Dynamic testing of a damaged bridge

In this paper the results of a campaign of dynamic tests carried out on an existing reinforced concrete single-span bridge subjected to increasing levels of damage are presented. The deck structure consists of a slab and three simply supported beams. The damage is represented by a series of notches made on a lateral beam to simulate the effect of incremental concentrated damage. The modal parameters of the lower vibration modes were estimated from frequency response measurements obtained under harmonic excitation. The variation of natural frequencies shows an anomalous increase in the transition from one intermediate configuration to the next damage configurations. Changes in vibration modes are appreciable from the earliest level of damage. In particular, changes in modal curvature of lower modes do provide indication on the damage location.     

Honeycomb damage detection in a reinforced concrete beam using frequency mode shape regression

The objective of the study was to propose a technique to determine the location and severity of honeycomb damage in a reinforced concrete beam using frequency mode shape regression focusing on minimal data. Simply supported reinforced concrete beams were constructed with two different volumes of honeycomb materials implanted at mid-span of the beams. The technique necessitated the performance of linear and eigen analyses on a control beam, and nonlinear analysis on the test beams with damage. Local stiffness indicators obtained from regression using the Levenberg–Marquardt algorithm and residuals from regression of the frequency mode shapes using the Chebyshev series rational and transformation and application into the fourth order centered finite divided difference formula were utilized. Both approaches were successful in determining the location of the honeycomb damage. The Chebyshev series rational method was unable to determine the severity of damage.     

Sensitivity of fundamental mode shape and static deflection for damage identification in cantilever beams

Fundamental mode shape and static deflection are typical features frequently used for identification of damage in beams. Regarding these features, an interesting question, still pending, is which one is most sensitive for use in damage identification. The present study addresses the key sensitivity of these features for damage identification in cantilever beams, wherein these features are extremely similar in configurations. The intrinsic relation between the fundamental mode shape and static deflection is discussed, and in particular, an explicit generic sensitivity rule describing the sensitivity of these features to damage in cantilever beams is proposed. The efficiency of this rule in identifying damage is investigated using Euler-Bernoulli cantilever beams with a crack. The validity of the approach is supported by three-dimensional elastic finite element simulation, incorporating the potential scatter in actual measurements. The results show that the generic sensitivity rule essentially provides a theoretical basis for optimal use of these features for damage identification in cantilever beams.     

Natural frequencies of stepped thickness rectangular plates

This paper presents the natural frequencies of stepped thickness square and rectangular plates together with the mode shapes of vibration. The transverse deflection of a stepped thickness plate is written in a series of the products of the deflection functions of beams parallel to the edges satisfying the boundary conditions, and the frequency equation of the plate is derived by the energy method. By use of the frequency equation, the natural frequencies (the eigenvalues of vibration) and the mode shapes are calculated numerically in good accuracy for square and rectangular plates with edges simply supported or elastically restrained against rotation, having square, circular or elliptical stepped thickness, from which the effects of the stepped thickness on the vibration are studied.     

Sliding-mode control of a six-phase series/parallel connected two induction motors drive

In this paper, a parallel configuration is proposed for two quasi six-phase induction motors (QIMs) to feed them from a single six-phase voltage source inverter (VSI). A direct torque control (DTC) based on input–output feedback linearization (IOFL) combined with sliding mode (SM) control is used for each QIM in stationary reference frame. In addition, an adaptive scheme is employed to solve the motor resistances mismatching problem. The effectiveness and capability of the proposed method are shown by practical results obtained for two QIMs in series/parallel connections supplied from a single VSI. The decoupling control of QIMs and the feasibility of their torque and flux control are investigated. Moreover, a complete comparison between series and parallel connections of two QIMs is given.     

基于倒塌分析的连续梁桥地震损伤评估方法

为了掌握钢筋混凝土连续梁桥在地震作用下从完好到倒塌的破坏历程,首先,基于振动台试验研究对两跨连续梁桥模型进行倒塌仿真分析;其次,建立结构层次的单一倒塌准则;最后,根据影响结构倒塌的关键构件提出两跨连续梁桥地震损伤的整体评价指标D和破坏等级划分标准。结果表明:提出的能量比指标可以有效识别出地震损伤时刻甚至倒塌时刻,当能量比小于能量比限值时即可判定进入倒塌阶段;纵向地震动作用下中墩墩柱和固定支座是关键受力构件;基于关键构件提出的两跨连续梁桥地震损伤整体评价指标D可对不同损伤程度的两跨连续梁模型桥进行评估,该评价体系也可为同类桥型的地震损伤评估和抗震加固提供参考。     

