Article(id=1242116897873924974, tenantId=1146029695717560320, journalId=1146031591421210625, issueId=1242116867230339865, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1226851200000, receivedDateStr=2008-11-17, revisedDate=1230998400000, revisedDateStr=2009-01-04, acceptedDate=null, acceptedDateStr=null, onlineDate=1233072000000, onlineDateStr=2009-01-28, pubDate=1233072000000, pubDateStr=2009-01-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1233072000000, onlineIssueDateStr=2009-01-28, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774073345863, creator=sys-migrate, updateTime=1774073345863, updator=sys-migrate, issue=Issue{id=1242116867230339865, tenantId=1146029695717560320, journalId=1146031591421210625, year='2009', volume='27', issue='0902', pageStart='3', pageEnd='126', issueExtLink='null', onlineDate='null', pubDate='1233072000000', pubDateStr='2009-01-28', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=3, issueType=-1, specialIssue=null, createTime=1774073338558, creator='sys-migrate', updateTime=1774073338558, updator='sys-migrate', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=53, endPage=61, ext={EN=ArticleExt(id=1242116905109099403, articleId=1242116897873924974, tenantId=1146029695717560320, journalId=1146031591421210625, language=EN, title=Non-linear Dynamics and Control of Flutter of Airfoil, columnId=1242116903087440448, journalTitle=Science & Technology Review, columnName=Spescial Issues, runingTitle=null, highlight=null, articleAbstract=This paper presents our studies on the flutter of airfoil by using modern nonlinear dynamics and control methods, including mainly the following three parts. (1) Studies on Hopf bifurcation flutter of airfoil in a supersonic flow field using the normal form direct method. An analysis of the obtained coefficients of the normal form indicates that the Hopf bifurcation can change from super-critical type to sub-critical type, consequently, the flutter instability changes from "benign" type to "catastrophic" type, as the flight Mach number increases. (2) The wash-out filter technique is used to control the flutter of a two dimensional airfoil with cubic non-linearity in an incompressible flow. For the introduced wash-out filter controller, the linear control gain of the controller is determined according to the Hopf bifurcation condition and the non-linear one is determined based on a relationship between the bifurcation type and the parameters of the normal form obtained by the normal form direct method. As a result the sub-critical Hopf bifurcation can be transformed to the super-critical one. (3) Influence of initial conditions on flutter of airfoil with bilinear structural nonlinearity is investigated by the improved cell mapping technique. Different types of motions, including damped stable motion, limit cycle oscillation, complicated periodic motion, chaotic motion and divergent flutter are determined as a function of initial conditions., authors=null, authorsList=null, authorCompany=null, correspAuthors=null, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=3WaPrvJcHNkZN3QtMrRIXg==, pdfFileSize=1782195, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1242116902508630916, articleId=1242116897873924974, tenantId=1146029695717560320, journalId=1146031591421210625, language=CN, title=机翼颤振的非线性动力学和控制研究, columnId=1242116902361830275, journalTitle=科技导报, columnName=专题论文, runingTitle=null, highlight=null, articleAbstract=介绍应用现代非线性动力学和控制的理论和方法对机翼颤振问题进行的一些研究，主要包括3部分：① 针对用活塞理论建立的（高）超音速流中机翼的颤振方程，首先进行稳定性分析，证明Hopf分岔导致系统颤振失稳。然后应用规范型直接法推导出Hopf分岔的规范型，分析其系数表明，随着飞行马赫数提高，Hopf分岔由超临界形式变成亚临界形式，对结构的危害性增大；② 针对不可压缩流中具有立方非线性俯仰刚度的二元机翼颤振，应用wash-out滤波器技术进行主动控制。对于引入的wash-out滤波控制器，先按Hopf分岔条件确定线性控制增益，再用规范型直接法得到受控系统的规范型，由分岔类型与规范型系数的关系确定非线性控制增益，从而可以将危害性较大的亚临界Hopf分岔变为危害性较小的超临界Hopf分岔；③ 基于空间Poincaré截面并引入轨迹追踪技术，改进胞映射方法，分析初始条件对含双线性结构刚度因素的机翼颤振的影响。结果显示，初始条件对系统动力学行为有着很大的影响。当两段刚度之比小于某临界值时，不同的初始条件会导致平衡点、极限环振动、复杂的周期运动、混沌和发散运动等不同的运动形式。, authors=丁千,陈予恕, authorsList=丁千;陈予恕, authorCompany=天津大学力学系, correspAuthors=null, authorNote=null, correspAuthorsNote=丁千, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=tfsZhiNGJzya2c08OdQyNA==, pdfFileSize=1782195, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, 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