Damage estimation on beam-like structures using the multi-resolution analysis

This work proposes a vibration-based damage evaluation method that can detect, locate, and size damage utilizing only a few of the lower mode shapes. The proposed method is particularly advantageous for beam-like structures with uncertain applied axial load, mass density, and foundation stiffness. Based on a small damage assumption, a linear relationship between damaged and undamaged curvatures is revealed in the context of elasticity. It turns out that the resulting damage index equation inherently suffers from singularities near inflection nodes. The transformation of the problem into the multi-resolution wavelet domain provides a set of coupled linear equations. With the aid of the singular value decomposition technique, the solution to the damage index equation is achieved in the wavelet space. Next, the desired physical solution to the damage index equation is reconstructed from the one in the wavelet space. The performance of the proposed method is compared with two existing damage detection methods using a set of numerical simulations. The proposed method attempts to resolve the mode selection problem, the singularity problem, the axial force problem, and the absolute severity estimation problem, all of which remained unsolved by earlier attempts.     

Crack identification method in beam-like structures using changes in experimentally measured frequencies and Particle Swarm Optimization

In this paper, a technique is presented for the detection and localization of an open crack in beam-like structures using experimentally measured natural frequencies and the Particle Swarm Optimization (PSO) method. The technique considers the variation in local flexibility near the crack. The natural frequencies of a cracked beam are determined experimentally and numerically using the Finite Element Method (FEM). The optimization algorithm is programmed in MATLAB. The algorithm is used to estimate the location and severity of a crack by minimizing the differences between measured and calculated frequencies. The method is verified using experimentally measured data on a cantilever steel beam. The Fourier transform is adopted to improve the frequency resolution. The results demonstrate the good accuracy of the proposed technique.     

Eigenanalysis and continuum modelling of pre-twisted repetitive beam-like structures

A repetitive pin-jointed, pre-twisted structure is analysed using a state variable transfer matrix technique. Within a global coordinate system the transfer matrix is periodic, but introduction of a local coordinate system rotating with nodal cross-sections results in an autonomous transfer matrix for this Floquet system. Eigenanalysis reveals four real unity eigenvalues, indicating tension–torsion coupling, and equivalent continuum properties such as Poisson’s ratio, cross-sectional area, torsion constant and the tension–torsion coupling coefficient are determined. A variety of real and complex near diagonal Jordan decompositions are possible for the multiple (eight) complex unity eigenvalues and these are discussed in some detail. Analysis of the associated principal vectors shows that a bending moment produces curvature in the plane of the moment, together with shear deformation in the perpendicular plane, but no bending–bending coupling; the choice of a structure having an equilateral triangular cross-section is thought responsible for this unexpected behaviour, as the equivalent continuum second moments of area are equal about all cross-sectional axes. In addition, an asymmetric stiffness matrix is obtained for bending moment and shearing force coupling, and possible causes are discussed.     

Free and forced linear dynamics of a homogeneous model for beam-like structures

A homogeneous shear beam model is used here to address the free and forced dynamic behavior of a multi-story building. After a brief recall of the model, which is taken from the literature, and the hypotheses on which it is grounded, discussion on the free dynamics is carried out, highlighting the intriguing organization of the natural frequencies and modes in triplets, as functions of the wave-number. Then, the properties of the undamped and proportionally damped forced response to external loads is evaluated, and a discussion on the effects of the tip mass related to the top story is addressed. A case-study is analyzed to show the reliability of the homogeneous model, after comparing the outcomes with those provided by F.E.M. procedures applied to the corresponding multi-d.o.f. structure.

     

A damage identification technique for beam-like and truss structures based on FRF and Bat Algorithm

In this paper, a Structural Health Monitoring (SHM) technique for damage identification in beam-like and truss structures using Frequency Response Function (FRF) data coupled with optimization techniques is presented. Genetic Algorithm (GA) and Bat Algorithm (BA) are used to estimate the location and severity of damage. The damage in the structures is simulated by reduction in rigidity of specific members. Both optimization techniques are coupled with modelled structures using Finite Element Method (FEM). The approach is based on minimizing an objective function by comparing measured and calculated FRFs. The results show that better accuracy is obtained using BA than using GA in terms of precision and computational time. Furthermore, it is found that the proposed approach provides faster solution than other approaches in the literature.     

Ultrasonic detection and measurement of fatigue cracks in notched specimens

An ultrasonic technique was developed and used to observe the formation and growth of fatigue cracks in notched cylindrical specimens subjected to reversed axial cyclic loading. Fatigue curves of life-to-initial detectable cracks as well as life-to-fracture were obtained for an aluminum-, a titanium- and a cobaltbase alloy, as well as a maraging steel. Depth of initially detectable cracks ranged between approximately 0.0005 and 0.004 in. (0.013 and 0.10 mm). Curves were also obtained relating ultrasonic system output voltage to crack depth up to 0.030 in. (0.76 mm) for three materials. These curves were used to demonstrate the capability of the device for monitoring crack growth.     

The eduction of structures from flow imagery using wavelets Part I. The mixing layer

 Using two-dimensional Mexican hat wavelets, digitized imagery from the flow visualization pictures of a mixing layer by Brown and Roshko have been analysed. The objective of the present study is to “calibrate” the proposed wavelet technique for educing structures in a flow whose large-scale organization is well established. It is found that, with appropriate thresholds on wavelet-transform coefficients, considerable insight into the structure of the flow at different scales can be obtained. In particular, the analysis reveals that the small-scale structure within the large-scale vortices is approximately homogeneous, and has characteristic scales that do not vary significantly with downstream distance. Received: 5 March 1998 / Accepted: 28 October 1998     

Effect of plastic zone on the fatigue crack propagation behavior between two fatigue cracks

In this study, the fatigue crack propagation behavior in the stress interaction field between two different fatigue cracks is studied by experiment and finite element analysis. In the experiment, the offset distance between two cracks and the applied stress are varied to create different stress interaction fields. The size of the plastic zone area is used to examine the crack propagation path and rate. Three types of crack propagation in the interaction field were found by experiment, and the crack propagation behavior of two cracks was significantly changed as different stresses were applied. The size of the plastic zone obtained by finite element analysis can be used to explain crack propagation behavior qualitatively.     

