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1 48 1 Vol. 48 No Chnese Journal of Theoretcal and Appled Mechancs Jan ) 2) ( ) O326 A do / THEORETICAL INVESTIGATION ON AERODYNAMIC FORCE MEASUREMENT INTERFERED BY STRUCTURAL VIBRATIONS IN LARGE SHOCK TUNNEL 1) Meng Baoqng Han Gula 2) Jang Zongln (State Key Laboratory of Hgh Temperature Gas Dynamcs, Insttute of Mechancs, Chnese Academy of Scences, Bejng , Chna) Abstract Structural vbraton of aerodynamc measurement system s caused by the mpulse forces generated by startup process of the shock tunnel, and the test tme s too short to allow the vbraton to decay. Therefore, the aerodynamc force measurement can be consdered as a dynamc process, durng whch the sgnals outputted by balance are consst of aerodynamc force sgnals and vbraton sgnals. Exstng methods are lack of support of theory and the accuraces of them are lmted. Theoretcal analyss s used n ths paper and we obtan the analytcal solutons of fundamental characterstcs of free vbratons and forced vbratons. Study of free vbratons focuses on the dscplnes of aerodynamc force measurement nterfered by a sngle vbraton shape and ampltude of nterference changed wth secton of force measurement. The nferences of dfferent vbraton shapes durng forced vbraton motvated by vared forces are nvestgated n research of forced vbraton. Results show that there are theoretcal defects for tradtonal acceleraton compensaton technques because the zero ponts of ampltude of nterference and acceleraton are nconsstent. What s more, the nfluences of secton for force measurement, actng poston of force and type of force should be consdered to determne the man source of nterference n experments. Key words shock tunnel, aerodynamc force measurement, vbraton nterference, theoretcal nvestgaton , ) ( ). 2) /. E-mal: hangula@mech.ac.cn,,.., 2016, 48(1): Meng Baoqng, Han Gula, Jang Zongln. Theoretcal nvestgaton on aerodynamc force measurement nterfered by structural vbratons n large shock tunnel. Chnese Journal of Theoretcal and Appled Mechancs, 2016, 48(1):

2 ms JF12 1] ms.. ( ) ] 3] 4-5] 6-7]. ( ) Hz. 2. 8] ( ). ( ). 9-11] ]. ( ) 14].. 15].. (JF12) km m 3.5 m 6 8 m.. JF12... ( ).. x

3 JF JF12 5 t x y(x, t) L E c ρ c Ē Ī 4 ȳ ( x, t ) x 4 + ρ Ā 2 ȳ ( x, t ) t 2 = 0 (1) x = x/l ȳ = y/l ρ = ρ/ρ c Ē = E/E c Ā = A/L 2 Ī = I/L 4 t = t/t c T c = ρ c L 2 /E c.. (1) 16] y(x, t) = Y(x)T(t) (2) Y (x) = C cos (β x) ch (β x) + r sn (β x) sh (β x) ] } T (t) = b sn(ωt + ϕ) EJ 4 y(x, t) x 4 + ρa 2 y(x, t) t 2 = P(x, t)δ(x l) (3) E c L 2 δ (x l). (3) 16] Y (x) t y (x, t) = q (τ) sn ω (t τ)] dτ (4) ω q (t) = P (x, t) δ (x l) Y (x) dx M (x, t) = EI 2 y (x, t) x 2 (5) Q (x, t) = EI 3 y (x, t) x 3 (6). (2) (4) M (x, t) = Q (x, t) = A M (x) sn (ω t + ϕ ) (7) A Q (x) sn (ω t + ϕ ) (8) (7) A M (x) = EIb C β 2 cos (β x) cosh (β x) r sn (β x) + snh (β x) ] } (9) x.

4 1 105 EIb C β 2 m (x) = cos (β x) cosh (β x) r sn (β x) + snh (β x) ] (10) m (x) 1 2 m (x) m (0) = 1 1. (1) x = 1. x = 1.. (3). y t a (x) = cos (β x) cosh (β x) + r sn (β x) snh (β x) ] (11) 2 m 2 (x) a 2 (x) 2 m (x) a (x).. 2 x = x x = x (a) 1 (a) The frst order vbraton shape 2 2 m(x) a(x) Fg. 2 The dstrbuton of ptchng moment ampltude m(x) and acceleraton ampltude a(x) of the second vbraton shape (b) 2 (b) The second order vbraton shape 1 m (x) Fg. 1 The free vbraton shapes of force measurement structure and correspondng m (x) dstrbuton (2) ( 2) 1 (x 1) 1(b) x = x (8) A Q (x) = EJb C β 3 sn(β x) snh(β x) r (cos(β x) + cosh(β x)) ] (12)

