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Research Papers

Numerical Analysis of Panel Flutter on Inertial Manifolds With Delay

[+] Author and Article Information
Jiazhong Zhang

e-mail: jzzhang@mail.xjtu.edu.cn

Zhuopu Wang

School of Energy and Power Engineering,
Xi'an Jiaotong University,
Xi'an 710049, Shaanxi Province, PRC

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 15, 2012; final manuscript received May 25, 2012; published online July 23, 2012. Assoc. Editor: Hiroshi Yabuno.

J. Comput. Nonlinear Dynam 8(2), 021009 (Jul 23, 2012) (11 pages) Paper No: CND-12-1031; doi: 10.1115/1.4006948 History: Received February 15, 2012; Revised May 25, 2012

Inertial manifolds with delay (IMD) are applied to the numerical analysis for two-dimensional and three-dimensional panel flutter problems in order to demonstrate their high efficiency in continuous dynamic systems or systems with infinite dimensions. First, Von Kármán's large deformation theory and the first-order piston theory are used to model the system, and a set of nonlinear partial differential equations is obtained. Then, the nonlinear Galerkin method based on IMD is introduced to approach the original infinite dimensional dynamic system, and some expressions with time delay are proposed to reveal the interactions between the higher modes and lower modes. As a result, the degrees-of-freedom of the system are reduced, and computing time can be saved remarkably. Finally, the dynamic behaviors of the system are simulated numerically to make a detailed comparison between IMD and the traditional Galerkin method (TGM). Finally, a conclusion can be drawn that IMD could reduce the computation time up to 7–50%, keeping the same accuracy, and thus its high efficiency is proved. Moreover, the method presented can be extended and applied to other dissipative dynamic systems with large degrees-of-freedom.

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Figures

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Fig. 1

Two-dimensional panel flutter model

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Fig. 2

Stability regions obtained by theoretical analysis

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Fig. 3

Convergence study of modes by TGM

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Fig. 4

Time history of the flat and stable system by TGM

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Fig. 5

Time history of the flat and stable system by IMD

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Fig. 6

Time history of the buckled and dynamically stable system by TGM

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Fig. 7

Time history of the buckled and dynamically stable system by IMD

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Fig. 8

Time histories of the simple harmonic oscillation system by TGM and IMD

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Fig. 9

Time history of the inharmonic oscillation system by TGM

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Fig. 10

Time history of the inharmonic oscillation system by IMD

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Fig. 11

Spectrum analysis of the inharmonic oscillation system by TGM

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Fig. 12

Spectrum analysis of the inharmonic oscillation system by IMD

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Fig. 13

LCO amplitude w¯ versus λ

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Fig. 14

Buckling deformation w¯ versus R

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Fig. 15

Stability regions

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Fig. 16

Three-dimensional panel flutter model

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Fig. 17

Convergence study of modes by TGM

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Fig. 18

Time history of the flat and stable system by TGM

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Fig. 19

Time history of the flat and stable system by IMD

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Fig. 20

Time history of the buckled and dynamically stable system by TGM

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Fig. 21

Time history of the buckled and dynamically stable system by IMD

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Fig. 22

Time histories of the simple harmonic oscillation system by TGM and IMD

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Fig. 23

Time history of the inharmonic oscillation system by TGM

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Fig. 24

Time history of the inharmonic oscillation system by IMD

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Fig. 25

Spectrum analysis of the inharmonic oscillation system by TGM

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Fig. 26

Spectrum analysis of the inharmonic oscillation system by IMD

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Fig. 27

LCO amplitude w¯ versus λ

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Fig. 28

Buckling deformation w¯ versus R

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Fig. 29

Stability regions

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