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Vibration energy flow analysis of the Van der Pol oscillator

Vibration energy flow analysis of the Van der Pol oscillator
Vibration energy flow analysis of the Van der Pol oscillator

This paper investigates the forced Van der Pol oscillator from a viewpoint of vibration flow and energy exchange. The method of averaging and the method of harmonic balance are used to derive analytical formulations of time-averaged power flow variables associated with steady-state periodic and quasi-periodic responses, respectively. Effects of bifurcations on time-averaged power flow are investigated both by analytical methods and numerical integrations. It is found that the time-averaged input power by the external harmonic force may become negative at some excitation frequencies. Correspondingly, the damping nonlinearity may lead to positive time-averaged dissipated power. The frequency band where there is negative time-averaged dissipated power is formulated through analytical approximations. It is also found that bifurcations of the forced oscillator from periodic to quasi-periodic responses may not lead to jump phenomenon in time-averaged input power. The work provides some new understanding of the power flow characteristics of the Van der Pol oscillator and demonstrates potential benefits of using such systems for vibration energy harvesting.

Bifurcation, Nonlinear damping, Power flow analysis, Quasi-periodic motion, Van der Pol oscillator
1985-1992
International Institute of Acoustics and Vibration (IIAV)
Yang, Jian
32e8b622-9602-48ff-8e89-71c9e0ac1e64
Xiong, Ye Ping
51be8714-186e-4d2f-8e03-f44c428a4a49
Xing, Jing Tang
d4fe7ae0-2668-422a-8d89-9e66527835ce
Yang, Jian
32e8b622-9602-48ff-8e89-71c9e0ac1e64
Xiong, Ye Ping
51be8714-186e-4d2f-8e03-f44c428a4a49
Xing, Jing Tang
d4fe7ae0-2668-422a-8d89-9e66527835ce

Yang, Jian, Xiong, Ye Ping and Xing, Jing Tang (2018) Vibration energy flow analysis of the Van der Pol oscillator. In 25th International Congress on Sound and Vibration 2018, ICSV 2018: Hiroshima Calling. vol. 4, International Institute of Acoustics and Vibration (IIAV). pp. 1985-1992 .

Record type: Conference or Workshop Item (Paper)

Abstract

This paper investigates the forced Van der Pol oscillator from a viewpoint of vibration flow and energy exchange. The method of averaging and the method of harmonic balance are used to derive analytical formulations of time-averaged power flow variables associated with steady-state periodic and quasi-periodic responses, respectively. Effects of bifurcations on time-averaged power flow are investigated both by analytical methods and numerical integrations. It is found that the time-averaged input power by the external harmonic force may become negative at some excitation frequencies. Correspondingly, the damping nonlinearity may lead to positive time-averaged dissipated power. The frequency band where there is negative time-averaged dissipated power is formulated through analytical approximations. It is also found that bifurcations of the forced oscillator from periodic to quasi-periodic responses may not lead to jump phenomenon in time-averaged input power. The work provides some new understanding of the power flow characteristics of the Van der Pol oscillator and demonstrates potential benefits of using such systems for vibration energy harvesting.

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More information

Published date: 2018
Venue - Dates: 25th International Congress on Sound and Vibration 2018: Hiroshima Calling, ICSV 2018, Japan, 2018-07-07 - 2018-07-11
Keywords: Bifurcation, Nonlinear damping, Power flow analysis, Quasi-periodic motion, Van der Pol oscillator

Identifiers

Local EPrints ID: 427296
URI: http://eprints.soton.ac.uk/id/eprint/427296
PURE UUID: bd5dfb17-c17f-451f-87b6-7a0271fa977d
ORCID for Ye Ping Xiong: ORCID iD orcid.org/0000-0002-0135-8464

Catalogue record

Date deposited: 11 Jan 2019 17:30
Last modified: 27 Jan 2020 13:38

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