A method for determining the location and depth of cracks in double-cracked beams

The influence of two transverse open cracks on the antiresonances of a double cracked cantilever beam is investigated both analytically and experimentally. It is shown that there is a shift in the antiresonances of the cracked beam depending on the location and size of the cracks. These antiresonance changes, complementary with natural frequency changes, can be used as additional information carrier for crack identification in double cracked beams. Experimental results from tests on plexiglas beams damaged at different locations and different magnitudes are found to be in good agreement with theoretical predictions. Based on the results of the present work, an efficient prediction scheme for crack localization and characterization in double cracked beams is proposed.     

CRACK DETECTION IN BEAM-TYPE STRUCTURES USING FREQUENCY DATA

A practical method to non-destructively locate and estimate size of a crack by using changes in natural frequencies of a structure is presented. First, a crack detection algorithm to locate and size cracks in beam-type structures using a few natural frequencies is outlined. A crack location model and a crack size model are formulated by relating fractional changes in modal energy to changes in natural frequencies due to damage such as cracks or other geometrical changes. Next, the feasibility and practicality of the crack detection scheme are evaluated for several damage scenarios by locating and sizing cracks in test beams for which a few natural frequencies are available. By applying the approach to the test beams, it is observed that crack can be confidently located with a relatively small localization error. It is also observed that crack size can be estimated with a relatively small size error.     

MODELLING OF TRANSVERSE VIBRATION OF SHORT BEAMS FOR CRACK DETECTION AND MEASUREMENT OF CRACK EXTENSION

The method of detection of location of crack in beams based on frequency measurements is extended here to short beams, taking into account the effects of shear deformation and rotational inertia through the Timoshenko beam theory and representing the crack by a rotational spring. Methods for solving both forward (determination of frequencies of beams knowing the crack parameters) and inverse (determination of crack location knowing the natural frequencies) problems are included. A method to estimate crack extension from a change in the first natural frequency is presented. Both numerical and experimental studies are given to demonstrate the accuracy of the methods. The accuracy of the results is quite encouraging.     

Flexural vibration of non-uniform beams having double-edge breathing cracks

Flexural vibration of non-uniform Rayleigh beams having single-edge and double-edge cracks is presented in this paper. Asymmetric double-edge cracks are formed as thin transverse slots with different depths at the same location of opposite surfaces. The cracks are modelled as breathing since the bending of the beam makes the cracks open and close in accordance with the direction of external moments. The presented crack model is used for single-edge cracks and double-edge cracks having different depth combinations. The energy method is used in the vibration analysis of the cracked beams. The consumed energy caused by the cracks opening and closing is obtained along the beam's length together with the contribution of tensile and compressive stress fields that come into existence during the bending. The total energy is evaluated for the Rayleigh-Ritz approximation method in analysing the vibration of the beam. Examples are presented on simply supported beams having uniform width and cantilever beams which are tapered. Good agreements are obtained when the results from the present method are compared with the results of Chondros et al. and the results of the commercial finite element program, Ansys^©. The effects of breathing in addition to crack depth's asymmetry and crack positions on the natural frequency ratios are presented in graphics.     

DYNAMIC RESPONSE OF A BEAM WITH A CRACK SUBJECT TO A MOVING MASS

An iterative modal analysis approach is developed to determine the effect of transverse cracks on the dynamic behavior of simply supported undamped Bernoulli-Euler beams subject to a moving mass. The presence of crack results in higher deflections and alters the beam response patterns. In particular, the largest deflection in the beam for a given speed takes longer to build up, and a discontinuity appears in the slope of the beam deflected shape at the crack location. Crack effects become more noticeable as crack depth increases. The effect of the inertia force due to the moving mass is, in general, qualitatively similar and additive to the effect of the crack. The exact effect of crack and mass depends on the speed, time, crack size, crack location, and the moving mass level. Other approximate methods, namely a stationary mass model and a single iteration technique, are also evaluated. The stationary mass approach is useful for light moving masses (<20% of beam mass) and cracks at mid-span. For other cases, the errors can be unacceptably large. The results of the single-iteration approximation are quite close to the iterative modal analysis approach, which indicates that this approximate solution is an excellent tool for the analysis of the moving mass problem.     

