Operational mode-shape normalisation with a structural modification for small and light structures

When dealing with small and light structures, difficulties occur when measuring the modal parameters. The resonant frequencies are usually relatively high and therefore a wide frequency range is needed for the measurement. Furthermore, the mass that is added to the structure by the sensors causes structural modifications. To overcome these difficulties, an improved method using an operational modal analysis instead of an experimental modal analysis is proposed in this study. It is derived from the sensitivity-based operational mode-shape normalisation with a consideration of the mode-shape variation. The measurement of the excitation force is not needed, because the operational modal analysis is used and only two simultaneous response measurements at an unknown excitation are required. The proposed method includes the cancellation of the added mass, resulting in mode shapes and resonant frequencies of the unmodified structure. The numerical and experimental results on small and light structures are compared with the results of the experimental modal analysis. The comparison shows that the proposed approach allows measurements over a wide frequency range and increases the accuracy of the results compared to the sensitivity-based operational mode-shape normalisation and also compared to the particular experimental modal analysis method that was used in this study. The advantages of the proposed method can be seen whenever the mass that is added to the structure by the accelerometer is not negligible and therefore a variation of the mode shapes occurs.     

PREDICTION OF IMPACT AND HARMONIC FORCES ACTING ON ARBITRARY STRUCTURES: THEORETICAL FORMULATION

This work presents a new general approach in developing the force-prediction model. The two types of unknown forces dealt with in this study are the impact and the harmonic forces. Theoretical background of force-prediction model is extensively reviewed and categorised into two approaches, the direct and the optimisation approaches. Both approaches can also be further divided into the time- and the frequency-domain method. The structural response due to the unknown forces is then derived. The new approach, an optimisation approach, to predict the force magnitude and location simultaneously is developed for both time- and frequency-domain method. The implementation of the prediction model is also discussed. Special concerns about the applications to engineering problems are addressed.     

几种常用损伤动力指纹的适用性研究

通过讨论几种常用动力指纹的模态灵敏度,研究了它们的适用性。采用特征灵敏度分析技术,导出了频率、振型和模态柔度对结构参数的灵敏度计算表达式,在此基础上定义了模态加权指针来定量描述各阶模态的损伤动力指纹对结构损伤的灵敏度。通过典型模态稀疏和模态密集结构模型的数值模拟研究发现：对于模态稀疏的简单结构。低阶模态柔度对结构损伤较为敏感;对于模态密集的复杂结构。低阶频率、振型和模态柔度的损伤灵敏度均较差,而且模态柔度在低阶模态条件下远没有在高阶模态条件下对结构损伤敏感。     

基于Hilbert-Huang变换与理想带通滤波器的系统识别

针对经验模态分解存在模态混叠现象,提出基于Hilbert-Huang变换与理想带通滤波器的系统识别方法。该方法利用傅里叶变换得到结构加速度响应频响函数,粗略估计固有频率范围,通过半功率带宽法设计理想带通滤波器,定量化确定通带带宽,使信号在经过滤波器后频域内零相移,同时不改变其幅值谱。结构响应通过指定频带的理想带通滤波器产生若干窄带信号,利用经验模态分解获取结构模态响应,经Hilbert变换构造模态响应解析信号,并通过线性最小二乘拟合提取结构模态参数与物理参数。结果表明:半功率带宽法可实现带通滤波器频带的定量化设计,理想带通滤波器的零相移特点较好契合Hilbert-Huang变换用于系统识别的要求,两者结合可有效地解决模态混叠现象,减少虚假模态,大大提高结构系统识别精度。     

RESEARCH ON MODELING AND CHARACTERISTICS OF THE SPINDLE DYNAMIC COUPLING ABSORBERING SYSTEM OF A SUPER－PRECISION SURFACE GRINDING MACHINE

The bearing is described by constrain matrix, and the spindle system of a NC surface grinding machine is simplified as elastic-coupling beam, then modal synthesis method is used to establish the dynamic model of beam. Moreover, the response of the end of rotor is analyzed, and the natural frequency, principle mode and other dynamic characteristics of the coupling system are studied, the law of bearing stiffness to coupling frequency and amplitude of rotor is also found. Finally, according to the actual condition, a dynamic absorber is designed. The simulation and experimental results show that the amplitude of spindle can be declined effectively when the dynamic absorber is attached.     

