歐陽(yáng)克儉,陳政清
(1.國(guó)網(wǎng)湖南省電力公司電力科學(xué)研究院,長(zhǎng)沙 410007;2.湖南大學(xué)風(fēng)工程研究中心,長(zhǎng)沙 410082)
附加攻角效應(yīng)對(duì)顫振穩(wěn)定性能影響
歐陽(yáng)克儉1,陳政清2
(1.國(guó)網(wǎng)湖南省電力公司電力科學(xué)研究院,長(zhǎng)沙 410007;2.湖南大學(xué)風(fēng)工程研究中心,長(zhǎng)沙 410082)
用強(qiáng)迫振動(dòng)裝置識(shí)別攻角從-3°~+4°細(xì)化步長(zhǎng)變化為1°的洞庭湖二橋主梁斷面氣動(dòng)導(dǎo)數(shù);將該氣動(dòng)導(dǎo)數(shù)擬合成折減風(fēng)速、攻角的三維曲面,只需獲取某一有效攻角的具體數(shù)值即可自動(dòng)求得所有氣動(dòng)導(dǎo)數(shù)值。通過(guò)在ANSYS中的三維TABLE表存儲(chǔ)各攻角的氣動(dòng)導(dǎo)數(shù),自動(dòng)計(jì)入附加攻角對(duì)顫振穩(wěn)定性影響。全模態(tài)顫振分析結(jié)果表明,附加攻角效應(yīng)可降低該類(lèi)橋梁的顫振臨界風(fēng)速。若按常規(guī)試驗(yàn)方法以3°攻角為步長(zhǎng)進(jìn)行氣動(dòng)導(dǎo)數(shù)插值計(jì)算,顫振分析有可能得到錯(cuò)誤結(jié)論。
大跨橋梁;顫振;附加攻角;強(qiáng)迫振動(dòng);ANSYS
附加攻角一般認(rèn)為橋梁斷面在靜風(fēng)荷載作用下的扭轉(zhuǎn)角度,存在于橋梁風(fēng)工程中的風(fēng)洞試驗(yàn)、氣彈流固耦合CFD模擬中[1]。對(duì)蘇通大橋進(jìn)行全橋氣彈模型試驗(yàn)時(shí)發(fā)現(xiàn),接近顫振失穩(wěn)臨界狀態(tài)[2]的附加攻角達(dá)5°。曹豐產(chǎn)等[3]通過(guò)節(jié)段模型試驗(yàn)對(duì)附加攻角進(jìn)行研究。針對(duì)國(guó)內(nèi)14座不同橋型、跨徑橋梁的試驗(yàn)分析發(fā)現(xiàn),節(jié)段模型附加攻角大小與扭矩系數(shù)斜率密切相關(guān),接近顫振臨界狀態(tài)時(shí)西侯門(mén)橋附加攻角達(dá)2.7°。朱青等[4]針對(duì)節(jié)段模型試驗(yàn)存在附加攻角問(wèn)題,設(shè)計(jì)出附加攻角測(cè)量、修正裝置。試驗(yàn)研究知,附加攻角對(duì)扭轉(zhuǎn)阻尼有一定影響,附加攻角修正后的模型顫振臨界風(fēng)速高于修正前;人為初始激勵(lì)在0°風(fēng)攻角對(duì)有效攻角影響非常明顯;附加攻角使氣動(dòng)導(dǎo)數(shù)A2、A1、H3顯著變大,從而提高顫振臨界風(fēng)速。因此進(jìn)行三維顫振分析時(shí),若氣動(dòng)導(dǎo)數(shù)按初始攻角取值,則與橋梁實(shí)際有效攻角間有較大誤差。應(yīng)對(duì)橋梁在靜風(fēng)荷載作用下的有效攻角如實(shí)評(píng)判后再取橋梁結(jié)構(gòu)有效攻角對(duì)應(yīng)的氣動(dòng)導(dǎo)數(shù)進(jìn)行相關(guān)顫振分析。文獻(xiàn)[5-8]在三維顫振分析中考慮附加攻角造成的氣動(dòng)力非線性對(duì)顫振穩(wěn)定性影響,用氣動(dòng)導(dǎo)數(shù)插值方法處理。對(duì)氣動(dòng)導(dǎo)數(shù)處理,由于通常不考慮附加攻角修正值及存在兩插值攻角間步長(zhǎng)過(guò)寬,因而導(dǎo)致插值計(jì)算誤差過(guò)大。本文以斜拉懸索橋洞庭湖二橋方案橋(簡(jiǎn)稱(chēng)洞庭湖二橋)為例開(kāi)展附加攻角效應(yīng)研究。
由于橋梁結(jié)構(gòu)在顫振前后始終作用靜風(fēng)荷載,顫振發(fā)生前有小于顫振臨界風(fēng)速的靜風(fēng)荷載。在其作用下結(jié)構(gòu)會(huì)發(fā)生幾何變形,進(jìn)而導(dǎo)致主梁攻角發(fā)生改變,見(jiàn)圖1,其中θ0為初始攻角;θ為在橋面施加靜風(fēng)荷載U后結(jié)構(gòu)的有效攻角;α為靜風(fēng)荷載引起結(jié)構(gòu)變形的附加攻角。
圖1 附加攻角示意圖Fig.1 Schematic additional angle of attack