IDENTIFICATION OF CRACK LOCATION IN VIBRATING BEAMS FROM CHANGES IN NODE POSITIONS

It is known that the effect of a single crack in an axially vibrating thin rod is to cause the nodes of the mode shapes move toward the crack. This paper is an analytical/experimental investigation of the analogous problem for a thin beam in bending vibration. The monotonicity property linking changes in node position and crack location does not hold in the bending case. The analysis of the direct problem, however, shows that the direction by which nodal points move may be useful for predicting damage location. Analytical results agree well with experimental tests performed on cracked steel beams.     

Detecting cracks in a longitudinally vibrating beam with dissipative boundary conditions

This paper focuses on detecting a small open crack in an axially vibrating beam with viscous boundary conditions by using non-destructive dynamical measurements. The damage is simulated by an equivalent linear elastic spring. It is shown that the measurement of the changes in a suitable pair of eigenvalues leads to the solution of the diagnostic problem, namely identification of crack location and severity. Results apply to uniform beams under various sets of boundary conditions.     

NON-DESTRUCTIVE EVALUATION OF HORIZONTAL CRACK DETECTION IN BEAMS USING TRANSVERSE IMPACT

Numerical and experimental studies for crack detection in beam employing transverse impact are presented. In the numerical study, a beam model of wave propagation is developed to calculate the time history of beam response before, over and after the crack region. It is expected that the resulting wave in the beam will be scattered by the crack and will carry information on the location and geometry of the crack. Experiments using a scanning laser vibrometer on specimens containing simulated crack are then conducted to verify the numerical results. Comparison study between the numerical results and experimental observations are conducted; good correlation between theory and experiment is observed. The beam model of wave propagation and adaptive multilayer perceptron networks (MLP) are then used for inverse identification of crack parameters (i.e., crack location, depth and length) in the beams. Time-domain displacement responses calculated using the present beam model containing predetermined crack parameters are used as training data for the MLP. Once the MLP is trained, the MLP networks are then employed for inverse determination of an unknown crack in a beam using experimental displacement responses measured with a scanning laser vibrometer. Examples show that the procedure performs well for the determination of a wide range of values for the location, depth and length of the crack.     

双环径向偏振涡旋光束经介质界面的深聚焦

基于矢量德拜理论,研究了双环径向偏振涡旋光束经介质分界面的深聚焦特性。当选取适当的入射光束拦截比时(即透镜孔径半径与入射光束的束腰半径的比),在聚焦场中可以得到一个极小的局域空心光束。局域空心光束的大小不仅与透镜的数值孔径有关,还与聚焦场介质的折射率有关。另外,还研究了透镜的数值孔径、入射光束的拦截比以及探测深度对聚焦光束实际焦点位置的影响。通过对聚焦光束的实际焦点位置的计算发现:当选取一定的光束拦截比时,聚焦光束存在一个焦点开关。     

Crack detection in beams using changes in frequencies and amplitudes of frequency response functions

In recent years, significant efforts have been devoted to developing non-destructive techniques for damage identification in structures. The work reported in this paper is part of an ongoing research on the experimental investigations of the effects of cracks and damages on the integrity of structures, with a view to detect, quantify, and determine their extents and locations. Two sets of aluminum beams were used for this experimental study. Each set consisted of seven beams, the first set had fixed ends, and the second set was simply supported. Cracks were initiated at seven different locations from one end to the other end (along the length of the beam) for each set, with crack depth ratios ranging from 0.1d to 0.7d (d is the beam depth) in steps of 0.1, at each crack location. Measurements of the acceleration frequency responses at seven different points on each beam model were taken using a dual channel frequency analyzer.The damage detection schemes used in this study depended on the measured changes in the first three natural frequencies and the corresponding amplitudes of the measured acceleration frequency response functions.     

