Integration of Freeplay-Induced Limit Cycles Based on a State Space Iterating Scheme
Time integration is commonly used to obtain accurate system responses, such as the limit cycle oscillations (LCOs) for an aeroelastic system with freeplay. However, the integrations that start with various initial conditions (I.C.s) are usually studied case by case, so only a few system states can p...
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doaj-b0f04ef70feb4c7db35137f2955d906c2021-01-15T00:02:22ZengMDPI AGApplied Sciences2076-34172021-01-011174174110.3390/app11020741Integration of Freeplay-Induced Limit Cycles Based on a State Space Iterating SchemeXiangyu Wang0Zhigang Wu1Chao Yang2School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, ChinaSchool of Aeronautic Science and Engineering, Beihang University, Beijing 100191, ChinaSchool of Aeronautic Science and Engineering, Beihang University, Beijing 100191, ChinaTime integration is commonly used to obtain accurate system responses, such as the limit cycle oscillations (LCOs) for an aeroelastic system with freeplay. However, the integrations that start with various initial conditions (I.C.s) are usually studied case by case, so only a few system states can possibly be focused on. This paper proposes a state space iterating (SSI) scheme to find LCO solutions using time integration by using another method. First, a large number of arbitrary I.C. cases are used for time integrations, but only a very short integration time is required for each I.C. case. Second, system behaviors are depicted visually through a method that combines a modified Poincaré map and Lorenz map, in which the LCO solutions are found as fixed points via visual inspections. To verify the SSI scheme’s ability to find LCOs, a typical plunge–pitch wing section is established numerically. Time integrations with both the classic scheme and the proposed SSI scheme are carried out. The LCO results of the SSI scheme are well-aligned with those from the classic scheme. The SSI scheme visualizes the patterns of system responses using arbitrary I.C. cases and analyzes the LCO stability, which provides more mathematical insights into an aeroelastic system with freeplay.https://www.mdpi.com/2076-3417/11/2/741time integrationinitial conditionlimit cycle oscillationfreeplayPoincaré mapLorenz map |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Xiangyu Wang Zhigang Wu Chao Yang |
spellingShingle |
Xiangyu Wang Zhigang Wu Chao Yang Integration of Freeplay-Induced Limit Cycles Based on a State Space Iterating Scheme Applied Sciences time integration initial condition limit cycle oscillation freeplay Poincaré map Lorenz map |
author_facet |
Xiangyu Wang Zhigang Wu Chao Yang |
author_sort |
Xiangyu Wang |
title |
Integration of Freeplay-Induced Limit Cycles Based on a State Space Iterating Scheme |
title_short |
Integration of Freeplay-Induced Limit Cycles Based on a State Space Iterating Scheme |
title_full |
Integration of Freeplay-Induced Limit Cycles Based on a State Space Iterating Scheme |
title_fullStr |
Integration of Freeplay-Induced Limit Cycles Based on a State Space Iterating Scheme |
title_full_unstemmed |
Integration of Freeplay-Induced Limit Cycles Based on a State Space Iterating Scheme |
title_sort |
integration of freeplay-induced limit cycles based on a state space iterating scheme |
publisher |
MDPI AG |
series |
Applied Sciences |
issn |
2076-3417 |
publishDate |
2021-01-01 |
description |
Time integration is commonly used to obtain accurate system responses, such as the limit cycle oscillations (LCOs) for an aeroelastic system with freeplay. However, the integrations that start with various initial conditions (I.C.s) are usually studied case by case, so only a few system states can possibly be focused on. This paper proposes a state space iterating (SSI) scheme to find LCO solutions using time integration by using another method. First, a large number of arbitrary I.C. cases are used for time integrations, but only a very short integration time is required for each I.C. case. Second, system behaviors are depicted visually through a method that combines a modified Poincaré map and Lorenz map, in which the LCO solutions are found as fixed points via visual inspections. To verify the SSI scheme’s ability to find LCOs, a typical plunge–pitch wing section is established numerically. Time integrations with both the classic scheme and the proposed SSI scheme are carried out. The LCO results of the SSI scheme are well-aligned with those from the classic scheme. The SSI scheme visualizes the patterns of system responses using arbitrary I.C. cases and analyzes the LCO stability, which provides more mathematical insights into an aeroelastic system with freeplay. |
topic |
time integration initial condition limit cycle oscillation freeplay Poincaré map Lorenz map |
url |
https://www.mdpi.com/2076-3417/11/2/741 |
work_keys_str_mv |
AT xiangyuwang integrationoffreeplayinducedlimitcyclesbasedonastatespaceiteratingscheme AT zhigangwu integrationoffreeplayinducedlimitcyclesbasedonastatespaceiteratingscheme AT chaoyang integrationoffreeplayinducedlimitcyclesbasedonastatespaceiteratingscheme |
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1724337868726337536 |