5 x. EJb C β 3 q (x) = sn (β x) snh (β x) r cos (β x) + cosh (β x) ] (13) q (x) 1 2 q (x) q (0) = 1 3(a) 3(b) 2.1. q (x). (3). q (x) a (x), 4 q 2 (x) a 2 (x) x = x 3 x = x q(x) a(x) Fg. 4 The dstrbuton of normal force ampltude q(x) and acceleraton (a) 1 (a) The frst order vbraton shape ampltude a(x) of the second order vbraton shape ] (b) 2 (b) The second order vbraton shape 3 q (x) Fg. 3 The free vbraton shape of force measurement structure and correspondng q (x) dstrbuton (1) x = 1. x = 1. (2) ( 2) q (x) 1 (x 1) 4 x = x 3 0 (a) (b) (a) Harmonc (b) Rectangular pulse 5 3 Fg.5 Schematcs of three dfferent loads

6 1 107 (c) (c) Parabolc 5 3 ( ) Fg.5 Schematcs of three dfferent loads (contnued). 3.1 P(x, t) = P 0 δ(x 1) cos ωt ω = ω 1 + (ω 2 ω 1 ) ω 1, ω 2 1, 2. y(x, t) = C P 0 Y (1) cos(β x) cosh(β ω 2 ω 2 x)+ r sn(β x) snh(β x)] } (cos ω t cos ωt) (14) C P 0 Y (1)β 2 M(x, t) = cos(β x) cosh(β ω 2 ω 2 x)+ r sn(β x) snh(β x)] } cos(ω t) cos(ωt)] (15) Q(x, t) = C P 0 Y (1)β 3 sn(β x) snh(β ω 2 ω 2 x)+ r cos(β x) cosh(β x)] } cos(ω t) cos(ωt)] (16) (14) 6. ANSYS. 1 m 0.1 m 0.1 m 200 GPa kg/m rad/s P 0 = N 0.02 s. 6 y(x, t) Fg. 6 Theoretcal and numercal soluton of the dsplacement y(x, t) under the harmonc load 3.2 P(x, t) = P(t)δ(x P 0, 0 t t s 1) P(t) =. 0, else y(x, t) = M(x, t) = C Y (1)P 0 cos(β x) cosh(β ω 2 x)+ r sn(β x) snh(β x)] } 1 cos(ω t)], 0 t t s C Y (1)P 0 W ω 2 (x)1 cos(ω t s )] cosω (t t s )]+ sn(ω t s ) snω (t t s )]}, t > t s (17) 0 t t s C Y (1)P 0 β 2 ω 2 cos(β x) cosh(β x)+ r sn(β x) snh(β x)] } 1 cos(ω t)] (18) Q(x, t) = C Y (1)P 0 β 3 ω 2 sn(β x) snh(β x)+ r cos(β x) cosh(β x)] } 1 cos(ω t)] (19) (17) 7. 1 m 0.1 m 0.1 m 200 GPa kg/m 3 P 0 = N.

7 y(x, t) Fg. 7 Theoretcal and numercal soluton of the dsplacement y(x, t) under a rectangular pulse load 3.3 y(x, t) = P (x, t) = P 0 t 2 δ (x 1) C P 0 Y (1) cos(β ω 2 x) cosh(β x)+ r sn(β x) snh(β x)]} t cos(ω ω 2 ω 2 t) (20) M(x, t) = EI C P 0 Y (1) β 2 ω 2 cos(β x) cosh(β x)+ r sn(β x) snh(β x)]} t cos(ω ω 2 ω 2 t) (21) Q(x, t) = EIC P 0 Y (1) β 3 ω 2 sn(β x) snh(β x)+ r cos(β x) cosh(β x)]} t cos(ω ω 2 ω 2 t) (22) (20) 8. 1 m 0.1 m 0.1 m 200 GPa kg/m 3 P 0 = N. 8 y(x, t) Fg. 8 Theoretcal and numercal soluton of the dsplacement y(x, t) under a parabolc load 3.4. A M (x) (15), (18) (21) t. (21) A M (x) = EIC P 0 Y (1) β 3 ω 2 sn(β x) snh(β x) + r cos(β x) cosh(β x)] } (23) η (x) = A M (x) / A M (x) (24). 13 1% 12.. (1). ( = 0.2 ) (25) , x > , 4 1, 2.

8 A M (x) = EIP 0 C 2 W (1)β 2 ω 2 ω 2 cos(β x) cosh(β x) + r sn(β x) snh(β x)] } (25) 11 3 Fg. 11 Relatve magntude of nterference to ptchng moment by the thrd order vbraton shape under loads actng on two dfferent postons respectvely A M (x) = ρap 0C 2W (x 0 ) cos(β x) cosh(β β 2 x)+ r sn(β x) snh(β x)] } (26) 9 ( = 0.2) 4 Fg. 9 Relatve magntude of nterference to ptchng moment by the frst four-order vbraton shapes under a harmonc load ( = 0.2) (2). x 0 (26) x 0 = x 0 = Fg. 10 Schematc of loads actng on two dfferent postons and the thrd order vbraton shape. (3) 1, ( ) Table 1 The man source of ptchng moment nterference under dfferent loads Load form (x 0 = 1.0) harmonc load ( = 0.2) harmonc load ( = 0.5) harmonc load ( = 0.8) rectangular pulse load parabolc load The frst order ( ) ( ) The second order ( ) ( ) The thrd order (4) , 4 2 3, 4 1, 2..