厚介质情况下激光“热像”的演化规律分析

以“热像”形成的衍射理论模型和分步傅里叶算法为基础，模拟研究了厚介质情况下“热像”的形成特点.重点分析了散射点调制系数(包括振幅调制和相位调制)、散射点与介质前表面之间的距离、散射点大小、入射光强等参数的变化对“热像”点位置以及强度的影响.数值模拟结果与解析理论结果进行了对比，在散射点调制系数和入射光强的变化对“热像”的影响两种情况下，得出了与解析理论基本一致的结论；在散射点大小的变化对“热像”的影响情况下，得出了与解析理论预言不同的结论.此外，还发现散射点与介质前表面距离为零时，在介质后表面也可能出现“热像”效应. 关键词： 热像 小尺度自聚焦 分步傅里叶算法 散射点     

碳纤维布补强梁裂尖奇异性的光学焦散线实验研究

通过光学焦散线方法对碳纤维布加固含裂纹梁进行三点弯荷载下的静荷载和冲击实验,研究了其断裂特性。在静态实验研究中,记录了不同载荷状态下裂纹的焦散斑光学图像,计算了与之对应的裂纹尖端的应力强度因子,分析了试件在粘贴加固不同长度的碳纤维布情况下焦散斑和应力强度因子演化规律。在动态实验中,记录了裂纹扩展的过程和在此过程中不同时刻的焦散斑和裂纹扩展的路线。通过各瞬间的焦散斑图像,分析裂纹的扩展长度及速度,并得到各时刻的动态应力强度因子。     

斜入射SH波厚壁管道内壁裂纹检测方法研究

厚壁管道常被用于军事装备及其他流程工业中,长期使用后内壁会产生较多微裂纹,成为影响构件安全运行的重大隐患。为此,本文针对厚壁管道内壁裂纹难以检测的问题,提出基于斜入射SH(Shear Horizontal)波的厚壁管道检测方法,对厚壁管道内壁不同深度的裂纹进行检测。本文首先对斜入射SH波的激励原理进行分析,建立声场模型优选激励频率,研究斜入射SH波与厚壁管道内壁裂纹径向深度的作用规律,并通过实验对仿真结果进行验证。研究结果表明,斜入射SH波对该型管道最佳检测频率为1MHz;随着裂纹径向深度增加,缺陷回波幅值呈现曲折型上升;斜入射SH波可有效对厚壁管道内壁轴向长8mm,径向深1mm和周向宽1mm的微裂纹进行检测,验证了斜入射SH波厚壁管道内壁裂纹检测方法的科学性和可行性。     

Propagation properties of Gaussian beams through the anamorphic fractional Fourier transform system with an eccentric circular aperture

As known, it is important for the propagation of Gaussian beams in optics. In this paper, based on the expanding a hard-edge circular aperture function as a finite sum of complex Gaussian functions and the scalar Rayleigh-Sommerfeld diffraction formula, an approximation analytical solution for Gaussian beams propagating through the anamorphic fractional Fourier transform system with an eccentric circular aperture is performed. Then, the detailed numerical calculation for the two-dimensional Gaussian beams in the above-mentioned optical system is presented. The simulation also shows that different location and size of aperture result in the change of diffracted field, including location, intensity and width. All these characteristics help us understand Gaussian beams propagation better.     

Band gap control of phononic beam with negative capacitance piezoelectric shunt

Periodic arrays of negative capacitance shunted piezoelectric patches are employed to control the band gaps of phononic beams. The location and the extent of induced band gap depend on the mismatch in impedance generated by each patch. The total impedance mismatch is determined by the added mass and stiffness of each patch as well as the shunting electrical impedance. Therefore, the band gap of the shunted phononic beam can be actively tuned by appropriately selecting the value of negative capacitance. The control of the band gap of phononic beam with negative capacitive shunt is demonstrated numerically by employing transfer matrix method. The result reveals that using negative capacitive shunt to tune the band gap is effective.     

