UNIFICATION of POINCARÉ and FLOQUET THEORY for TIME PERIODIC SYSTEMS

Susheelkumar C. Subramanian; Sangram Redkar

doi:10.1115/DETC2020-22524

UNIFICATION of POINCARÉ and FLOQUET THEORY for TIME PERIODIC SYSTEMS

Susheelkumar C. Subramanian, Sangram Redkar

Engineering, Ira A. Fulton Schools of (IAFSE)

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)
Publisher	American Society of Mechanical Engineers (ASME)
ISBN (Electronic)	9780791883914
DOIs	https://doi.org/10.1115/DETC2020-22524
State	Published - 2020
Event	ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2020 - Virtual, Online Duration: Aug 17 2020 → Aug 19 2020

Publication series

Name	Proceedings of the ASME Design Engineering Technical Conference
Volume	2

Conference

Conference	ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2020
City	Virtual, Online
Period	8/17/20 → 8/19/20

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

Access to Document

10.1115/DETC2020-22524

Cite this

Subramanian, S. C., & Redkar, S. (2020). UNIFICATION of POINCARÉ and FLOQUET THEORY for TIME PERIODIC SYSTEMS. In 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC) Article V002T02A042 (Proceedings of the ASME Design Engineering Technical Conference; Vol. 2). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC2020-22524

UNIFICATION of POINCARÉ and FLOQUET THEORY for TIME PERIODIC SYSTEMS. / Subramanian, Susheelkumar C.; Redkar, Sangram.
16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC). American Society of Mechanical Engineers (ASME), 2020. V002T02A042 (Proceedings of the ASME Design Engineering Technical Conference; Vol. 2).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Subramanian, SC & Redkar, S 2020, UNIFICATION of POINCARÉ and FLOQUET THEORY for TIME PERIODIC SYSTEMS. in 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)., V002T02A042, Proceedings of the ASME Design Engineering Technical Conference, vol. 2, American Society of Mechanical Engineers (ASME), ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2020, Virtual, Online, 8/17/20. https://doi.org/10.1115/DETC2020-22524

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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.",

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note = "Publisher Copyright: Copyright {\textcopyright} 2020 ASME. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.; ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2020 ; Conference date: 17-08-2020 Through 19-08-2020",

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N2 - 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.

AB - 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.

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KW - Normal forms

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UNIFICATION of POINCARÉ and FLOQUET THEORY for TIME PERIODIC SYSTEMS

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

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