為在數(shù)值計(jì)算中有效評(píng)估附加攻角對(duì)顫振影響,需用含攻角信息的氣動(dòng)導(dǎo)數(shù)反應(yīng)氣動(dòng)力。在有限元計(jì)算中考慮靜風(fēng)荷載對(duì)附加攻角影響需采用內(nèi)外兩重迭代方法,引入松弛因子易于快速得到收斂解,本文中松弛因子取0.4。靜風(fēng)荷載有限元理論計(jì)算見(jiàn)文獻(xiàn)[9]。洞庭湖二橋主梁斷面見(jiàn)圖2,節(jié)段模型縮尺比1:80,試驗(yàn)獲得風(fēng)軸坐標(biāo)系下三分力系數(shù)見(jiàn)圖3。
圖2 洞庭湖二橋成橋狀態(tài)模型斷面Fig.2 Completed model section of Dongting lake bridge
圖3 洞庭湖二橋風(fēng)軸三分力系數(shù)Fig.3 Third axis wind force coefficient of Dongting lake bridge
在已知節(jié)段模型三分力系數(shù)前提下,由于在不同風(fēng)速下靜力平衡時(shí)阻尼力不起作用,故可通過(guò)理論計(jì)算獲得節(jié)段模型的附加攻角,即
式中:Kt為模型抗扭剛度;θ為附加攻角;α為實(shí)際攻角;B,L分別為模型寬度及長(zhǎng)度。
由式(1)可知自由振動(dòng)識(shí)別的氣動(dòng)導(dǎo)數(shù)本身含附加攻角效應(yīng)影響,若在此基礎(chǔ)上插值計(jì)算附加攻角對(duì)應(yīng)的氣動(dòng)導(dǎo)數(shù)則會(huì)有偏差。而對(duì)彈性懸掛節(jié)段模型進(jìn)行氣動(dòng)導(dǎo)數(shù)識(shí)別時(shí)所給模型的初始激勵(lì)有較大人為因素,難以控制,故初始激勵(lì)影響、造成附加攻角變化及附加攻角影響會(huì)極大降低自由振動(dòng)識(shí)別氣動(dòng)導(dǎo)數(shù)的準(zhǔn)確性。此時(shí)應(yīng)選用強(qiáng)迫振動(dòng)法以克服自由振動(dòng)法中存在的靜風(fēng)附加攻角問(wèn)題[10-12],并以攻角變化1°為一個(gè)步長(zhǎng)進(jìn)行氣動(dòng)導(dǎo)數(shù)識(shí)別,可降低不同攻角氣動(dòng)導(dǎo)數(shù)插值的誤差。只有在有限元數(shù)值計(jì)算中考慮附加攻角影響才能有效計(jì)算橋梁結(jié)構(gòu)的顫振臨界風(fēng)速。
本文以主跨徑1 800 m的洞庭湖二橋?yàn)檠芯繉?duì)象,在湖南大學(xué)-Ⅱ號(hào)風(fēng)洞低速段進(jìn)行-3°,-2°,-1°,0°,+1°+2°,+3°,+4°計(jì)8個(gè)工況的強(qiáng)迫振動(dòng)氣動(dòng)導(dǎo)數(shù)識(shí)別試驗(yàn)。具體參數(shù)見(jiàn)表1。
表1 附加攻角強(qiáng)迫振動(dòng)試驗(yàn)參數(shù)Tab.1 Additional angle of attack for forced vibration test parameters
圖4 成橋狀態(tài)節(jié)段模型強(qiáng)迫振動(dòng)試驗(yàn)Fig.4 Completed bridge section model forced vibration tests
經(jīng)強(qiáng)迫振動(dòng)試驗(yàn)識(shí)別洞庭湖二橋斷面在8個(gè)不同攻角下的氣動(dòng)導(dǎo)數(shù),振動(dòng)形式為三自由度耦合振動(dòng),成橋狀態(tài)節(jié)段模型強(qiáng)迫振動(dòng)試驗(yàn)見(jiàn)圖4。圖5為不同攻角在折減風(fēng)速為9.85時(shí)A的數(shù)值變化。由圖5看出,隨攻角由負(fù)變正A2值逐漸變大,說(shuō)明攻角越大斷面流線性能越差。圖中虛線表示若在0°、+3°,0°、-3°,0°、+4°之間繼續(xù)用線性差值法,A值則會(huì)產(chǎn)生較大誤差,從而影響顫振分析。H及A(i=14)隨攻角變化對(duì)比見(jiàn)圖6,將不同攻角下同一氣動(dòng)導(dǎo)數(shù)值用二元插值擬合成一個(gè)曲面見(jiàn)圖7,并編制計(jì)算程序,只需獲取某一有效攻角值即可自動(dòng)求得所有氣動(dòng)導(dǎo)數(shù)值。由圖6、圖7看出,H及A(i=14)隨攻角由負(fù)變正均有一定規(guī)律性:低折減風(fēng)速下氣動(dòng)導(dǎo)數(shù)變化不明顯,隨折減風(fēng)速增大,各不同攻角下氣動(dòng)導(dǎo)數(shù)差值較明顯,A,A,A,H隨攻角由負(fù)變正氣動(dòng)導(dǎo)數(shù)值逐漸變小,A,H隨攻角由負(fù)變正氣動(dòng)導(dǎo)數(shù)值逐漸變大。而量級(jí)較小的A隨攻角變化也體現(xiàn)出較好的規(guī)律性,說(shuō)明強(qiáng)迫振動(dòng)試驗(yàn)精度能得到有效保障。