9 Table 2 The man source of normal force nterference under dfferent loads Load form (x 0 = 1.0) The frst order The second order The thrd order The fourth order harmonc load ( = 0.2) ( ) ( ) ( ) ( ) harmonc load ( = 0.5) ( ) ( ) harmonc load ( = 0.8) ( ) ( ) rectangular pulse load ( ) ( ) parabolc load ( ) ( ) 4... ( ) ( 0). 1,,.., 2012, 44(5): (Jang Zongln, L Jnpng, Zhao We, et al. Investgatng nto technques for extendng the testdurng of detonaton-drven shock tunnels. Chnese Journal of Theoretcal and Appled Mechancs, 2012, 44(5): (n Chnese)) 2 Lynn KC, Commo SA, Parker PA. Wnd-tunnel balance characterzaton for hypersonc research applcatons. 2012, 49(2): Journal of Arcraft, 3,,.., 2015, 36(1): (Tang Zhgong, Xu Xaobn, Yang Yanguang, et al. Research progress on hypersonc wnd tunnel aerodynamc testng technques. Acta Aeronautca et Astronautca Snca, 2015, 36(1): (n Chnese)) 4 Robnson MJ, Mee DJ, Tsa CY, et al. Three-component force measurements on a large scramjet n a shock tunnel. Journal of Spacecraft and Rockets, 2004, 41(3): Smth AL, Mee DJ, Danel WJT, et al. Desgn, modellng and analyss of sx component force balance for hypervelocty wnd tunnel testng. Computers & Structures, 2001, 79(11): ,,..,2001, 23(6): (Xe Habn, Xe Hongwe, Long Zhqang. Nonlnear ftness of calbraton model of magnetc suspenson and balance system. Journal of Natonal Unversty of Defense Technology, 2001, 23(6): (n Chnese)) 7,.., 2005, 22(8): (Lu Humn, Yn Lmng. The 2D fnte element analyss of msbs lftng electro magnetc feld. Computer Smulaton, 2005, 22(8): 37-49(n Chnese)) 8,.., 1996, 10(1): (Luo Yefan, B Zhxan. The accelerometer force balance used n the mpulse wnd tunnel. Aerodynamc Experment and Measurement & Control, 1996, 10(1): (n Chnese)) 9,,.., 1999, 13(4): (Cheng Zhongyu, Chen Hong, Zhang Q. Inerta compensaton technology based on multaccelerometer vbraton separatng. Journal of Experments n Flud Mechancs, 1999, 13(4): (n Chnese)) 10 Smolnsk G. Proof of concept for testng acceleraton compensaton force balance technques n short duraton flows wth a CEV capsule. AIAA Paper, , Marneau E, MacLean M, Mundy E, et al. Force measurements n hypervelocty flows wth an acceleraton compensated stran gage balance. Journal of Spacecraft and Rockets, 2012, 49(3): ,,.., 2009, 30(6): (Ja Quyao, Yang Ynong, Jang Zenghu. The precson and accuracy of wnd tunnel free-flght experment result. Journal of Astronautcs, 2009, 30(6): (n Chnese)) 13 Laurence SJ, Hornung HG. Image-based force and moment measurement n hypersonc facltes. Experments n Fluds, 2009, 46(2): ,,.., 2003, 17(1): (Guo Dahua, Gao Bng, Ln Zhenbn. The exploraton of a new knd of free-released balance n mpulsve wnd tunnels. Experments and Measurement n Flud Mechncs, 2003, 17(1): (n Chnese)) 15,,.., 2006, 20(1): (Lu Hongshan, Xu Xang, Jang Hua, et al. The applcaton of the stress wave force balance n shock tunnel n Chna. Journal of Experments n Flud Mechancs, 2006, 20(1): (n Chnese)) 16..,1989 (N Zhenhua. Vbraton Mechancs. X an: X an JaoTong Unversty Press, 1989 (n Chnese)) ( : ) ( : )

中文版样板

中文版样板航空学报 Acta Aeronautca et Astronautca Snca http://hkxb.buaa.edu.cn hkxb@buaa.edu.cn Jan. 5 014 Vol.35 No.X: XX-XX ISSN 1000-6893 CN 11-199/V DOI: 10.757/S1000-6893.016.0069 基于 Krgng 模型的风洞应变天平