Computation of periodic orbits for piecewise linear oscillator by Harmonic Balance Methods

Lijun Pei; Antonio Simon Chong Escobar; Ekaterina Pavlovskaia; Marian Wiercigroch

doi:10.1016/j.cnsns.2021.106220

Computation of periodic orbits for piecewise linear oscillator by Harmonic Balance Methods

Lijun Pei, Antonio Simon Chong Escobar, Ekaterina Pavlovskaia, Marian Wiercigroch^* (Corresponding Author)

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

4 Downloads (Pure)

Abstract

In this paper, Harmonic Balance based methods, namely Incremental Harmonic Balance Method and the method of Harmonic Balance with Alternating Frequency and Time traditionally used to compute periodic orbits of smooth nonlinear dynamical systems are employed to investigate dynamics of a non-smooth system, a piecewise linear oscillator with a play. The Incremental Harmonic Balance Method was used to compute the period one orbits including those exhibiting grazing and large impacts. The method of Harmonic Balance with Alternating Frequency and Time was implemented to calculate more complex orbits and multi stability. A good agreement between obtained approximate solutions and numerically calculated responses indicates robustness of the implemented HBMs, which should allow to effectively study the global dynamics of non-smooth systems.

Original language	English
Article number	106220
Number of pages	18
Journal	Communications in Nonlinear Science & Numerical Simulation
Volume	108
Early online date	4 Feb 2022
DOIs	https://doi.org/10.1016/j.cnsns.2021.106220
Publication status	Published - 1 May 2022

Bibliographical note

Acknowledgments
The authors would like to acknowledge the financial support by NNSF of China (Nos. 11372282 and 10702065) and Scholarship of China; The National Secretariat of Science, Technology and Inno- vation of Ecuador (SENESCYT); The Escuela Superior Politcnica del Litoral of Ecuador (ESPOL).

Keywords

Piecewise linear oscillator with play
Incremental Harmonic Balance Method
IHBM
Harmonic Balance with Alternative Frequency and Time
HB-AFT
Computation of periodic orbits

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Cite this

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title = "Computation of periodic orbits for piecewise linear oscillator by Harmonic Balance Methods",

abstract = "In this paper, Harmonic Balance based methods, namely Incremental Harmonic Balance Method and the method of Harmonic Balance with Alternating Frequency and Time traditionally used to compute periodic orbits of smooth nonlinear dynamical systems are employed to investigate dynamics of a non-smooth system, a piecewise linear oscillator with a play. The Incremental Harmonic Balance Method was used to compute the period one orbits including those exhibiting grazing and large impacts. The method of Harmonic Balance with Alternating Frequency and Time was implemented to calculate more complex orbits and multi stability. A good agreement between obtained approximate solutions and numerically calculated responses indicates robustness of the implemented HBMs, which should allow to effectively study the global dynamics of non-smooth systems.",

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author = "Lijun Pei and {Chong Escobar}, {Antonio Simon} and Ekaterina Pavlovskaia and Marian Wiercigroch",

note = "Acknowledgments The authors would like to acknowledge the financial support by NNSF of China (Nos. 11372282 and 10702065) and Scholarship of China; The National Secretariat of Science, Technology and Inno- vation of Ecuador (SENESCYT); The Escuela Superior Politcnica del Litoral of Ecuador (ESPOL).",

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AU - Chong Escobar, Antonio Simon

AU - Pavlovskaia, Ekaterina

AU - Wiercigroch, Marian

N1 - Acknowledgments The authors would like to acknowledge the financial support by NNSF of China (Nos. 11372282 and 10702065) and Scholarship of China; The National Secretariat of Science, Technology and Inno- vation of Ecuador (SENESCYT); The Escuela Superior Politcnica del Litoral of Ecuador (ESPOL).

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N2 - In this paper, Harmonic Balance based methods, namely Incremental Harmonic Balance Method and the method of Harmonic Balance with Alternating Frequency and Time traditionally used to compute periodic orbits of smooth nonlinear dynamical systems are employed to investigate dynamics of a non-smooth system, a piecewise linear oscillator with a play. The Incremental Harmonic Balance Method was used to compute the period one orbits including those exhibiting grazing and large impacts. The method of Harmonic Balance with Alternating Frequency and Time was implemented to calculate more complex orbits and multi stability. A good agreement between obtained approximate solutions and numerically calculated responses indicates robustness of the implemented HBMs, which should allow to effectively study the global dynamics of non-smooth systems.

AB - In this paper, Harmonic Balance based methods, namely Incremental Harmonic Balance Method and the method of Harmonic Balance with Alternating Frequency and Time traditionally used to compute periodic orbits of smooth nonlinear dynamical systems are employed to investigate dynamics of a non-smooth system, a piecewise linear oscillator with a play. The Incremental Harmonic Balance Method was used to compute the period one orbits including those exhibiting grazing and large impacts. The method of Harmonic Balance with Alternating Frequency and Time was implemented to calculate more complex orbits and multi stability. A good agreement between obtained approximate solutions and numerically calculated responses indicates robustness of the implemented HBMs, which should allow to effectively study the global dynamics of non-smooth systems.

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KW - Harmonic Balance with Alternative Frequency and Time

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JO - Communications in Nonlinear Science & Numerical Simulation

JF - Communications in Nonlinear Science & Numerical Simulation

M1 - 106220

ER -

Computation of periodic orbits for piecewise linear oscillator by Harmonic Balance Methods

Abstract

Bibliographical note

Keywords

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