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1、JournalofMechanicalStrength2006,28(5):674～679X利用传递矩阵法对阶梯悬臂梁的裂纹参数识别IDENTIFICATIONOFCRACKPARAMETERSINASTEPPEDCANTILEVERBEAMUSINGTRANSFERMATRIXMETHOD王志华XX1 张伟伟1 赵勇刚1 马宏伟1,2(1.太原理工大学应用力学研究所,太原030024)(2.暨南大学理工学院,广州510632)1111,2WANGZhiHuaZHANGWeiWeiZHAOYongGangMAHongWei(1.In
2、stituteofAppliedMechanics,TaiyuanUniversityofTechnology,Taiyuan030024,China)(2.CollegeofScience&Engineering,JinanUniversity,Guangzhou510632,China)摘要 基于Bernoulli2Euler梁振动理论,以等效弹簧模拟裂纹引起的局部软化效应,利用传递矩阵法推导阶梯悬臂梁振动频率的特征方程,对于含多个裂纹以及复杂边界条件的阶梯梁,仅需求解4×4的行列式即可获得相应的频率特征方程。直接利用该特征方程,提
3、出两种有效估计裂纹参数的方法———等值线法和目标函数最小化法,并应用两段阶梯悬臂梁的数值算例说明方法的有效性。算例结果表明,只需结构前三阶频率即可识别裂纹位置和深度。应用“零设置”可减小计算频率与理论频率不相等对识别结果的影响。等值线法可以直观给出裂纹位置和裂纹深度参数,目标函数最小化法可给出最优的裂纹参数结果,并且该方法可推广应用到含多个裂纹复杂梁(如非完全固支、弹性支撑等)结构的裂纹参数识别中。关键词 振动诊断 裂纹参数识别 阶梯悬臂梁 传递矩阵法中图分类号 TH165.3TP206.3TN911.6O235AbstractThep
4、roblemofcrackparameteridentificationinasteppedcantileverbeamstudyed.Thelocaleffectof“softening”atthecracklocationcanbesimulatedbyanequivalentspringconnectingthetwosegmentsofthebeam.CombinedwiththeBernoulli2Eulertheoryforbeams,thecharacteristicequationofasteppedcantilever
5、beammodelisderivedbyusingtransfermatrixmethod.Theresultedfrequencyequationofacrackedbeamisgenerallydependsontheboundaryconditionsincludingthecloser(elastic)endsupportsandcanbeformulatedanalyticallybyusingsymboliccodes.Theprocedureproposedsimplyoperatesonsomefourthorderde
6、terminantssothatthecomputationaleffortsforcalculatingnaturalfrequenciesaresignificantlyreduced.Basedonthischaracteristicequation,twoidentificationmethods,thecontourcurvemethodandtheminimizingobjectfunctionone,aredevelopedtoidentifythelocationandthedepthofthecrack,whichon
7、lyrequiresthefirstthreetestednaturalfrequencies.Theproposedapproachesareverifiedthroughanexamplewithasin2gle2steppedcantileverbeam.Itisshownthatthelocationandthedepthofthecrackcanbeworkedoutaslongasthefirstthreenaturalfrequenciesareknown.Itisalsoshownthatmakinga“zerosett
8、ing”mayofferatremendousimprovementinidentificationofcrackpa2rameters.Moreover,theminimizingobjectfuncti
