On the use of damped updated FE model for dynamic design

Model updating techniques are used to update the finite element model of a structure, so that updated model predicts the dynamics of a structure more accurately. The application of such an updated model in dynamic design demands that it also predicts the effects of structural modifications with a reasonable accuracy. Most of the model updating techniques neglect damping and so these updated models cannot be used for predicting amplitudes of vibration at resonance and antiresonance frequencies. This paper deals with updating of the finite element model using the FRF data with damping identification using complex modal data and its subsequent use for predicting the effects of structure modifications. The updated model is obtained in two steps. In the first step, mass and stiffness matrices are updated using FRF-based model updating method. In the second step, damping is identified using updated mass and stiffness matrices, which are obtained in first step. Structural modifications in terms of mass and beam modifications are then introduced to evaluate the updated model for its usefulness in dynamic design.     

步兵战车车体结构有限元模型修正

针对某型步兵战车整车刚柔耦合发射动力学中柔性车体有限元模型精度低的问题,基于模态试验数据,应用支持向量机响应面模型修正理论对车体结构有限元模型进行了修正。应用ANSYS有限元分析软件对车体结构进行模态分析,提取前6阶模态的固有频率和振型。为验证模型,设计了模态试验方案,实测了车体结构的模态信息。基于有限元模型数据与实测数据的相对误差,采用支持向量机响应面模型修正方法对车体结构弹性模量和密度进行修正。模型确认结果和动力学模型应用结果表明,修正后的车体有限元模型精度有了大幅度提高,能更加真实地反映车体的结构特征,为射击精度分析提供了准确的模型基础。     

基于灵敏度分析的刀形天线有限元模型修正

准确可靠的有限元模型是结构动态特性分析、设计改进的基础,文中利用模态试验得到的模态参数对某刀形天线进行有限元模型修正.首先建立天线结构的参数化模型,然后通过灵敏度分析选择合适的设计参数作为后续优化对象,利用计算与试验的模态频率之间的相对误差构造加权的优化目标函数,最后应用1阶优化方法修正结构的有限元模型.修正后有限元模型的模态频率最大相对误差降低至10%以内,模态置信度(MAC)均大于0.8.该修正模型可用于后续的动力学分析.     

信息融合与响应面联合的渡槽结构模型修正

针对大型渡槽损伤诊断研究中有限元模型精度问题,提出一种基于信息融合与响应面法(response surface method,简称RSM)的有限元模型修正方法,能够兼顾优化目标和参数优化两个环节。以某灌区渡槽为研究对象,建立初始有限元模型,采用试验设计方法构建待修正参数与特征频率的设计空间,经过参数筛选后建立设计样本的响应面模型;引入自适应噪声的完整集成经验模态分解和奇异值分解(complete ensemble empirical mode decomposition with adaptive noise-singular value decompose,简称CEEMDAN-SVD)降噪方法联合方差贡献率数据级融合算法,对正常运行工况下覆盖三跨槽身振测信号进行多通道融合处理以获取完整有效的实测频率,并以此为目标值对响应面模型进行最优化求解,实现多跨渡槽有限元模型的参数优化。结果表明,修正后的有限元模型计算出的频率与实测频率吻合较好,最大误差为-4.38%,有效解决了大型渡槽结构有限元模型的精度问题,为后续结构损伤诊断等仿真研究提供基准模型。     

基于MIGA的结构模型修正及其应用

为了寻找到优化域内的全局最优解,获得更准确的结构有限元模型,提出将多岛遗传算法(MIGA)应用到模型修正中,以响应面替代模型简化有限元计算分析,以有限元理论分析模态与结构实测模态残差为目标优化函数.在参数灵敏度分析的基础上,建立桥梁结构动力响应、单元弹性模量、密度以及截面面积的优化数学模型,采用MIGA作为优化策略,对桥梁结构进行了动力测试和模型修正.结果表明,模型修正效果良好,可真实反映结构的动力学特性,证明了该方法的有效性和可行性.     