Free vibration analysis of beams and frames with multiple cracks for damage detection

The problem of calculating the natural frequencies of beams with multiple cracks and frames with cracked beams is studied. The natural frequencies are obtained using a new method in which a rotational spring model is used to represent the cracks. For beams, dynamic stiffness matrices of order 4 are obtained in a recursive manner, according to the number of cracks, by applying partial Gaussian elimination. The Wittrick–Williams algorithm is used to compute the natural frequencies in the resulting transcendental eigenvalue problem. Published numerical examples for cracked beams are used for validation. The global dynamic stiffness matrix of a frame with multiply cracked members is then assembled. A published two bay frame example is used to evaluate the new method. The effect of changing the location of a crack in a two bay two storey frame is studied numerically, giving insight into the inverse problem of damage detection.     

An electro-mechanical impedance model of a cracked composite beam with adhesively bonded piezoelectric patches

A model of a laminated composite beam including multiple non-propagating part-through surface cracks as well as installed PZT transducers is presented based on the method of reverberation-ray matrix (MRRM) in this paper. Toward determining the local flexibility characteristics induced by the individual cracks, the concept of the massless rotational spring is applied. A Timoshenko beam theory is then used to simulate the behavior of the composite beam with open cracks. As a result, transverse shear and rotatory inertia effects are included in the model. Only one-dimensional axial vibration of the PZT wafer is considered and the imperfect interfacial bonding between PZT patches and the host beam is further investigated based on a Kelvin-type viscoelastic model. Then, an accurate electro-mechanical impedance (EMI) model can be established for crack detection in laminated beams. In this model, the effects of various parameters such as the ply-angle, fibre volume fraction, crack depth and position on the EMI signatures are highlighted. Furthermore, comparison with existent numerical results is presented to validate the present analysis.     

球形粒子在聚焦拉盖尔-高斯光束中的散射特性研究

研究了球形粒子在聚焦拉盖尔-高斯光束中的散射特性. 根据广义Mie理论, 推导出球形粒子在聚焦拉盖尔-高斯光束中散射系数的解析公式. 针对光束的电场分布及粒子散射强度进行了数值仿真, 讨论了散射强度随散射角、散射球粒子半径和拓扑荷的变化特性, 并通过散射系数解释了散射强度分布的振荡现象. 结果表明, 在聚焦拉盖尔-高斯光束照射下, 球形粒子的后向散射强度随着粒子半径的增大而逐渐增大; 后向散射强度开始增大时对应的粒子半径与拓扑荷有关. 通过与高斯光束的对比, 可以看出球形粒子在聚焦拉盖尔-高斯光束中散射特性的差异, 使其在粒径测量、光通信和大气后向散射探测等方面具有潜在应用价值.     

SIMPLIFIED MODELS FOR THE LOCATION OF CRACKS IN BEAM STRUCTURES USING MEASURED VIBRATION DATA

A new simplified approach to modelling cracks in beams undergoing transverse vibration is presented. The modelling approach uses Euler-Bernoulli beam elements with small modifications to the local flexibility in the vicinity of cracks. This crack model is then used to estimate the crack locations and sizes, by minimizing the difference between the measured and predicted natural frequencies via model updating. The uniqueness of the approach is that the simplified crack model allows the location and damage extent to be estimated directly. The simplified crack model may also be used to generate training data for pattern recognition approaches to health monitoring. The proposed method has been illustrated using the experimental data on beam examples.     

Study on inspection method of glass defect based on phase image processing

To solve the problem in projecting grating method, the paper presents an inspection method based on phase image processing for glass defects. In the proposed method, the wrapped phase difference is achieved according to the images of defect-free and defect-containing. The unwrapping phase algorithm, based on jump corrected is used to eliminate jump error. The segmentation of defect region is implemented by integrating grayscale mathematical morphology with high-low threshold segmentation, and the boundary coordinate of connected region is used to calculate the size and location of defect. The results demonstrate that the proposed method provides reliable identification of defects.