Application of residuals from regression of experimental mode shapes to locate multiple crack damage in a simply supported reinforced concrete beam

The objective of the study was to propose an effective, simple and reliable technique to determine the location of triple-crack damage in a simply-supported reinforced concrete beam using the method of mode shape regression. The study required simply supported finite element reinforced concrete beam models to be constructed with one as control and another as the test beam with predetermined triple-cracks along the length of the beam. The technique necessitated the performance of linear and Eigen analyses on the control beam, and nonlinear analysis on the beam with triple-cracks. Residuals obtained from regression of the mode shape using the Chebyshev series rational on the modal frequencies and transformation and application into the fourth order centered finite divided difference formula were used. The use of the regressed mode shapes for the reinforced concrete beam model showed large residuals around the areas of the crack damage. The results showed that the method was successful in determining the locations of the triple cracks and was comparable with other techniques proposed by other researchers in terms of its simplicity and reliability.     

Examining the trend in loss of flexural stiffness of simply supported RC beams with various crack severity using model updating

The flexural stiffness of simply supported cracked reinforced concrete beams was determined by model updating. The beams were 150 mm wide, 250 mm deep and 2200 mm long. Different FE models were created which include a datum and models with a single crack at three different locations along the length of the beam. The mode shape equation was obtained by using non-linear regression. The equation used in the regression was the generalized solution of transverse vibration of a prismatic beam. Local flexural stiffness, EI, at each coordinate point was derived by substituting the regressed data by using the centered-finite-divided-difference formula. Experimental modal analysis was performed on a control beam and beams with load-induced cracks at predetermined loading. Results from FE analyses showed the trend in the loss of stiffness was similar to the results obtained on the experimental beams. The more severe the damage, the higher the loss of stiffness and the loss patterns are similar for damage at different locations along the beam. The updating technique is able to indicate the trend in the loss of stiffness as a result of cracks of varying severity in the RC beams showing good agreement with experimental results.     

Dynamic identification of a reinforced concrete damaged bridge

The results of a series of harmonically forced tests carried out on a reinforced concrete single-span bridge subjected to increasing levels of damage are interpreted in this paper. The deck structure of the bridge 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 variation of lower natural frequencies shows an anomalous increase in the transition from one intermediate damage configuration to the next ones. Vibration mode shapes show an appreciable asymmetry in the reference configuration, despite the nominal symmetry of the bridge. A justification of this unexpected dynamic behavior is presented in this paper. The analysis is based on progressive identification of an accurate finite element model of the reference configuration and on reconstruction of damage evolution from natural frequency and vibration mode measurements. Changes in modal curvature of the first two vibration modes evaluated along the main beams are successfully used to identify the location of the damage.     

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.     

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     

常幅循环载荷下纤维薄板增强钢筋砼梁的损伤行为研究

以碳纤维薄板增强钢筋混凝土梁为研究对象,通过对常幅循环载荷作用下增强梁的弯曲试验研究,揭示其疲劳破坏机理,建立描述构件损伤、断裂过程的结构损伤累积模型.试验得到增强梁的疲劳寿命曲线以及跨中挠度、抗弯刚度的演化规律.提出的由构件抗弯刚度表达的非线性结构疲劳损伤演化方程,描述包括混凝土开裂、碳纤维薄板与混凝土界面剥离等破坏模式在内的损伤、破坏过程,并能够对构件疲劳寿命进行预测.     

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.     

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.     

Transverse vibrations of an Euler–Bernoulli uniform beam carrying two particles in-span

Vibrations of beams carrying different combinations of particles, heavy bodies and spring-mass systems which are located on or off resilient supports have been tackled by several researchers. Most of the approaches were based mainly on various approximate methods. In this paper an analytical solution based on the classical beam eigenvalue technique is presented for the vibrations of a beam carrying two particles. For purpose of analysis, the beam was divided into a portion from one end to the first particle, a portion between particles and a portion from the second particle to the other end. The frequency equation is expressed in closed form as a 2nd order determinant equated to zero. Schemes are presented to compute the 4 elements of the determinant and to evaluate the roots of the frequency equation. Computational difficulties were not encountered in the implementation of the schemes. The first three natural frequency parameters are tabulated for 16 combinations of the classical boundary conditions and several combinations of the location and mass of the particles. The beam mode shape is the juxtaposition of the mode shapes of the three portions of the beam. Some examples of normalised beam mode shapes and location/s of node/s are also presented. The results may be used to judge the accuracy of values obtained by approximate methods.     