Conceptual damage-sensitive features for structural health monitoring: Laboratory and field demonstrations

The use of damage-sensitive features to evaluate structural condition or health is a very critical aspect of structural health monitoring. The purpose of this paper is to investigate the potential of two different damage-sensitive features for detecting damage. Different damage scenarios are simulated on a large-scale laboratory structure and a three-span highway bridge for demonstration. The features presented in this paper are the modal flexibility-based deflection and curvature both of which are obtained directly from dynamic properties. In the literature, flexibility associated with mode shapes and mode shapes curvatures have been mostly explored. In this study, multi-input–multi-output dynamic data are used to obtain modal flexibility, which is a close approximation to the actual flexibility. A main novelty is that the curvature is calculated from the deflected shapes using the modal flexibility as opposed to using modal vectors. In this paper, the theory of the methodology is explained and then experimental studies and results are presented. For the experimental studies, the laboratory specimen and the three-span bridge were gradually damaged. It is shown that both deflection and curvature are conceptual and physically meaningful features for damage detection and localization. The issues and the requirements for these features to perform successfully are also presented.     

梁的破损对频率振型及振型曲率的影响

本文用欧拉梁振动理论，改变简支梁中某一小段的高度以模拟破损。仿真结果表明，破损对某些阶频率、振型的影响不大，对振型曲率的影响较大．用振型曲率监测简支梁的破损优于用频率或振型的监测方法。     

Dynamic characteristics and model updating of damaged slab from ambient vibration measurements

This paper reports a field investigation using ambient vibration testing on a damaged floor slab of a reinforced concrete frame building. Due to unexpected heavy rainfall, the hill slope at the rear of building failed triggering a major landslide and causing major damage to the perimeter beams and parts of the slab on the first floor. The modal parameters namely natural frequencies and mode shapes were acquired using output only identification technique and the results obtained from the undamaged and damaged floor slabs were compared. It was observed that there was a 25–53% drop in natural frequencies of the damaged slab compared to the undamaged slab, with a much bigger drop for the lower modes. The irregularities in mode shapes identified correlates with the location of the cracks as revealed from visual examination on the damaged slab. Two finite element models of the slab were created using a finite element software package. The damaged slab was updated manually so as to match the modal parameters obtained experimentally. The results from this study further highlight the possibility and feasibility of using non-destructive vibration testing for condition monitoring of structures over more conventional testing techniques.     

Semi-analytical approach for free vibration analysis of cracked beams resting on two-parameter elastic foundation with elastically restrained ends

In present study, free vibration of cracked beams resting on two-parameter elastic foundation with elastically restrained ends is considered. Euler-Bernoulli beam hypothesis has been applied and translational and rotational elastic springs in each end considered as support. The crack is modeled as a mass-less rotational spring which divides beam into two segments. After governing the equations of motion, the differential transform method (DTM) has been served to determine dimensionless frequencies and normalized mode shapes. DTM is a semi-analytical approach based on Taylor expansion series that converts differential equations to recursive algebraic equations. The DTM results for the natural frequencies in special cases are in very good agreement with results reported by well-known references. Also, the DTM procedure yields rapid convergence beside high accuracy without any frequency missing. Comprehensive studies to analyze the effects of crack location, crack severity, parameters of elastic foundation and boundary conditions on dimensionless frequencies as well as effects of elastic boundary conditions on cracked beams mode shapes are carried out and some problems handled for first time in this paper. Since this paper deals with general problem, the derived formulation has capability for analyzing free vibration of cracked beam with every boundary condition.     

