Study on the fluttering characteristics of multi-articulated flat plate in the mean-flow

৻᭽ᵹਛߦ߅ߌࠆᄙ㑐▵ᐔ᧼ߩᝄേ․ᕈߦ㑐ߔࠆ⎇ⓥ

ጊጯ⌀ᐘ㧔㐳ጟ㜞ኾ㧕㧘ᷰㆺ㆐ᒎ㧔㐳ጟᛛᄢ㧕

Study on the fluttering characteristics of multi-articulated flat plate in the mean-flow

M. yamagishi ^* and T. Watanabe ^**

* Dept. of Mech. Eng., Nagaoka National College of Tech.

** Dept. of Mech. Eng., Nagaoka University of Tech.

ABSTRACT

The flag jointed some flat plates by articulations flutters itself in the mean-flow, and it has steady fluttering mode. The fluttering characteristics of this ‘multi-articulated flat plate’ were investigated experimentally in a wind tunnel. In this paper, the shape of the flat plate is rectangular in several aspect ratios and areas. The results show that the frequency of the fluttering increases with increasing the mean-flow velocity in all shape flat plates. The frequency is large in the large aspect ratio and the small area of the flat plate. Almost all cases show the fluttering mode with node-less flutter. On the other hand, the fluttering mode with node is seen in the shape with low aspect ratio.

Key Words: Flow induced vibration, Flutter, Wind/Water power generation

1.

ᵹ૕ᝄേ೑↪ᣇᑼ㘑᳓ജ⊒㔚ࠍ⋡ᜰߒ㧘ᝄേ૕ߣߒߡ ᣛߩߪߚ߼߈ࠍࡕ࠺࡞ൻߒߚᄙ㑐▵ᐔ᧼ࠍ⠨᩺ߒߚ㧚⊒

㔚ࠪࠬ࠹ࡓࠍ᭴▽ߔࠆ਄ߢᦨㆡߥᒻ⁁ࠍ⸳⸘ߔࠆᜰ㊎

ࠍᓧࠆߚ߼㧘৻᭽ᵹਛߦ߅ߌࠆᄙ㑐▵ᐔ᧼ߩᝄേ․ᕈࠍ

⺞ᩏߒߚ㧚

ᵹ૕ᝄേࠍ೑↪ߒߚ⊒㔚ᣇᑼߪㄭᐕ⎇ⓥ⠪ߦࠃ ࠅឭ᩺ߐࠇࠆࠃ߁ߦߥߞߡ߈ߚ^{1, 2)}߇㧘⪺⠪ࠄߪᵹ

૕ᝄേߦࠃࠅ࿶㔚⚛ሶ ³⁾ࠍᝄേߐߖࠆߎߣࠍ⋡⊛

ߣߒߡ޿ࠆ㧚࿶㔚⚛ሶࠍᝄേߐߖࠆᝄേ૕ߣߒߡ㧘 ᣛߩ᭴ㅧࠍන⚐ൻߐߖߚ㧘㑐▵ࠍ᦭ߔࠆᐔ᧼ߩࡕ

࠺࡞㧔ᄙ㑐▵ᐔ᧼㧕ࠍ⠨᩺ߒ㧘ߘߩᝄേ․ᕈࠍ⺞ᩏ ߒߡ߈ߚ ^4,5)㧚ᄙ㑐▵ᐔ᧼ߪ৻᭽ᵹਛߢᭂ߼ߡ቟ቯ ߒߚ⥄ബᝄേࠍⴕ޿㧘ߘߩᝄേᢙߪᵹㅦߣ౒ߦჇ ടߔࠆ㧚ߒ߆ߒߘߩᝄേ․ᕈߪਇ᣿ߥὐ߇ᄙߊ㧘

⹏ଔᣇᴺ߽᣿⏕ߢߪߥ޿㧚㘃ૃߩ⎇ⓥߣߒߡ㧘ᣛ ߩߪߚ߼߈ߦ㑐ߔࠆታ㛎^{6, 7)}㧘ࠪ࡯࠻ߩ߫ߚߟ߈ߦ 㑐ߔࠆ⎇ⓥ⁸⁾㧘⚦♻ߦࠃࠆ㧞ᰴరታ㛎⁹⁾ߥߤ߇޽ࠅ㧘 ߎࠇࠄࠍෳ⠨ߦᝄേ․ᕈߩ⺞ᩏߣ⹏ଔᣇᴺߩᬌ⸛

ࠍⴕߞߚ㧚

2.