圖5 不同攻角A2值Fig.5 Different A2values of the angle of attack
圖6 不同攻角下洞庭湖二橋氣動(dòng)導(dǎo)數(shù)對(duì)比Fig.6 Different angle of attack aerodynamic derivatives contrast of Dongting Lake bridge
岳陽(yáng)洞庭湖二橋方案橋?yàn)樾崩瓚宜鲄f(xié)作體系,跨徑為310 m+1800 m+310 m。兩310 m邊跨為雙索面斜拉區(qū),主梁用混凝土箱梁,斜拉索間距12 m。主跨1800 m采用斜拉-懸索協(xié)作體系,懸吊區(qū)長(zhǎng)1168 m,斜拉區(qū)長(zhǎng)度388 m,拉吊結(jié)合區(qū)長(zhǎng)72 m,橋型布置見(jiàn)圖8。
靜風(fēng)荷載對(duì)顫振臨界風(fēng)速影響主要表現(xiàn)為:①對(duì)結(jié)構(gòu)動(dòng)力特性產(chǎn)生影響。在基于ANSYS進(jìn)行顫振分析時(shí)需選用有預(yù)應(yīng)力的模態(tài)分析求解器,有效計(jì)入靜風(fēng)荷載及結(jié)構(gòu)自重對(duì)動(dòng)力特性影響;②主梁發(fā)生扭轉(zhuǎn)變形時(shí)產(chǎn)生的附加攻角必改變風(fēng)橋的流固耦合機(jī)制,影響顫振性能。
圖7 不同攻角下氣動(dòng)導(dǎo)數(shù)擬合曲面Fig.7 Fitting surface of different angles of attack aerodynamic derivatives
圖8 洞庭湖二橋橋型布置Fig.8 Type layout of Dongting lake bridge
為在ANSYS全模態(tài)顫振分析中有效考慮附加攻角對(duì)顫振性能影響[13-15],本文利用ANSYS中TABLE表的行、列、面三維數(shù)組功能存儲(chǔ)不同攻角氣動(dòng)導(dǎo)數(shù)。TABLE表每個(gè)面存儲(chǔ)一個(gè)攻角氣動(dòng)導(dǎo)數(shù),每行存儲(chǔ)一個(gè)折減風(fēng)速對(duì)應(yīng)不同氣動(dòng)導(dǎo)數(shù)。將不同攻角定義為面的下標(biāo),在獲得每一特定風(fēng)速對(duì)應(yīng)的附加攻角及折減風(fēng)速時(shí)即可用TABLE表的線性插值功能自動(dòng)獲得任意有效攻角對(duì)應(yīng)的氣動(dòng)導(dǎo)數(shù),程序?qū)崿F(xiàn)非常方便。TABLE表具體設(shè)置見(jiàn)圖9,其中“ANGLE”對(duì)應(yīng)的第一行為面的下標(biāo)即有效攻角?!癢IND”對(duì)應(yīng)的第一列為折減風(fēng)速。洞庭湖二橋是否考慮附加攻角效應(yīng)的顫振臨界風(fēng)速、顫振頻率對(duì)比見(jiàn)表2。由表2看出,由于0°攻角在顫振臨界風(fēng)速前的附加攻角較小,由附加攻角效應(yīng)引起的顫振性能改變不大。盡管+3°攻角、0°攻角在不考慮附加攻角時(shí)的顫振臨界風(fēng)速基本相等,但由于橋梁斷面在+3°攻角時(shí)對(duì)應(yīng)的升力矩系數(shù)較大,引起的附加攻角亦較大,對(duì)顫振臨界風(fēng)速改變較顯著。
表2 附加攻角效應(yīng)顫振分析結(jié)果對(duì)比Tab.2 The results comparing of additional effects of angle of attack flutter analysis
圖10、圖11分別為0°及+3°兩攻角在計(jì)及附加攻角效應(yīng)時(shí)的顫振形態(tài)。由兩圖看出,兩攻角的顫振形態(tài)較接近,為彎扭耦合振型。對(duì)該類(lèi)橋梁斷面形式,附加攻角起到降低顫振臨界風(fēng)速作用,因此在橋梁抗風(fēng)設(shè)計(jì)中需充分考慮附加攻角對(duì)顫振影響,否則會(huì)得到偏危險(xiǎn)結(jié)論。
圖9 ANSYS三維數(shù)據(jù)表Fig.9 Three-dimensional data table of ANSYS
圖100 °攻角顫振形態(tài)圖Fig.10 0°Angle of attack flutter modality map