Atomic force microscopy imaging using a tip-on-chip: opening the door to integrated near field nanotools

We describe in detail how atomic force microscopy (AFM) images can be routinely achieved with macroscopic silicon-based chips integrating mesoscopic tips, paving the way for the development of new near field devices combining AFM imaging with any kind of functionality integrated on a chip. The chips have been glued at the end of the free prong of 100 kHz quartz tuning forks mounted in Qplus configuration. Numerical simulations by modal analysis have been carried out to clarify the nature of the vibration modes observed in the experimental spectra. It is shown that two low frequency modes can be used to drive the system and scan the surface with a great stability in amplitude modulation as well as in frequency modulation AFM under ultrahigh vacuum. The AFM capabilities are demonstrated through a series of examples including phase and dissipation contrast imaging, force spectroscopy measurements, and investigations of soft samples in weak interaction with the substrate. The lateral resolution with the tips grown by focused ion beam deposition already matches the one achieved in standard amplitude modulation mode AFM experiments.     

LOCALISATION OF DAMAGE IN SMART STRUCTURES THROUGH SENSITIVITY ENHANCING FEEDBACK CONTROL

The concept of sensitivity enhancing control (SEC) introduced previously by the authors exploits the relationship between feedback control gains and classic measures of root and system sensitivity in order to increase the magnitude of variation in modal characteristics when damage occurs. This paper further develops the SEC concept, focusing on the ability tolocate damage in smart structures. Two distinct methods are considered for locating damage. Forward methods rely on a priori knowledge of how certain damage scenarios affect modal properties. Using this information, the correlation between measured modal frequency shifts and predicted modal frequency shifts for a given set of damage scenarios is used to identify damage location. Inverse, or model updating methods attempt to update mass and/or stiffness matrices of structural models based on measured modal frequencies and mode shapes. The resulting perturbation matrices indicate damage location. Here, both methods are evaluated through finite-element simulation of controlled structures with local stiffness damage, with the goal of determining whether inclusion of modal data from feedback controlled structures enhances the localisation process. Results show that application of both forward and inverse methods to measured closed-loop modal characteristics increases both the accuracy with which stiffness damage can be located and the ability to tolerate noise in measurement of modal properties used to locate damage.     

短时脉冲激励下隧道振动响应与模态参数识别

为了研究短时脉冲激振力下隧道结构振动响应及有效地提取隧道结构的模态特征。首先分析了锤击作用下的不同短时脉冲激振力精度及其频域特性,其次将短时脉冲激振力应用于上海地铁12号某盾构隧道进行了现场动力测试,最后分析了脉冲激振与隧道结构响应之间的传递函数,并结合随机减量、正交多项式法及自回归滑动平均模型法有效地提取隧道结构的模态参数。结果表明:短时脉冲激振力的中低频振动信号在隧道结构中传递特性较好,传递距离较远。隧道结构的模态频率呈现明显低频特征,前10阶模态频率在100 Hz以下。因此,短时脉冲激振力能够很好地应用于隧道动力测试及模态识别,可为基于模态特征的隧道结构损伤识别及健康监测多个研究领域提供有效的支撑和参考依据。     

双层隔振系统模态匹配分析及其振动特性

针对出口内燃动车动力包的双层隔振问题,根据双层隔振系统的结构参数,建立双层隔振系统的有限元模型。对双层隔振系统进行了模态计算,掌握了系统的频率特性。根据柴油机组激振力的频率特性,定量对双层隔振系统进行模态匹配分析。对双层隔振系统进行谐响应计算,准确判断构架和机组是否发生共振,验证模特匹配的合理性。施加怠速工况下的各个激振力,对双层隔振系统进行了强迫振动计算,计算双层隔振系统的振动烈度和传递率。结果表明：双层隔振系统的隔振性能良好,能满足实际工程需求,研究结果可为实际工程提供参考。     

Localization and quantification of damage in beam-like structures using sensitivities of principal component analysis results

Principal component analysis (PCA) is known as an efficient method for dynamic system identification and diagnosis. This paper addresses a damage diagnosis method based on sensitivities of PCA in the frequency domain for linear-form structures. The aim is not only to detect the presence of damage, but also to localize and to evaluate it. The Frequency response functions measured at different locations on the beam are considered as data for the PCA process. Sensitivities of principal components obtained from PCA to beam parameters are computed and inspected according to the location of sensors; their variation from the healthy state to the damaged state indicates damage locations. The damage can be evaluated next providing that a structural model is available; this evaluation is based on a model updating procedure. It is worth noting that the diagnosis process does not require a modal identification achievement. Both numerical and experimental examples are used for better illustration.     