ᵹ૕ᝄേࠍ⊒↢ߐߖࠆᝄേ૕ߣߒߡ⠨᩺ߒߚ㧘 ᄙ㑐▵ᐔ᧼ߩ᭎⇛ࠍ࿑㧝ߦ␜ߔ㧚ᄙ㑐▵ᐔ᧼ߪ㧘 ᣛߩ᭴ㅧࠍන⚐ൻߐߖߚࡕ࠺࡞ߢ㧘ᡰᜬゲࠍ฽߼

ߚⶄᢙゲߢㅪ⚿ߐࠇߚ㧞ᨎએ਄ߩᐔ᧼⟲ࠍ⸒߁㧚

੹࿁↪޿ߚᄙ㑐▵ᐔ᧼ߪ㧘޿ߕࠇ߽㧟ゲ㧟ᨎᐔ᧼ߢ

᭴ᚑߐࠇߡ޿ࠆ㧚਄ᵹ஥ࠃࠅ㑐▵ゲࠍߘࠇߙࠇ╙

㧝㑐▵㧘╙㧞㑐▵㧘╙㧟㑐▵㧘߹ߚᐔ᧼ࠍ╙㧝ᐔ᧼㧘

╙㧞ᐔ᧼㧘╙㧟ᐔ᧼ߣ๭⒓ߔࠆߎߣߣߔࠆ㧚ฦᐔ

᧼ߪ㐳ᣇᒻߢ㧘㧟ᨎߣ߽ห৻ᒻ⁁ߢ޽ࠆ㧚ᄙ㑐▵

Support shaft (First articulation) z

b

Second articulation

Third articulation First plate

Second plate

Third plate l l l

Polyethylene sheet Plastic plate

x y

1mm 1mm

࿑㧝 ᄙ㑐▵ᐔ᧼

ࠕቃ⏺ᒙ㑄⛣ࡢゎ᫂࡜ไᚚࠖ◊✲఍ㅮ₇ㄽᩥ㞟㸦➨ ᅇ࣭➨ ᅇ㸧

41

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ᐔ᧼ߪ㧘ෘߐ

0.08 mm

ෘߐ

0.5 mm

޿ࠆ㧚ࡊ࡟࡯࠻㑆ߦߪ

1 mm

࿁ォߦ⋧ᒰߔࠆ㧚ߥ߅㧘ࡐ࡝ࠛ࠴࡟ࡦ⵾ࠪ࡯࠻ߩ ᦛߍ೰ᕈߪᭂ߼ߡዊߐ޿ߚ߼㧘㑐▵ߦߪᓳరജ෸߮

ᷫ⴮ജ߇↢ߓߥ޿߽ߩߣ઒ቯߒߚ㧚

3.

ታ㛎ߪ็಴ߒญᢿ㕙Ⓧ

400 mm

400 mm

ߒᑼ㘑ᵢࠍ↪޿ߡⴕߞߚ㧚ᄙ㑐▵ᐔ᧼ߪ㧘㧞ᨎߩ ᐔⴕߥ┵᧼ߦࠃࠅᡰᜬߐࠇߡ߅ࠅ㧘┵᧼ߩ㑆㓒ߪ

200 mm

৻᭽ᵹਛߢᝄേߔࠆᄙ㑐▵ᐔ᧼ߩᄌ૏ࠍ㧘ࠪ࡯࠻

ဳ࡟࡯ࠩ࡯ᄌ૏⸘ߢ⸘᷹ߒߚ㧚࡟࡯ࠩ࡯ᄌ૏⸘ߪࠪ

࡯࠻శࠍㆤࠆ‛૕ߩਛᄩ૏⟎߇⸘᷹ߢ߈㧘੹࿁ߪ╙

㧝ᐔ᧼ߩᄌ૏ࠍ⸘᷹ߒߚ㧚ᄙ㑐▵ᐔ᧼ߩᝄേᢙߪ㧘 ᄌ૏ߩᤨ♽೉࠺࡯࠲ߩࠬࡍࠢ࠻࡞ࠃࠅ᳞߼ߚ㧚ߐࠄ ߦ࠺ࠫ࠲࡞ࠞࡔ࡜ߦࠃࠅㅪ⛯౮⌀ࠍ᠟ᓇߒ㧘↹௝ࠍ วᚑߔࠆߎߣߢᝄേࡕ࡯࠼ࠍ⺞ᩏߒߚ㧚ㅪ⛯ߔࠆ㧞 ᨎߩ↹௝ߩᏅಽ୯ߦࠃࠅ⒖േ૕ㇱಽࠍ᛽಴ߒ㧘Ⓧ▚