Crack detection in simply supported beams without baseline modal parameters by stationary wavelet transform

There are significant changes in the vibration responses of cracked structures when the crack depth is significant in comparison to the depth of the structure. This fact enables the identification of cracks in structures from their vibration response data. However when the crack is relatively small, it is difficult to identify the presence of the crack by a mere observation of the vibration response data. A new approach for crack detection in beam-like structures is presented and applied to cracked simply supported beams in this paper. The approach is based on finding the difference between two sets of detail coefficients obtained by the use of the stationary wavelet transform (SWT) of two sets of mode shape data of the beam-like structure. These two sets of mode shape data, which constitute two new signal series, are obtained and reconstructed from the modal displacement data of a cracked simply supported beam. They represent the left half and the modified right half of the modal data of the simply supported beam. SWT is a redundant transform that doubles the number of input samples at each iteration. It provides a more accurate estimate of the variances at each scale and facilitates the identification of salient features in a signal, especially for recognising noise or signal rupture. It is well known that the mode shape of a beam containing a small crack is apparently a single smooth curve like that of an uncracked beam. However, the mode shape of the cracked beam actually exhibits a local peak or discontinuity in the region of damage. Therefore, the mode shape ‘signal’ of a cracked beam can be approximately considered as that of the uncracked beam contaminated by ‘noise’, which consists of response noise and the additional response due to the crack. Thus, the modal data can be decomposed by SWT into a smooth curve, called the approximation coefficient, and a detail coefficient. The difference of the detail coefficients of the two new signal series includes crack information that is useful for damage detection. The modal responses of the damaged simply supported beams used are computed using the finite element method. For real cases, mode shape data are affected by experimental noise. Therefore, mode shape data with a normally distributed random noise are also studied. The results show that the proposed method has great potential in crack detection of beam-like structures as it does not require the modal parameters of an uncracked beam as a baseline for crack detection. The effects of crack size, depth and location, and the effects of sampling interval are examined.     

Characterization of extensional multi-layer microbeams in pull-in phenomenon and vibrations

This paper presents an analysis of the pull-in instability and vibrational behaviors for a multi-layer microbeam actuated electrostatically. Based on the accurate geometrically nonlinear theory of Euler–Bernoulli beams, a distributed electromechanical model that accounts for finite deformation and residual stress is proposed. The governing differential equations are established in the form similar to those of the single-layer beam theory by re-determination of the neutral axis. These equations, in conjunction with corresponding boundary conditions, are transformed into two two-point boundary value problems. The geometrical nonlinearity is taken into account in static deformation research. The pull-in parameters are obtained using the shooting method through taking the applied voltage as an unknown and the central deflection as a control parameter. The same algorithm is applied to the small-amplitude free vibration around the predeformed bending configuration following an assumed harmonic time mode. The corresponding fundamental natural frequency is presented. The proposed method is validated by comparing several case studies with available published simulations. The influences of pivotal parameters on the pull-in instability behavior and natural frequency are examined, including the length, thickness and residual stress of the microbeam.     

钢筋混凝土简支梁超载后动力特性试验研究

基于采用动态法评估桥梁结构构件超载后损伤的目的,设计和开展了试验研究和相应理论分析。通过对钢筋混凝土简支梁进行反复超载试验,测出构件从完整到破损,以及不同超载幅值和次数对应损伤状态下的频率和阻尼比等模态参数,考查了其与构件承载力的关系,为采用结构动力参数评估结构损伤分析了频率和阻尼比随损伤状态不同的变化规律,根据试验结果得到频率和荷载等级关系的经验公式,为采用动态法评估既有桥梁提供了理论依据     

一种基于高频频响函数的无基准疲劳裂纹识别方法

传统的线性频响函数损伤识别方法依赖于与健康基准对比来识别损伤,限制了其应用范围。提出了一种基于非线性高频频响函数的无基准疲劳裂纹损伤识别方法。通过分析出现裂纹时损伤界面的非线性特征,提出利用不同幅值激励下高频频响函数不同的特性,在无基准情况下提取非线性频响成分,构造损伤指数表征非线性损伤,同时分析了不同频率段对疲劳裂纹的敏感程度。实验表明该方法可以在无基准情况下有效识别疲劳裂纹。     

应用“PXE+虚拟磁盘技术”的CAD工程实践基地管理模式研究

目前实验室的标准实验用机配置方式为有盘、单机管理模式。这种配置方式通常会给实验室的管理工作带来装机工作量巨大、硬盘损耗严重、系统易被病毒感染及组网方式不便等弊端。基于以上管理模式的不足,本文以黑龙江科技学院电气与信息学院CAD工程实践基地实验室管理模式改革试点为例,分别从管理模式和技术实现层面介绍一种应用"PXE+虚拟磁盘技术"的实验室管理模式。从试点改革收效和技术成本分析层面证明该种实验室管理模式可以完全应对有盘管理模式的不足,高效可行。     