平面3自由度并联机构弹性动力学研究

以平面3自由度并联机构为例,将机构划分成杆单元和平面三角形单元,用有限元理论建立机构微分运动方程。分析机构模态频率和主振型随机构位姿的变化情况。研究机构在主动力和惯性力激励下的动力响应,将机构真实运动与其刚体运动比较,揭示了机构瞬时振动的型态,找出了机构主要柔性环节。研究机构在加速、匀速和减速运动状态下,动平台的位置和姿态误差的变化规律,清楚了机构速度和加速度的动力特性,结果显示,在机构加速或减速过程中位姿误差和动应力显著增大。     

Enhanced meta-modelling technique for analysis of mode crossing, mode veering and mode coalescence in structural dynamics

In this paper, an enhanced meta-modelling procedure for the approximation of structural eigenfrequencies and eigenvectors is introduced. The procedure allows for correct prediction of the modal parameters in case of mode crossing, veering, and coalescence phenomena that can be observed when variations of the structural parameters occur. The procedure overcomes the erroneous approximation of these phenomena which results from a direct approximation of the modal parameters. The methodology is based on the response surface approximation of the structural matrices and on the concept of modal reduction. A comparison with a direct response surface approximation of the eigenfrequencies shows a considerable improvement in the accuracy as it is presented for a finite element frame structure.     

基于应变模态的模态应变能损伤识别方法

传统模态应变能计算需要完备模态振型信息,而模态振型信息中存在转角自由度难以准确获取的问题,为解决该问题,开展基于应变模态的模态应变能损伤识别研究,实现了结构损伤的定量识别。首先,通过基于应变与位移之间的联系,推导出应变模态与位移模态之间的转换矩阵;其次,利用应变模态代替位移模态计算单元模态应变能,建立基于灵敏度分析的损伤识别方程组;最后,根据奇异值截断法求解该方程组识别结构损伤。以一两端固支梁结构为对象,开展数值仿真和实验研究。结果表明,该方法可以有效识别出结构的损伤位置和损伤程度,相对于基于振型扩充的模态应变能损伤识别方法,具有更好精度和抗噪性能。     

On the estimate of the FRFs from operational data

In this paper, the effects of different mass loadings required for the estimation of the frequency response functions, FRFs, from data gained by the emerging technique of operational modal testing, is proposed. This technique allows the evaluation of the natural frequencies, mode shapes and damping ratios from operational data achieved from a first session of tests, then the scaling factors are derived from a further experimental investigation. The approach is based on the sensitivity of the eigenproperties to structural modifications, such as the mass and stiffness distribution. It is shown that the generalized modal parameters could be derived by the measurements of the natural frequency shifts due to a controlled mass variation in the structure, assuming negligible changes in the mode shapes. Such generalized modal parameters are finally used to estimate the FRFs. This mode shape scaling technique, together with the investigation of the effects of the mass positioning on the uncertainties in the estimates of the scaling factors will be experimentally investigated on simple aerospace structures.     

基于μ综合的压电柔性结构振动主动控制

利用模态理论和μ综合方法,对智能柔性悬臂梁进行振动主动控制研究。以压电陶瓷为作动器,电阻应变计为传感器,采用有限元方法和实验模态测试方法建立结构动力学模型,对两种方法所得结果进行比较分析可知有限元模型与实际系统存在误差。考虑外部扰动和量测噪声的不确定性,同时考虑系统固有频率、阻尼比和作动器参数的不确定性,选择模态位移信号为评价量,根据信号的频率特性选择合适的加权函数,利用μ综合方法设计振动控制器。从频域角度分析控制器的有效性,结果表明该控制器能抑制不确定干扰对输出应变的影响,能在系统不确定性情况下满足控制要求,说明控制器具有鲁棒性。进行了振动主动控制实验研究,结果表明,所设计的控制器能有效抑制结构的振动响应。     

负载口独立控制系统主被动加载试验台振动特性分析

主被动加载试验台是对负载口独立控制系统进行主动和被动控制性能试验测试的关键设备。为了分析试验台加载过程中加载力对试验台的振动特性的影响,采用有限元网格划分软件Hypermesh对试验台整机进行了网格划分,定义了材料属性,并通过有限元仿真软件ANSYS Workbench对主被动加载试验台分别进行了静力学分析、模态分析、位移谐响应分析和加速度谐响应分析。仿真结果表明:从试验台的振动过程中的固有频率变化、振幅变化、位移响应分布、加速度响应分布、振动传动路径等可知,主被动试验台在加载试验中,将加载力的频率控制在35 Hz以内,可以避免由于加载而产生的试验台共振现象。     