ߦࠃࠅวᚑ↹௝ࠍ૞ᚑߒߡ޿ࠆ㧚

ᄙ㑐▵ᐔ᧼ߪ㧘

1

b/l

b×l

ෘߐߪోߡห৻ߢ޽ࠆޕᐔ᧼ߩᒻ⁁ߪ㧘㕙Ⓧߩᄢዊ 㧔

S

M

L

1

2

3

⚵ߺวࠊߖߢ⴫⸥ߔࠆ㧚ᣛ߿ࠪ࡯࠻ߦ㑐ߔࠆ⎇ⓥߢ ߪ㧘ࠬࡄࡦᣇะ㐳ߐ

b

Ⓧߦ㑐ଥߔࠆߚ߼㧘ᧄታ㛎ߢߪࠬࡄࡦᣇะ㐳ߐ෸߮

㕙Ⓧ߽ࡄ࡜ࡔ࡯࠲ߣߒߡ⠨ᘦߒߚ㧚ߥ߅❑ᮮᲧ

b/l = 1.0

b×l = 2500 mm

M2

4.

4-1.

ၮḰᒻ⁁ߢ޽ࠆ

M2

㧝ߦ␜ߔ㧚ߥ߅ᝄ᏷ߪyᣇะᄌ૏

Y

r.m.s.୯ߢ⴫ߒߡ޿

ࠆ㧚ᄙ㑐▵ᐔ᧼ߦ߅޿ߡ㧘Ⴧㅦߒߡᝄേࠍᆎ߼ࠆᵹㅦߣ㧘

ᷫㅦߒߡᝄേ߇ᱛ߹ࠆᵹㅦ߇⇣ߥࠆߎߣ߇ಽ߆ߞߚ㧚ᝄ

േࠍᆎ߼ࠆᵹㅦߪᄖੂߦᄢ߈ߊᓇ㗀ߐࠇ㧘ੱὑ⊛ߦੂࠇ ࠍਈ߃ࠇ߫ࠃࠅૐ޿ᵹㅦߢᝄേࠍᆎ߼ࠆ㧚ߚߛߒᝄേ߇ ᱛ߹ࠆᵹㅦએਅߢߪᝄേߪ⿠ߎࠄߥ޿㧚ᄖੂ߇ዊߐ޿႐ วߪ㧘ᄙ㑐▵ᐔ᧼ᓟ✼߆ࠄߩ᷵᡼಴ߦࠃࠆ㧘ᓟ✼ߩᓸዊ ᝄേ߇߈ߞ߆ߌߣߥߞߡ޿ࠆ㧚߹ߚ৻ᐲᝄേࠍᆎ߼ߚᄙ 㑐▵ᐔ᧼ߪ㧘ߘߩᵹㅦߢ㕒ᱛߐߖࠆߎߣ߇಴᧪ߥ޿ߎߣ ߇ಽ߆ߞߚ㧚ߥ߅ߎߩࡅࠬ࠹࡝ࠪࠬߦߟ޿ߡߪ㧘ઁߩ㧤

⒳㘃ߦߟ޿ߡ߽᷹ⷰߐࠇߚ㧚

Zhang

state

flapping state

޽ࠆ㐳ߐߩ⚦♻ߦ߅޿ߡߪᄖੂߩ⒟ᐲߦࠃߞߡ㧞ߟߩ

቟ቯ⁁ᘒࠍ㘧߮⒖ࠆߎߣࠍ᣿ࠄ߆ߦߒߚ㧔

bistability

⴫

1 ᄙ㑐▵ᐔ᧼ᒻ⁁᧦ઙ

0.0 1.0 2.0 3.0 4.0 5.0 6.0

0.0 2.0 4.0

U ₀ (m/s) Y

(mm)

1.0 2.0 3.0 4.0 5.0

0.0 1.0 2.0 3.0 4.0

f ( 1/ s)

࿑㧝 ᵹㅦߣᝄേᢙ࡮ᝄ᏷ߩ㑐ଥ㧔M2㧕

࿑㧝ߩࡅࠬ࠹࡝߽ࠪࠬߎߩ

bistability

⠨߃ࠄࠇࠆ߇㧘ᄙ㑐▵ᐔ᧼ߢߪᝄേࠍ㕒ᱛߐߖࠆ 㧔

flapping state ψ stretched straight state㧕ߎߣ߇ߢ߈ߥ޿

ὐ߇⇣ߥࠆ㧚

4-2.