含集中参数弹性梁振动特性解析与实验识别

基于Laplace变换推导出含集中质量与集中刚度弹性梁的振型函数和典型边界条件对应的频率方程,针对有一个集中质量与一个集中刚度的悬臂梁,求解出其固有特性,并利用基于自然激励技术(natural excitation technique,简称NExT)的特征系统实现算法(eigensystem realization algorithm,简称ERA),即NExT-ERA法对相应结构系统进行了模态识别。通过对比解析结果和实验结果,分别讨论了集中质量与集中刚度大小变化和位置变化时对梁振动特性的影响,得出了集中质量和集中刚度在悬臂梁上位置和大小变化时,悬臂梁固有频率的相应变化规律,为工程中具有集中质量和集中刚度等直弹性梁的振动分析方法和集中参数布置设计提供了参考。     

A two-stage method to identify structural damage sites and extents by using evidence theory and micro-search genetic algorithm

A two-stage method of determining the location and extent of multiple structural damages by using information fusion technique and genetic algorithm is presented in this paper. First the damage detection strategy is to localize the damage sites by using an evidence theory, which can perfectly integrate the damage identification information coming from both natural frequencies and mode shapes. Then, a micro-search genetic algorithm (MSGA) is proposed to determine the damage extent. A cantilever beam is analyzed as a numerical example to compare the performance of the proposed method with the multiple damage location assurance criterions (MDLAC) and the simple genetic algorithms. Simulation results show that identification results of the evidence theory are better than those both of the frequency MDLAC method and the mode shape MDLAC method, and the MSGA is also more accurate and effective than the simple genetic algorithms. Therefore, the two-stage method is very effective for the identification of multiple structural damages.     

基于曲率模态的木梁损伤定量识别

为对木结构构件局部缺陷进行 有效检测,结合试验模态分析和有限元模拟方法,对含不同位置、大小和数量孔洞缺陷的木梁 进行研究,计算其第1阶位移模态振型和曲率模态,分析木梁损伤前后的曲率模态变化,探讨 模态分析方法在木材缺陷检测中的适用性。研究结果表明:曲率模态是一个对木梁损伤比较 敏感的参数,可用于对孔洞位置、大小及数量进行定量的估计;通过降低有限元模型局部单 元的弹性模量能够较好地模拟木梁损伤,有限元模态分析和试验模态分析得到的位移模态振 型及曲率模态吻合均较好,验证了模态分析对木梁无损检测是一种有效的方法。     

Crack detection in beams using experimental modal data and finite element model

In this paper, an analytical, as well as experimental approach to the crack detection in cantilever beams by vibration analysis is established. An experimental setup is designed in which a cracked cantilever beam is excited by a hammer and the response is obtained using an accelerometer attached to the beam. To avoid non-linearity, it is assumed that the crack is always open. To identify the crack, contours of the normalized frequency in terms of the normalized crack depth and location are plotted. The intersection of contours with the constant modal natural frequency planes is used to relate the crack location and depth. A minimization approach is employed for identifying the cracked element within the cantilever beam. The proposed method is based on measured frequencies and mode shapes of the beam.     

A Method for Evaluating Failure in Reinforced Concrete under Bending Based on the Response of Electrical Parameters to an Impact Action

The regularities of changes in the properties of the electrical response of reinforced concrete to an impact action in a four-point bending flexural test and the influence of the rebar cage configuration on the processes of failure in reinforced beams and on electrical response parameters have been studied. Criteria have been proposed for determining the stages of failure in reinforced concrete beams, based on electrical response parameters. The nucleation and growth of macrocracks in the tensile zones of reinforced beams is accompanied by a drop in the maximum cross-correlation coefficient of signal spectra at the current and previous loading levels to 0.45–0.6. An increase in the energy attenuation coefficient of electrical responses in a reinforced beam by 1.5–2.5 times can serve as a precursor to its impending catastrophic breakdown.     

