An Order Reduction Method of Bridge Flutter Equation and a Simplified Formula of Critical Flutter Wind Velocity

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1 Jounal of Highway and Tanspotation Reseach and Development Vol. 8 No. 11 Nov. 011 doi /j. issn Van de Put A An Ode Reduction Method of idge Flutte Equation and a Simplified Fomula of Citical Flutte Wind Velocity QI Ke SN Zuoyu School of Civil Engineeing Guangzhou nivesity Guangzhou Guangdong China Astact ased on the flutte theoy of flat plate the D coupled flutte equation of idge in ai involving 8 flutte deivatives was estalished and an ode eduction method was poposed y easonale assumptions and simplified analysis though making oth sides of the eal and imaginay pats equal. The equation ode was educed and the fomula was simplified compaing with the typical method and othe methods. esides accoding to the vetical ending and tosional fundamental fequency fomulas of long-span idge in Windesistant Design Specification fo Highway idges the simplified citical flutte wind velocity fomula fo longspan cale-stayed idge was estalished ased on Van de Put fomula and some engineeing pojects. The vetical-fequency appoximate fomula and simplified citical flutte wind speed fomula ae simple and the accuacy is satisfied with equiements y compaing with pactical engineeing. Key wods idge engineeing simplified fomula ode eduction method flutte citical wind velocity qiuke. 678@ 163. com

2 106 8 h t = h 0 e iω 0 t 1 α t = α 0 e iω 0 1 ω { m ω h - ω 0 h 0 h = H h * m ḧ + ξ h ω h h + ω hh = ρ KH * 1 + K ρ 3 α 0 + H * 0 3 mξ h ω h ω 0 h 0 ω = H α * 0 h 0 KH * + K H * 3 α + K H * h Kρ 1 + ω 0 α 0 H* 1 { I ω - α ω 0 α 0 h = A h * I α + ξ α ω α α + ω αα = ρ KA * 1 + K ρ 3 α 0 + A * 0 Iξ α ω α ω 0 α 0 ω = A α * 0 h 0 KA * + K A * 3 α + K A * h Kρ 1 + ω 0 α 0 A* K = ω 0 m I ω h ω α 3 X = 1 /ω 0 ξ h ω h X - ξ hω h X ξ α ρ H * 3 H * H * 3 K = ω ρ H * - ) H* 1 = 0 m H * ω A * i H * 3 H * i i = 1 5 ω α 3 K X - ξ αω α X A * H * 1 H * A * A * 1 A * ρ A * A * 3 H * H * 3 A * 1 A * 3 - ) A* = 0 I A * A * 1 h α 5 X K K H * i A * i. 1 { t K j j = ω j K j K K K. K K H * i A * i h α e iωt h t = h 0 e iω 0 t α t = 3 α 0 e iω 0 t Van de Put h α 1976 Van de Put Thiele ω c = η 1 + ε 槡 ) 0. 7μ ω h 6 K η c ε = ω α = f α μ = m ω h f h πρ. = 1 I 槡 m I m X j

3 f = 1 1 π π ρ ) E g I g + E i I f = C 1 7 ρ E g I g C 1 E i I i E c I c a s f t = C 槡 8 C ρ a ρ ag = σ c A c sinα 11 Ta. 1 1 Eo analysis of vetical ending fundamental fequencies of cale-stayed idges / / / / m Hz Hz % f k Ta. Eo analysis of tosional fundamental + k 3 槡 fequencies of cale-stayed idges /m /Hz /Hz /% c = η 1 + C % 6. 槡 7 槡 ) i + E ci [ c α ] a s sin 9 α s s cosα = / 9 ~ 11 f = 1 π 10 π E ) g I g + E i I ) i + E cg ρ σ c A c cosαsin α 1 槡 E gi g + E i I i ) ρ 3 E gi g + E i I i ) k ρ 1 3 k 1 α. E c 0 1 A c k k 3 f k 1 槡 13 1 k 6. 1 f 6. 槡 ) 0. 7μ π 6. 槡 15

4 108 8 k n = Fig. 1 1 Compaison of vetical ending fundamental fequencies 15 = η 1 + C 槡 ) 0. 7μ 6. π k n c 9. 3 槡 18 η 0. 5 C = k n c 槡 19 Refeences 3 1 SCANAN R H. Polematic in Fomulation of Wind-foce η s η α η 0. 6 Model fo idge Decks J. Jounal of Stuctual C = 1 15 k n Engineeing ASCE c 槡 ~ Ta. 3 3 Eo analysis of citical flutte wind velocities / / / m s - 1 / m m % c = k n 槡 μ 0. 6 ~ 0. 8 μ 0 ~ μ η s η α η 0. 5 C = 1 3 ~ 11 3 SCANAN R H. The Action of Flexile idges unde

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