࿑㧞ߦ㧥⒳㘃ߩᄙ㑐▵ᐔ᧼ߦߟ޿ߡ㧘ᵹㅦߣᝄേ

ᢙߩ㑐ଥࠍ␜ߔ㧚೨▵ߢ␜ߒߚߣ߅ࠅ㧘Ⴧㅦᄌൻߒ ߚ႐วᄙ㑐▵ᐔ᧼ߩೋേᵹㅦ߇ᄖੂߦᓇ㗀ߐࠇࠆ ߎߣ߆ࠄ㧘ᵹㅦߪᷫㅦᄌൻߐߖߡ⸘᷹ࠍⴕߥߞߡ޿

ࠆ㧚

޿ߕࠇߩᄙ㑐▵ᐔ᧼߽㧘ᵹㅦ߇ㅦ޿߶ߤᝄേᢙ߇ ᄢ߈޿㧚ᵹㅦ

3.0 m/s

3/4

l (mm)

b (mm)

b/l ( )

bul

(mm

) Symbol 43.3 28.9 0.66 1250 S1 61.2 40.8 0.66 2500 M1 75.0 50.0 0.66 3750 L1 35.4 35.4 1.0 1250 S2 50.0 50.0 1.0 2500 M2 61.2 61.2 1.0 3750 L2 25.0 50.0 2.0 1250 S3 35.4 70.7 2.0 2500 M3 43.3 86.6 2.0 3750 L3

JAXA–SP–09–014

42

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❑ᮮᲧߢᲧセߔࠆߣ㧘㕙Ⓧ߇ᄢ߈޿߶ߤᝄേᢙ߇ૐ

޿㧚ߐࠄߦ❑ᮮᲧ࡮㕙Ⓧ߇⇣ߥࠆᄙ㑐▵ᐔ᧼ߢ߽㧘 ᐔ᧼㐳ߐ

l

L1

4.8 m/s

േᢙ߇⚂

1.5

L3

Re

F

ᐔ᧼ߩᝄേᢙߪᐔ᧼㐳ߐ

l

㐳ߐߣߒߡ

l

0.02

Re

24000

࿑㧞ߢ⷗ࠄࠇߚߣ߅ࠅ㧘ᝄേᢙߪᵹㅦߩ

3/4

߶߷Ყ଀ߔࠆ㧚߹ߚ࿑㧡ߦ␜ߔࠃ߁ߦ㧘ᐔ᧼㐳ߐߩ

-3/4

4 3 0

¸

¹

¨ ·

© v §

l

f U ⁽¹⁾

ߣ⠨߃ࠄࠇࠆ㧚ߎߩ⚿ᨐࠍၮߦ㧘

10

10

: S1 : S2 : S3 : M1 : M2 : M3 : L1 : L2 : L3

U

(m/s)

f (1 /s )

3/4

5˜10

5˜10

࿑㧞 ᵹㅦ㧙ᝄേᢙߩ㑐ଥ

10

10

: L3 : L1

U

(m/s)

f (1 /s )

5

10

5

10

࿑㧟 ᵹㅦ㧙ᝄേᢙߩ㑐ଥ㧔L1㧘L3ߩߺ㧕

4 1 4 0

1 0 0 4 3

0

¸

¹

¨ ·

©

¸ §

¹

¨ ·

©

¸ §

¹

¨ ·

©

§

l F U l

U U

fl l

f U ⁽²⁾

ࠍ࡟ࠗࡁ࡞࠭ᢙߦኻߒߡ࿑␜ߒߚ߽ߩ߇࿑㧢ߢ޽

ࠆ㧚

(2)

ઙߩ୯߇

10000 < Re < 24000

0 10000 20000 30000

0.00 0.02 0.04 0.06 0.08

: S1 : S2 : S3 : M1 : M2 : M3 : L1 : L2 : L3

Re

F

࿑㧠 ࡟ࠗࡁ࡞࠭ᢙ㧙ήᰴరᝄേᢙߩ㑐ଥ

10

10

10

10

l (mm)

f (1 /s )

: U0 = 3.0 (m/s) : U₀ = 3.5 : U₀ = 4.0 : U₀ = 4.5 : U₀ = 5.0 : U₀ = 5.5

-3/4

࿑㧡 ᝄേᢙߣᐔ᧼㐳ߐߣߩ㑐ଥ

0 10000 20000 30000

0.00 0.01 0.02 0.03 0.04 0.05

: S1 : S2 : S3 : M1 : M2 : M3 : L1 : L2 : L3

Re F ( U

/ l )