Study on low frequency energy harvesting system in laminated aluminum beam structures with delamination

Piezoelectric material based energy harvesting system (EHS) has been designed and developed to study the influence of delamination on EHS in low frequency vibrating beam structures. The stiffness reduction due to the presence of delamination of specified size and its location is evaluated using the harvested energy in different vibrating elastic modes. Four aluminium beam specimens were fabricated, each having two layers of 1 mm thickness and a specified dimension of delamination was introduced by using a thin Teflon film. The beam without delamination is considered to be healthy and served as the reference structure. The PZT-5H patches were surface bonded on the beams to work as energy harvesting transducers. A suitable electronic circuit is developed to receive the energy from the vibrating beam. The experimental results in terms of energy generated by the four laminated beams have been compared with analytical results at resonant conditions and correlated to assess the effect of delamination on energy produced by low frequency vibration modes. The location of delamination has made a significant change in the harvested energy of second and third bendings; in particular, the delaminations at edge and root have displayed a clear trend. Resonant and off-resonant excitations have revealed that the edge delaminated beam produces lower energy output. The current work has demonstrated that energy harvesting from different elastic modes and with a variable frequency at constant force excitation can be a useful health monitoring technique, employing low frequency vibration, besides utilising the harvested energy itself.     

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。     

An experimental study on damage detection of structures using a timber beam

Using vibration methods for the damage detection and structural health monitoring in bridge structures is rapidly developing. However, very little work has so far been reported on timber bridges. This paper intends to address such shortcomings by experimental investigation on a timber beam using a vibration based method to detect damage. A promising damage detection algorithm based on modal strain energy was adopted and modified to locate/evaluate damage. A laboratory investigation was conducted on a timber beam inflicted with various damage scenarios using modal tests. The modal parameters obtained from the undamaged and damaged state of the test beam were used in the computation of damage index, were then applied using a damage detection algorithm utilising modal strain energy and a statistical approach to detect location of damage. A mode shape reconstruction technique was used to enhance the capability of the damage detection algorithm with limited number of sensors. The test results and analysis show that location of damage can be accurately identified with limited sensors. The modified method is less dependent on the number of modes selected and can detect damage with a higher degree of confidence.     

New rational interpolation functions for finite element analysis of rotating beams

A rotating beam finite element in which the interpolating shape functions are obtained by satisfying the governing static homogenous differential equation of Euler–Bernoulli rotating beams is developed in this work. The shape functions turn out to be rational functions which also depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. These rational functions yield the Hermite cubic when rotation speed becomes zero. The new element is applied for static and dynamic analysis of rotating beams. In the static case, a cantilever beam having a tip load is considered, with a radially varying axial force. It is found that this new element gives a very good approximation of the tip deflection to the analytical series solution value, as compared to the classical finite element given by the Hermite cubic shape functions. In the dynamic analysis, the new element is applied for uniform, and tapered rotating beams with cantilever and hinged boundary conditions to determine the natural frequencies, and the results compare very well with the published results given in the literature.     

ABAQUS钢筋混凝土有限元分析

介绍了混凝土损伤塑性模型的原理、钢筋和混凝土材料的塑性计算过程、混凝土损伤因子的定义及计算,通过对一根钢筋混凝土悬臂粱进行了有限元分析,对比了理论计算和有限元计算的差异,探讨了粘性系数和混凝土损伤对计算结果的影响等问题,为进一步利甩ABAQUs对钢筋混凝土进行有限元分析提供了参考.     

纤维增强FGM梁的自由振动和临界屈曲载荷分析

基于经典梁理论（CBT）研究轴向力作用下纤维增强功能梯度材料（FGM）梁的横向自由振动和临界屈曲载荷问题。首先考虑由混合律模型来表征纤维增强FGM梁的材料属性,其次利用Hamilton原理推导轴向力作用下纤维增强FGM梁横向自由振动和临界屈曲载荷的控制微分方程,并应用微分变换法（DTM）对控制微分方程及边界条件进行变换,计算了纤维增强FGM梁在固定-固定（C-C）、固定-简支（C-S）和简支-简支（S-S）3种边界条件下横向自由振动的无量纲固有频率和无量纲临界屈曲载荷。退化为各向同性梁和FGM梁,并与已有文献结果进行对比,验证了本文方法的有效性。最后讨论在不同边界条件下纤维增强FGM梁的刚度比、纤维体积分数和无量纲压载荷对无量纲固有频率的影响以及各参数对无量纲临界屈曲载荷的影响。