基于近似似然的频响函数不确定性模型修正

贝叶斯模型修正框架下，以频响函数作为目标，提出了一种使用近似似然函数的不确定性模型修正方法。相比于模态参数，频响函数包含了结构更加充分的信息，用于结构动力学模型修正时有诸多优点，但现有的不确定性模型修正方法并不能很好地实现将频响函数作为目标进行修正。针对此问题，介绍了频响函数和贝叶斯框架下的不确定性模型修正理论，基于近似贝叶斯计算提出了一种近似似然函数，可适用于频响函数作为目标进行不确定性修正。将提出的似然函数应用到三自由度数值和H型非对称梁的有限元模型修正算例中，并结合DREAM算法对不确定性参数进行识别。研究结果表明：修正后参数的上、下限与目标值相差无几，修正后模型的频响函数与目标值几乎重合，在一定噪声水平下仍具有较好的修正效果，验证了所提方法的有效性。     

使用有效模态质量和遗传算法的有限元模型修正

提出将模态频率和有效模态质量构造的残差作为遗传算法的目标函数进行结构动力学有限元模型修正的方法。有效模态质量不但可以为结构动力学响应分析提供一种判断模态贡献程度的方法,而且能够为有限元模型修正提供更多的信息量。介绍了有效模态质量的概念和基于遗传算法的结构动力学模型修正理论,在此基础上采用仿真算例验证了所提出方法的正确性和有效性。仿真结果显示,模型修正后参数最大误差为-0.062%,不管是在修正频段内还是修正频段外,频率和有效模态质量的均方误差都小于0.025%。研究表明,使用有效模态质量和遗传算法的结构动力学有限元模型修正是有效可行的。     

考虑模型偏差的结构动力学模型修正

针对结构有限元模型修正后仍可能存在模型偏差的问题,提出用待修正参数的不确定性来表征模型偏差的有限元模型修正方法。首先,基于响应面方法识别得到待修正参数的最优值,并通过计算结果与试验结果比较获得模型偏差;然后,基于响应面模型并结合灵敏度分析计算得到模型偏差对待修正参数的影响,从而得到考虑模型偏差后待修正参数的区间;最后,通过一个悬臂梁工程实例的模型修正,验证了笔者所提出方法的可行性。结果表明,考虑模型偏差的修正可以提高模型可靠性。     

基于ANSYS的有限元模型修正软件实现

为了提高有限元模型修正的效率与准确性,根据有限元模型修正理论在ANSYS平台上编写了适用于大型有限元模型并且抗噪性、稳健性较好的有限元模型修正算法;并基于Matlab开发了便于科研工作者使用的有限元模型修正软件。利用实测数据对某型航空发动机螺栓连接结构进行了模型修正,验证了所编写的模型修正软件的有效性及实用性。     

Comparative study of damped FE model updating methods

Most of finite element (FE) model updating techniques do not employ damping matrices and hence, cannot be used for accurate prediction of complex frequency response functions (FRFs) and complex mode shapes. In this paper, a detailed comparison of two approaches of obtaining damped FE model updating methods are evaluated with the objective that the FRFs obtained from damped updated FE models is able to predict the measured FRFs accurately. In the first method, damped updating FE model is obtained by complex parameter-based updating procedure, which is a single-step procedure. In the second method, damped updated model is obtained by the FE model updating with damping identification, which is a two-step procedure. In the first step, mass and stiffness matrices are updated and in the second step, damping matrix is identified using updated mass and stiffness matrices, which are obtained in the previous step. The effectiveness of both methods is evaluated by numerical examples as well as by actual experimental data. Firstly, a study is performed using a numerical simulation based on fixed–fixed beam structure with non-proportional viscous damping model. The numerical study is followed by a case involving actual measured data for the case of F-shaped test structure. The updated results have shown that the complex parameter-based FE model updating procedure gives better matching of complex FRFs with the experimental data.     

