【作者】 李剑；

【导师】 洪嘉振；

【作者基本信息】 上海交通大学 ， 一般力学， 2007， 硕士

【摘要】 本文基于实验数据对有限元模型修正的方法进行了研究。上个世纪70年代以来,有限元模型修正技术得到了迅速发展,并在工程领域广泛应用于改善有限元模型与实验数据的相关性、提高有限元模型的分析精度和可靠性。目前,模型修正的方法按修正对象可分为矩阵型修正法和参数型修正法。其中矩阵型修正法由于修正对象为有限元模型的系统矩阵而面临修正后物理含义模糊的问题;参数型修正法大多依赖于灵敏度分析的结果,而灵敏度分析常常对建模误差的位置做出错误判断,修改参数的合理性值得怀疑。因此,有限元模型修正的方法仍需进一步研究。目前,大多数参数型修改法主要面临以下三方面的问题:1、在实验未测的高阶部分,修正后的有限元模型与实验之间的相关性不能保证得到改善;2、修改的物理参数不一定符合测试对象物理特征;3、迭代计算效率较低,且存在发散的问题。通常,评价有限元模型修正效果的方法是分析有限元计算频率、模态与实验数据的相关性,本文根据模型修正的上述问题,认为在研究过程中需要增加两条验证标准:(1)用低阶实验数据修正后,不仅比较低阶数据上的相关性,还要比较“高阶”数据上的相关性;(2)需要对修改后参数的改变量进行物理意义上的考核,检查参数修改是否符合修正对象的物理特征。2006年,Hu等提出了一种参数型修改新方法:正交模型-正交模态(CMCM)法,该方法无需进行灵敏度分析且不需要进行迭代,具有较好的建模误差判断能力,计算效率较高。本文研究发现该方法在有限元模型与实验数据存在良好相关性时存在求解困难,甚至无法完成修正计算。对此,本文提出了一种改进的方法(ICMCM法)。通过若干典型数值实验比较了CMCM法、ICMCM法、矩阵型修正法和商业修正软件FEMtools的修正结果,验证了ICMCM的有效性。本文使用先进的激光测振系统对梁、板结构进行了振动实验,获得了高精度的实验数据,并以此比较ICMCM法和FEMtools软件的修正效果和修正结果。分析表明,本文提出的ICMCM可以有效提高有限元模型动态特性的计算精度,修改的参数符合实际对象物理特征。本文第一章介绍了模型修正的工程背景和意义,综述了迄今国内外模型修正领域的发展,提出了本文研究的目标和内容。第二章介绍了分析有限元模型可靠性的相关性分析方法,以及有限元模型与实验数据自由度匹配的方法。通过数值算例进行了比较和初步研究。第三章介绍了几种模型修正的方法,包括CMCM法、FEMtools软件,研究了CMCM法的缺陷并提出一种改进的ICMCM法。通过数值实验验证了ICMCM法的有效性。第四章介绍了先进的激光测振系统以及本文开发的修正程序。为基于实验数据进行模型修正做好了准备。第五章对梁、板结构进行了振动测试实验,并利用获得的实验数据比较了ICMCM法和FEMtools软件的修正效果。结果表明本文提出的ICMCM法可以有效提高有限元模型与实验数据的相关性,参数修正合理可靠,符合测试对象的物理特征。更多还原

【Abstract】 This paper focused on the investigation of finite element model updating based on measured modes.Finite element model updating has been developed rapidly since 2070s. Model updating is used to improve the correlation of FEM and measured data, amend the precision and reliability of results from FEM analysis. According to the object, model updating can be divided into two types: matrix type and parameter type. The matrix type came into the problem that the correction is vague; the parameter type mainly depends on the result of sensitivity analysis which may cause a wrong judgment of modeling errors. So, model updating is still a hotspot in research.Nowadays, most parametric model updating methods are facing those problems: 1. correlation between finite element model and experiment may not be improved in the unmeasured higher-order part; 2. modified parameters may not be fit with the measured object; 3. computational time for iterative is quite long, which may be not constringency.Usually, correlation between finite element model and test data is used to evaluate the reliability of finite element model, this investigation considering two more criterions: 1. a higher-order correlation is evaluated as well as lower-order part. 2. a physical meaning check of modified parameters needs to be considered.In 2006, Hu etc. proposed a parametric new method called CMCM, which needs no sensitivity analysis and no iterative. It finds the modeling errors correctly and has a high computational efficiency. A defect was found in this paper that CMCM method can’t finish updating with a numerical problem when the FE model has a good correlation with measured data. Then this paper developed a new method ICMCM based on CMCM. CMCM, ICMCM, some matrix type methods and the commercial model updating software FEMtools was compared in some numerical experiment. Result indicates that ICMCM method is effective and reliable.In this paper, the Laser Doppler Vibrometer is used to do vibration experiment with a beam and a plate, from which some sets of frequencies and modes were got in a high precision. ICMCM and FEMtools were compared using those test data. Result indicates that the ICMCM method can improve the correlation between FE model and measured data greatly and the parameters can be fixed reliable.In chapter 1, the engineering background of model updating is introduced, and the development in the field of model updating is discussed. The research aim and content are put forward.In chapter 2, correlation analysis methods for evaluating the reliability of FE model and freedom match is introduced. Numerical experiments are used to compare those methods.In chapter 3, some model updating methods are introduced including CMCM method and FEMtools software. The defect of CMCM method is investigated and an improvement named ICMCM method is proposed. Numerical experiments are used to compare those methods.In chapter 4, Laser Doppler Vibrometer and model updating codes based on ICMCM is introduced. It is prepared for model updating based on measured data.In chapter 5, vibration experiments for a beam and a plate are carried through. ICMCM and FEMtools are compared with measured data from those experiments. Results indicate that ICMCM method can greatly improve the correlation between FE model and measured data, the parameters are fixed reliable, considering the physical characters of test objects.更多还原