Lucid analysis of periodically forced nonlinear systems via normal forms

Peter M.B. Waswa; Sangram Redkar

doi:10.1115/DETC2019-97100

Lucid analysis of periodically forced nonlinear systems via normal forms

Peter M.B. Waswa, Sangram Redkar

Polytechnic Engineering Programs (EGR)

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

3 Scopus citations

Abstract

This paper presents a straightforward methodology to analyze periodically forced nonlinear systems with constant and periodic coefficients via normal forms. We demonstrate how the intuitive system state augmentation facilitates construction of normal forms by avoiding ad-hoc addition of equation variables, book-keeping parameters and detuning parameters. Moreover, this technique directly connects the periodic forcing terms and periodic coefficients of the nonlinearity with the augmented states–making it applicable to all periodically forced nonlinear systems. Accuracy of this approach is successfully verified via fulfilled compliance between analytical and numerical results of forced Duffing’s equation and Mathieu-Duffing equation.

Original language	English (US)
Title of host publication	15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
Publisher	American Society of Mechanical Engineers (ASME)
ISBN (Electronic)	9780791859261
DOIs	https://doi.org/10.1115/DETC2019-97100
State	Published - Jan 1 2019
Event	ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2019 - Anaheim, United States Duration: Aug 18 2019 → Aug 21 2019

Publication series

Name	Proceedings of the ASME Design Engineering Technical Conference
Volume	6

Conference

Conference	ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2019
Country/Territory	United States
City	Anaheim
Period	8/18/19 → 8/21/19

ASJC Scopus subject areas

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

Access to Document

10.1115/DETC2019-97100

Cite this

Lucid analysis of periodically forced nonlinear systems via normal forms. / Waswa, Peter M.B.; Redkar, Sangram.
15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. American Society of Mechanical Engineers (ASME), 2019. (Proceedings of the ASME Design Engineering Technical Conference; Vol. 6).

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

Waswa, PMB & Redkar, S 2019, Lucid analysis of periodically forced nonlinear systems via normal forms. in 15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Proceedings of the ASME Design Engineering Technical Conference, vol. 6, American Society of Mechanical Engineers (ASME), ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2019, Anaheim, United States, 8/18/19. https://doi.org/10.1115/DETC2019-97100

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abstract = "This paper presents a straightforward methodology to analyze periodically forced nonlinear systems with constant and periodic coefficients via normal forms. We demonstrate how the intuitive system state augmentation facilitates construction of normal forms by avoiding ad-hoc addition of equation variables, book-keeping parameters and detuning parameters. Moreover, this technique directly connects the periodic forcing terms and periodic coefficients of the nonlinearity with the augmented states–making it applicable to all periodically forced nonlinear systems. Accuracy of this approach is successfully verified via fulfilled compliance between analytical and numerical results of forced Duffing{\textquoteright}s equation and Mathieu-Duffing equation.",

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AB - This paper presents a straightforward methodology to analyze periodically forced nonlinear systems with constant and periodic coefficients via normal forms. We demonstrate how the intuitive system state augmentation facilitates construction of normal forms by avoiding ad-hoc addition of equation variables, book-keeping parameters and detuning parameters. Moreover, this technique directly connects the periodic forcing terms and periodic coefficients of the nonlinearity with the augmented states–making it applicable to all periodically forced nonlinear systems. Accuracy of this approach is successfully verified via fulfilled compliance between analytical and numerical results of forced Duffing’s equation and Mathieu-Duffing equation.

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Lucid analysis of periodically forced nonlinear systems via normal forms

Abstract

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