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Research Papers

Effects of Externally Mounted Store on the Nonlinear Response of Slender Wings

[+] Author and Article Information
Yuqian Xu, Huagang Lin

School of Astronautics,
Harbin Institute of Technology,
Harbin 150001, China

Dengqing Cao

School of Astronautics,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: dqcao@hit.edu.cn

Chonghui Shao

Harbin Turbine Company Limited,
Harbin 150046, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 16, 2017; final manuscript received January 27, 2018; published online February 26, 2018. Assoc. Editor: Tsuyoshi Inoue.

J. Comput. Nonlinear Dynam 13(4), 041003 (Feb 26, 2018) (12 pages) Paper No: CND-17-1456; doi: 10.1115/1.4039241 History: Received October 16, 2017; Revised January 27, 2018

The nonlinear characteristics of slender wings have been studied for many years, and the influences of the geometric structural nonlinearity on the postflutter responses of the wing have been received significant attention. In this paper, the effects of the external store on the nonlinear responses of the slender wing will be discussed. Based on the Hodges–Dowell beam model, the dynamical equations of the wing which include the geometric structural nonlinearity and store effects are constructed. The unsteady aerodynamic loading of the wing will be calculated by employing Wagner function and strip theory. The slender body theory is adopted to get the aerodynamic forces of the store. The Galerkin method is used to obtain the state equations of the system and the appropriate mode combination is obtained for the cases studied in this paper. Numerical simulations are given to show that the store spanwise position and the distance between the store mass center and the elastic center of the wing are two important factors which will affect the nonlinear characteristics of the wing. These two parameters will induce the occurrence of quasi-periodic motion and branch structure in bifurcation diagrams to the system. The peak of postflutter response is also related to these parameters and the lower response peak can be obtained when the store mass center is in front of the elastic center. The models and results are helpful to the design procedure of the slender wing with store in the preliminary stage.

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Topics: Wings
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References

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Figures

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Fig. 1

Schematic of the wing with store: (a) the wing with store before deformation and (b) the typical wing section with store attached in the process of deformation

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Fig. 2

Schematic of the slender store

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Fig. 3

The effects of the truncated mode number on the response peak of wing tip: (a) the bending response peak and (b) the torsional response peak

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Fig. 4

The effects of the truncated mode number on the response curves of wing tip at U = 37 m/s: (a) the bending response curves and (b) the torsional response curves

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Fig. 5

The bifurcation diagrams of the wing without store: (a) the bending motion bifurcation diagram of the wing tip and (b) the torsional motion bifurcation diagram of the wing tip

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Fig. 6

The bifurcation diagram of the wing with store for xs=l/2,ysce=−0.1  m

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Fig. 7

The frequency spectra for the motions of the wing tip under some typical freestream velocities: (a) U = 31.75 m/s, (b) U = 33.75 m/s, (c) U = 36.25 m/s, (d) U = 36.75 m/s, (e) U = 37.5 m/s, and (f) U = 38.75 m/s

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Fig. 8

Poincaré plots of some typical quasi-periodical motions for the wing tip under different freestream velocities: (a) U = 36.75 m/s and (b) U = 38.75 m/s

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Fig. 9

Time history curves of some typical quasi-periodical motions for the wing tip under different freestream velocities: (a) U = 36.75 m/s and (b) U = 38.75 m/s

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Fig. 10

Phase portraits of some typical quasi-periodical motions for the wing tip under different freestream velocities: (a) U = 36.75 m/s and (b) U = 38.75 m/s

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Fig. 11

The bifurcation diagrams of the wing under different mounted store conditions: (a) xs=l/2,ysce=0  m; (b) xs=l/2,ysce=0.1  m; (c) xs=l/4,ysce=−0.1  m;(d) xs=l/4,ysce=0  m; (e) xs=l/4,ysce=0.1  m; (f) xs=l/8,ysce=−0.1  m; (g) xs=l/8,ysce=0  m; and (h) xs=l/8,ysce=0.1  m

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Fig. 12

The response peak of the wing tip versus freestream velocity under different store mounted types: (a) the response peak of bending motion for xs=l/2, (b) the response peak of torsional motion for xs=l/2, (c) the response peak of bending motion for xs=l/4, (d) the response peak of torsional motion for xs=l/4, (e) the response peak of bending motion for xs=l/8, and (f) the response peak of torsional motion for xs=l/8

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