Uncertainty evaluation for twist drilling stability model

This paper describes the first uncertainty analysis for drilling stability using a frequency-domain drilling stability model. The stability model inputs include: the modal parameters for the torsional-axial vibration mode from the twist drill-holder-spindle axial frequency response function; and the mechanistic coefficients that relate the torque and thrust force to chip area for the selected drill-workpiece material combination. Monte Carlo simulation is applied to propagate the input uncertainties to output uncertainty in the predicted stability map, which separates stable from unstable (chatter) zones in the spindle speed-chip width parameter space. The mean stability boundary and its 95% confidence intervals are determined for five cases: varying all four inputs simultaneously and varying them individually. This enables the individual sensitivities to be compared. Experimental results from drilling tests are included for comparison to the prediction. Additionally, Matlab code is provided to implement the stability model and Monte Carlo uncertainty analysis.     

基于模态叠加法的声固耦合噪声仿真与实验

在ANSYS中建立了长方体箱体的有限元模型,并计算结构模态。将有限元模型和结构模态导入Virtual Lab,计算空腔声模态,用模态叠加法计算耦合声场对激励的响应,得到了声压级分布云图和场点频率响应曲线。设计了长方体箱体的振动噪声实验,将声卡采集得到的噪声信号在Matlab中进行傅立叶分解,得到声场内一点对激振频率的响应曲线。仿真数据与实验数据有较好的一致性。     

Effects of joint on dynamics of space deployable structure

Joints are necessary components in large space deployable truss structures which have significant effects on dynamic behavior of these joint dominated structures.Previous researches usually analyzed effects of one or fewer joint characters on dynamics of jointed structures.Effects of joint stiffness,damping,location,number,clearance and contact stiffness on dynamics of jointed structures are systematically analyzed.Cantilever beam model containing linear joints is developed based on finite element method,influence of joint on natural frequencies and mode shapes of the jointed system are analyzed.Analytical results show that frequencies of jointed system decrease dramatically when peak mode shapes occur at joint locations,and there are cusp shapes present in mode shapes.System frequencies increase with joint damping increasing,there are different joint damping to achieve maximum system damping for different joint stiffness.Joint nonlinear force-displacement is described by describing function method,one-DOF model containing nonlinear joints is established to analyze joints freeplay and hysteresis nonlinearities.Analysis results show that nonlinear effects of freeplay and hysteresis make dynamic responses switch from one resonance frequency to another frequency when amplitude exceed demarcation values.Joint contact stiffness determine degree of system nonlinearity,while exciting force level,clearance and slipping force affect amplitude of dynamic response.Dynamic responses of joint dominated deployable truss structure under different sinusoidal exciting force levels are tested.The test results show obvious nonlinear behaviors contributed by joints,dynamic response shifts to lower frequency and higher amplitude as exciting force increasing.The test results are further compared with analytical results,and joint nonlinearity tested is coincident with hysteresis nonlinearity.Analysis method of joint effects on dynamic characteristics of jointed system is proposed,which can be used in optimal design of joint parameters     

Operational modal analysis in the presence of harmonic excitations by the use of transmissibility measurements

Operational modal analysis (OMA) is based on the assumption that the forces on the structure are the result of a stochastic process, so being white noise. In practice, however, structural vibrations observed in operation cannot always be considered as pure white-noise excitation. In many mechanical structures the loading forces are often more complex and even harmonic components can be present in the response. This is especially true, when measuring on mechanical structures containing rotating parts (e.g. cars, turbines, windmills), but also civil engineering structures may have responses superimposed by harmonic components. OMA procedures are, strictly speaking, not applicable in these situations. Current techniques may encounter difficulties to correctly identify the modal parameters, especially for modes with eigenfrequencies close to the harmonic frequencies. In this paper a recently proposed OMA technique based on transmissibility measurements will be applied. This method reduces the risk to wrongly identify the modal parameters due to the presence of harmonics. The unknown operational forces can be arbitrary (coloured noise, swept sine, impact, etc.) as long as they are persistently exciting in the frequency band of interest.