࿑㧢 ৻᭽ᵹㅦ࡮ᐔ᧼㐳ߐࠍ⠨ᘦߒߚᝄേߩ৻⥸ൻ ࠕቃ⏺ᒙ㑄⛣ࡢゎ᫂࡜ไᚚࠖ◊✲఍ㅮ₇ㄽᩥ㞟㸦➨ ᅇ࣭➨ ᅇ㸧

43

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ߒߡ޿ࠆ㧚ߎߩߎߣ߆ࠄ㧘ᄙ㑐▵ᐔ᧼ߩᝄേߪ㧘ᵹ ㅦ㧘ᐔ᧼㐳ߐࠃࠅ૗ࠄ߆ߩήᰴరࡄ࡜ࡔ࡯࠲ߢ৻⥸

ൻߔࠆߎߣ߇น⢻ߢ޽ࠆߎߣ߇┍߃ࠆ㧚

4-3.

࿑㧣㨪㧥ߦ↹௝วᚑߦࠃࠅᓧࠄࠇߚᝄേࡕ࡯࠼

ࠍ␜ߔ㧚߶߷ోߡߩᒻ⁁࡮ᵹㅦߦ߅޿ߡ㧘࿑㧣㧘㧤 ߩࠃ߁ߥ▵ߩή޿ᝄേࡕ࡯࠼ߢ޽ࠅ㧘ᵹㅦ߇਄߇ࠆ ߦߟࠇߡⷺᝄ᏷߇ᄢ߈ߊߥࠆ㧚╙

3

ⷺᝄ᏷߇

90

߽⿠ߎࠆߎߣ߇ಽ߆ߞߚ㧚৻ᣇ㧘L1 ߩᄙ㑐▵ᐔ᧼

ߢߪ㧘ૐᵹㅦߢߪ࿑㧣ߦ⷗ࠄࠇࠆ᭽ߥ▵ߩή޿ᝄേ

ࡕ࡯࠼ߢ޽ߞߚ߇㧘ᵹㅦ⚂

4.8 m/s

਄ߦਇቢోߥ▵ࠍᜬߟᝄേࡕ࡯࠼ࠍ␜ߒߚ㧔࿑㧥㧕㧚 ᝄേࡕ࡯࠼߇ᄌൻߔࠆᵹㅦ⚂

4.8 m/s

ోߥ▵ߣߞߚ㧚࿑㧟ߦ⷗ࠄࠇߚᝄേᢙߩਇㅪ⛯ߥᄌ ൻߪ㧘ߎߩᝄേࡕ࡯࠼ߩᄌൻߦࠃࠆ߽ߩߢ޽ࠆߎߣ ߇ಽ߆ߞߚ㧚

5.

ᵹ૕ᝄേ೑↪ᣇᑼ㘑᳓ജ⊒㔚ࠍ⋡ᜰߒ㧘⠨᩺ߒߚᝄേ

૕ߢ޽ࠆᄙ㑐▵ᐔ᧼ߩᝄേߩၮ␆․ᕈࠍ⺞ᩏߒߚ㧚ߘߩ

⚿ᨐએਅߩ⍮⷗ࠍᓧߚ㧚

(1)

(2)

(3)

߶ߤᝄേᢙߪૐߊߥࠆ㧚

(4)

ߒ㧘ࡕ࡯࠼߇ᄌൻߔࠆ㓙㧘ᝄേᢙ߽ᄌൻߔࠆ㧚

ෳ⠨ᢥ₂

1)

:

2001

157433

P2001

157433A

. 2)

,

,

:

2006

226221

P2006

226221A㧕.

3)

E

Vol.

123㧘No.12 (2003)㧘pp. 534-540.

4)

,

,

,

:

5)

:

2008

, pp.47.

6) S. Taneda: Journal of the Physical Society of Japan (1968), Vol. 24, No.2, pp. 392 - 401.

7)

: JAXA-SP-05-012 (2006), pp.23-26.

8)

Vol.65, No.632 (1999), pp.1232-1239.

9) Zhang, J., Childress, S., Libchaber, A., Shelly, M.:

Nature (2000), Vol. 408, pp. 835 - 839.

࿑㧣 ᝄേࡕ࡯࠼ ( M2,

U

= 2.5 m/s )

࿑㧤 ᝄേࡕ࡯࠼

( M2, U

= 5.0 m/s )

࿑㧥 ᝄേࡕ࡯࠼

( L1, U

= 5.0 m/s ) Flow

Flow

Flow

node

JAXA–SP–09–014 44

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