DAMAGE ASSESSMENT USING MODE SHAPE SENSITIVITIES

In this paper, a method for the localisation and assessment of damage is presented. The method is based on the use of mode shape sensitivities to changes in mass or stiffness in the test structure. With these sensitivities, differences in the dynamical behaviour of the structure in its undamaged and damaged conditions can be translated into damage information (location and amount of changes in mass or stiffness). Since the sensitivities are calculated on the basis of the experimentally determined mode shapes, there is no need for a prior finite element model of the test structure. The applicability of this technique is discussed on the basis of damage detection experiments performed on a beam-like structure (laboratory conditions) as well as data from the experiments on the I-40 highway bridge in Albuquerque, New Mexico. A comparison is made with a variety of existing damage detection techniques which do not require a finite element model.     

Effect of axial force on free vibration of Timoshenko multi-span beam carrying multiple spring-mass systems

The situation of structural elements supporting motors or engines attached to them is usual in technological applications. The operation of machine may introduce severe dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli–Euler single-span beams carrying a number of spring-mass system and Bernoulli–Euler multi-span beams carrying multiple spring-mass systems are plenty, but that of Timoshenko multi-span beams carrying multiple spring-mass systems with axial force effect is fewer. This paper aims at determining the exact solutions for the first five natural frequencies and mode shapes of a Timoshenko multi-span beam subjected to the axial force. The model allows analyzing the influence of the shear and axial force effects and spring-mass systems on the dynamic behavior of the beams by using Timoshenko Beam Theory (TBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1–4 span beams are studied. The calculated natural frequencies of Timoshenko multi-span beam by using secant method for non-trivial solution for the different values of axial force are given in tables. The mode shapes are presented in graphs.     

桥式起重机有限元分析和疲劳寿命研究

以某180 t×24.85 m冶金桥式起重机为对象,应用有限元分析软件Ansys研究桥架的变形和应力分布状态,并与现场测试结果进行对比分析。结果表明,该起重机的最大挠度、静态Von Mises等效应力和第一阶固有频率均符合起重机设计规范要求。通过无损探伤发现桥架北主梁的下盖板上有裂纹,应用有限元分析和损伤容限设计对起重机裂纹的疲劳寿命进行研究,其分析数据可为起重机的日常维护检修和安全评估提供参考。     

Natural frequencies,modes and critical speeds of axially moving Timoshenko beams with different boundary conditions

In this paper, natural frequencies, modes and critical speeds of axially moving beams on different supports are analyzed based on Timoshenko model. The governing differential equation of motion is derived from Newton's second law. The expressions for various boundary conditions are established based on the balance of forces. The complex mode approach is performed. The transverse vibration modes and the natural frequencies are investigated for the beams on different supports. The effects of some parameters, such as axially moving speed, the moment of inertia, and the shear deformation, are examined, respectively, as other parameters are fixed. Some numerical examples are presented to demonstrate the comparisons of natural frequencies for four beam models, namely, Timoshenko model, Rayleigh model, Shear model and Euler–Bernoulli model. Finally, the critical speeds for different boundary conditions are determined and numerically investigated.     

Measurements of dynamic properties of a medium span suspension bridge by using the wavelet transforms

The aim of this paper is to show the capabilities of the real-time kinematic (RTK) global positioning network system (GPS) to measure the low-frequency vibration of a medium span suspension bridge. In particular, this paper presents the results of studies conducted on the identification of modal parameters including natural frequencies, damping coefficients and mode shapes of a suspension bridge using ambient excitation loads. A real-time kinematic (RTK) global positioning system (GPS) was designed and installed on the Nottingham Wilford Bridge to provide long-term and real-time measurement of bridge deck movement. An approach to estimate modal parameters, from only output data in the time domain using the wavelet transform, is presented. Displacements responses of the bridge are used in the wavelet transform to identify its dynamic characteristics. The modal properties were extracted using a two-step methodology. In the first step, the random decrement method was used to transform random signals in free vibration responses. Secondly, a wavelets-based technique was used to extract natural frequencies and to determine the mode shapes of the structure. This method was compared with the well-established techniques eigensystem realisation algorithm showing a difference of 1% in the estimated first natural frequency.The efficiency of RTK–GPS was demonstrated in the full-scale measurement. In particular, the results showed that the RTK–GPS data can be used for extracting modal properties from in-service-loads induced low-frequency vibration (<5 Hz) by processing the signal with the wavelets transform.