper, the authors have derived a closed form expression for the Lyapunov Floquet (L-F) transformation matrix analytically using intuitive state augmentation, Modal Transformation and Normal Forms techniques. The results are tested and validated with the numerical methods on a Mathieu equation with and without damping. This approach could be applied to any linear time periodic systems.

Original languageEnglish (US)
Title of host publication16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791883914
DOIs
StatePublished - 2020
Externally publishedYes
EventASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2020 - Virtual, Online
Duration: Aug 17 2020Aug 19 2020

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume2

Conference

ConferenceASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2020
CityVirtual, Online
Period8/17/208/19/20

Keywords

  • Floquet theory
  • Lf transformation matrix
  • Nonlinear dynamics
  • Normal forms

ASJC Scopus subject areas

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

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