基于频响函数 Neumann 级数展开的有限元模型修正

针对有限元模型修正中测试自由度不完备、求解不适定的问题,提出了一种基于频响函数Neumann级数展开的模型修正方法。首先,利用测试和有限元分析模态数据构造完整的实测频响函数。然后,根据Neumann级数展开式建立实测频响函数与有限元模型频响函数之间的关系式,以此构建模型修正目标函数。最后,采用改进鲸鱼优化算法求解目标函数获取修正结果。通过平面桁架数值算例表明,该方法具有较强的噪声鲁棒性,模型修正精度较好,15%噪声时修正后的平均相对误差不超过1%。利用4层剪力框架结构测试算例进一步验证所提方法,结果表明,修正后的模型能反映结构真实状况。     

Studies in dynamic design of drilling machine using updated finite element models

The aim of the present work is to develop updated FE models of a drilling machine using analytical and experimental results. These updated FE models have been used to predict the effect of structural dynamic modifications on vibration characteristics of the drilling machine. Two studies have been carried out on the machine. In the first study, modal tests have been carried out on a drilling machine using instrumented impact hammer. Modal identification has been done using global method of modal identification. For analytical FE modeling of the machine, a computer program has been developed. The results obtained using FEM, have been correlated with the experimental ones using mode shape comparison and MAC values. Analytical FE model has been updated, with the help of a program, which has been developed using direct methods of model updating. In the second study, modal testing has been carried out using random noise generator and modal exciter. Global method has been used for modal identification. Analytical FE modeling has been done using I-DEAS software. Correlation of FE results with the experimental ones has been carried out using FEMtools software. Updating of the analytical FE model has also been done using the above software, based on an indirect technique viz. sensitivity based parameter estimation technique. The updated FE models, obtained from both the studies have been used for structural dynamic modifications (SDM), for the purpose of dynamic design and the results of SDM predictions are seen to be reasonably satisfactory.     

基于模态综合技术的结构有限元模型修正

由于结构的动力分析需要大量的计算时间和占用大量的计算机内存,常规的数值迭代计算方法难以实现,提出了基于模态综合技术的模型修正方法。该方法首先得到缩减后结构模型的频率与振型,并将该振型转换为缩减前模型物理坐标下的振型。然后,用缩减后模型的频率和转换后的振型,共同构成模型修正的优化目标函数,进而通过优化求解实现结构的模型修正。该方法既保证了计算精度又提高了模型修正的计算效率,使大型复杂结构的模型修正成为可能。最后,对某吊杆拱桥模型进行了动态测试和模型修正,验证了该算法的有效性。     

DYNAMIC FINITE ELEMENT MODEL UPDATING BASED ON GLOBAL INFORMATION OF STRUCTURES

Finite element model updating method based on global information is proposed. Prior investigation upon design space of structural parameters is performed before updating using statistic analysis, including parameter screening using variance analysis and response surface fitting using regression analysis. The parameter screening method selects the design parameters considering the result of hypothesis testing, which is a kind of global information. Meanwhile, the traditional updating method considers local sensitivity which only gives the information at sole point in the design space. Response surface fitting constructs a close-form multinomial which describes the relationship between concerned structural feature and selected updating parameters. It is an approximation to finite element models(FEM) and used as a substitution in the updating iterations. The presented updating method can be applied without the restriction of linear assumption. In addition, there is no data exchange between the updating prog     

RESULTS OBTAINED BY MINIMISING NATURAL-FREQUENCY ERRORS AND USING PHYSICAL REASONING

A finite element model of the GARTEUR SM-AG19 test structure is updated. The philosophy applied in selecting the updating parameters is based on physical understanding, scrutiny of the mode shapes and sensitivity calculations. The ‘corrected’ model is shown not only to accurately reproduce test data used in the updating process, but also to provide results in agreement with test data (not used for updating) from the modified structure.     