圖11 +3°攻角顫振形態(tài)圖Fig.11+3°Angle of attack flutter modality map
(1)利用強(qiáng)迫振動(dòng)裝置識(shí)別由-3°~+4°攻角、步長(zhǎng)為1°的洞庭湖二橋主梁斷面氣動(dòng)導(dǎo)數(shù)。直接用兩間距過(guò)大攻角插值計(jì)算所得有效攻角氣動(dòng)導(dǎo)數(shù)會(huì)有較大誤差。
(2)用二元插值將不同攻角下同一氣動(dòng)導(dǎo)數(shù)值擬合成一個(gè)曲面,只需獲取某有效攻角的具體數(shù)值即可自動(dòng)求得所有氣動(dòng)導(dǎo)數(shù)值。H,A(i=14)隨攻角由負(fù)變正時(shí)在低折減風(fēng)速下氣動(dòng)導(dǎo)數(shù)變化不明顯;折減風(fēng)速增大A,A,A,H隨攻角由負(fù)變正氣動(dòng)導(dǎo)數(shù)值逐漸變小;A,H隨攻角由負(fù)變正氣動(dòng)導(dǎo)數(shù)值逐漸變大。對(duì)量級(jí)較小的A隨攻角變化的規(guī)律性較好。
(3)在ANSYS中用三維TABLE表存儲(chǔ)不同攻角的氣動(dòng)導(dǎo)數(shù)值,能自動(dòng)計(jì)入附加攻角效應(yīng)導(dǎo)致的氣動(dòng)力非線性對(duì)顫振穩(wěn)定性影響。附加攻角能降低顫振臨界風(fēng)速作用,橋梁抗風(fēng)設(shè)計(jì)中應(yīng)充分考慮附加攻角對(duì)顫振影響。
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Influence of static wind additive attack angle on flutter performance of bridges
OUYANG Ke-jian1,CHEN Zheng-qing2
(1.State Grid Hunan Electric Power Corporation Research Institute,Changsha 410007,China; 2.Wind Engineering Research Center,Hunan University,Changsha 410082,China)
Aerodynamic derivatives of Dongting Lake bridge girder sections were identified by forced vibration in wind tunnel,with the angle of attack changing in step of 1°from-3°to+4°.The aerodynamic derivatives were fitted to form a three-dimensional surface made up by reduced velocity,angle of attack and aerodynamic derivatives.Only if a specific value of the effective angle of attack is given,all aerodynamic derivatives can be automatically obtained.The data of aerodynamic derivatives were stored in a three-dimensional TABLE in ANSYS,the effect of additional angle of attack on flutter stability was naturally concerned.A full-mode flutter analysis indicate that the additional angle of attack may decline the critical flutter speed of typical bridges and the influenced extent is according to the type of bridges.
long-span bridge;flutter;additive attack angle;forced vibration;ANSYS
U446.1
A
10.13465/j.cnki.jvs.2015.02.008
國(guó)家自然科學(xué)基金重大研究計(jì)劃(重大建筑與橋梁強(qiáng)/臺(tái)風(fēng)災(zāi)變的集成研究91215303)
2013-11-01修改稿收到日期:2014-01-28
歐陽(yáng)克儉男,博士,工程師,1981年9月生郵箱:ouykj@126.com