Identification of prestress force from measured structural responses

A method for the identification of prestress force of a prestressed concrete bridge deck is presented using the measured structural dynamic responses. A Euler–Bernoulli beam finite element model is used to represent the bridge deck, and the prestress force is modelled as the axial prestress force in each beam element. The state-space approach is used to calculate the dynamic responses of the structure and the sensitivities of dynamic responses with respect to the structural parameters, such as the prestress force, flexural rigidity, etc. The prestress force in each beam element is taken to be a system parameter, and it is expressed explicitly in the system equation for forward analysis. The prestress force in each element is identified using a sensitivity-based finite element model updating method in the inverse analysis. Data obtained from a single or multiple accelerometers or strain gauges are used in the identification. Both sinusoidal and impulsive excitations are illustrated to give very good results. Two numerical simulations are presented to illustrate the effectiveness and robustness of the proposed method. Laboratory work on an axially prestressed concrete beam is also included as a practical application.     

RESULTS OBTAINED BY MINIMISING NATURAL FREQUENCY AND MAC-VALUE ERRORS OF A BEAM MODEL

This paper reports the procedure followed by the ‘LTAS-Vibrations et Identification des Structures’ research group to generate a low-order finite element (FE) model of the GARTEUR SM-AG19 structure. The model is made of beam elements, local inertia and rigid body elements. The philosophy of the updating method is first based on the correlation of the experimental data with the results of the FE model and on the localisation of errors in the model. Updating parameters are then selected using eigenvalue sensitivity and model error localisation analyses. After updating, the quality of the FE model is assessed in terms of accuracy of the response prediction to structural modifications.     

机床—主轴耦合系统动力学建模与模型修正

复杂精密零件的加工对机床装备的性能不断提出新的挑战。为了保证零件加工精度,有必要在设计阶段对机床整机的动态特性进行精确预测和评估。以机床主轴系统为研究对象,介绍一种机床—主轴系统耦合动力学模型,并指出该模型中存在结合面动态特性参数的辨识问题。为了修正该耦合模型,提出一种基于频率响应函数的有限元模型修正技术。采用包含平动自由度(Degree of freedom,DOF),转动DOF以及平动与转动耦合DOF的刚度矩阵来描述结合面的动态特性,通过测量结合面处的动态响应数据,辨识出高速主轴与机床之间结合面的刚度参数,从而达到模型修正的目的。试验结果表明,修正后的机床—主轴耦合模型反映出了机床结构对主轴动态特性的影响,能较好地预测主轴安装到机床上以后的动态特性,从而为高性能机床的数字化设计与制造提供理论依据。     

A constant scanning LDV technique for cylindrical structures: Simulation and measurement

The reliance of the aerospace industry on finite element models during the design of new products requires the best possible models for the prediction of the dynamic behaviour and so it is usually necessary to validate an original model using some additional reference data as the basis—usually data measured on a test structure. Finite element model updating can lead to the required accuracy, and while attempts are under way to minimise the required experimental testing involved in the process, measurements still are an integral part of the procedure. To improve the validation process, a major aim of current experimental research is to provide a more complete set of data from a single experiment in a shorter amount of time, so as to increase the overall efficiency of the updating routine. To this end, a new continuously scanning laser Doppler vibrometery measurement technique is presented for application to cylindrical structures. It allows the measurement of the dynamic behaviour of a cylindrical structure with a previously unachievable spatial resolution in a much shorter time than conventional measurement methods. The introduced method is evaluated through a detailed simulation in order to investigate its robustness and to ensure data quality, and the results from a proof-of-concept test rig are presented.     

自适应多重TMD在大跨楼板结构减振中的应用

双轴振镜系统是扫描式激光多普勒测振仪中控制激光束运动的核心部件。通过双轴振镜系统中X，Y振镜的空间位置关系及光学反射原理，建立了激光束方向与X，Y振镜偏转角度之间的关系及其数学模型， 并进一步基于多项式拟合算法实现了激光点从振镜系统坐标系到实测结构坐标系的坐标变换，从而可高精度控制扫描激光的姿态。 同时，利用高清摄像头将测试坐标系转换到屏幕坐标系，提高了该方法的实际操作性。最后，以某型压气机叶片为例对该方法进行了验证，结果表明本方法对实现激光在实测结构表面任意测点的精确位置控制提供了理论基础，具有较好的指导作用。