Analysis of multiple interfacial cracks in three-dimensional bimaterials using hypersingular integro-differential equation method

By using the concept of finite-part integral, a set of hypersingular integro-differential equations for multiple interracial cracks in a three-dimensional infinite bimaterial subjected to arbitrary loads is derived. In the numerical analysis, unknown displacement discontinuities are approximated with the products of the fundamental density functions and power series. The fundamental functions are chosen to express a two-dimensional interface crack rigorously. As illustrative examples, the stress intensity factors for two rectangular interface cracks are calculated for various spacing, crack shape and elastic constants. It is shown that the stress intensity factors decrease with the crack spacing.     

Transmissibility function-based fault diagnosis methods for beam-like engineering structures: a review of theory and properties

Nonlinear Dynamics - The beam-like structures commonly exist in engineering systems and there are many critical issues relevant to fault diagnosis of those structures. Noticeably, among all other...     

Surface finish of open holes on fatigue life

In this paper, the effect of surface finish of open holes on the fatigue life has been studied. Four defects of the surface finish are simulated. They are scratch, void, inclusion and roundness. Firstly, the effect of the four defects on the stress distributions around the holes has been studied by the finite element method (FEM). The fatigue lives are determined based on the stress distributions by the method of nominal stress approach. The results show that the fatigue lives are dependent on the quantity of the surface finished. There are the critical defect values of scratch, void and inclusion, smaller than which there is no effect of the surface finish on the fatigue life. For these three defects, the fatigue lives decrease with the increasing of the values of the defects. It is the same to the defect of roundness, e.g. the bigger roundness tolerance is, the shorter the life is. Further, an approximate quadratic curve has been found for the relationship between the roundness tolerances and their logarithmic fatigue lives.     

Experimental and theoretical study on numerical density evolution of short fatigue cracks

Fatigue testing was performed using a kind of triangular shaped specimen to obtain the characteristics of numerical density evolution for short cracks at the primary stage of fatigue damage. The material concerned is a structural alloy steel. The experimental results show that the numerical density of short cracks reaches the maximum value when crack length is slightly less than the average grain diameter, indicating grain boundary is the main barrier for short crack extension. Based on the experimental observations and related theory, the expressions for growth velocity and nucleation rate of short cracks have been proposed. With the solution to phase space conservation equation, the theoretical results of numerical density evolution for short cracks were obtained, which were in agreement with our experimental measurements. The project supported by the National Natural Science Foundation of China and the Chinese Academy of Sciences.     

Growth of part-through and through-thickness fatigue cracks in sheet glassy plastics

Linear-elastic fracture mechanics is used to interpret observations of through-thickness fatigue crack growth in sheet specimens of polymethylmethacrylate, polycarbonate and an unfilled epoxy, and to correlate measurements of the growth of part-through and through-thickness fatigue cracks in sheet polymethylmethacrylate. It is shown that at least one of these materials may be useful for model studies of the growth of part-through thickness fatigue cracks in metallic components.     

基于LS-WSVM的光纤陀螺漂移辨识

提出了一种最小二乘小波支持向量机(LS-WSVM)的光纤陀螺的漂移辨识算法.该方法将Mexihat小波函数作为核函数,与最小二乘支持向量机(LS_SVM)相结合建立起通用模型;用光纤陀螺漂移数据训练通用模型,从而得到该光纤陀螺的漂移模型.并用F法则检验了该模型的适应性.试验表明,在相同条件下,与基于Gauss核函数的最小二乘支持向量机模型相比,该模型拥有更高的辨识精度.证明了用最小二乘小波支持向量机对光纤陀螺的机漂移辨识是合适的,有效的.     

Identification of time-varying hysteretic structures using wavelet multiresolution analysis

In this paper, a wavelet multiresolution technique is proposed to identify time-varying properties of hysteretic structures. It is well known that arbitrary transient functions can be effectively and accurately approximated using wavelet multiresolution expansions due to wavelet's good time-frequency localization property. By decomposing the time-varying parameters with wavelet multiresolution expansion, a time-varying parametric identification problem can be transformed into a time-invariant non-parametric one. The identification in the time-invariant wavelet multiresolution domain can be achieved by choosing a wavelet basis function and performing a suitable parameter estimation technique. Since wavelet representation of arbitrary signal uses only a small number of terms, the orthogonal forward regression algorithm can be adopted for significant term selection and parameter estimation. Single and multiple degrees of freedom Bouc-Wen hysteretic structures with gradual and abrupt varying properties are used to illustrate the proposed approach. Results show that the wavelet multiresolution technique can identify and track the time-varying hysteretic parameters quite accurately. The effect of measurement noise is also studied. It is found that the presence of noise would affect more on the damping ratios and the Bouc-Wen parameters but less on the equivalent stiffness coefficients.     

裂纹损伤对塔壳结构动态特性的影响研究

基于数值方法研究裂纹损伤对塔式壳体结构动态特性的影响。建立了等截面直立塔壳结构有限元模型,采用刚度下降法模拟不同程度受损单元,计算了无损和不同损伤工况下(耳式支座与塔体角焊缝处环向裂纹损伤),结构的固有振动特性和脉动风载荷作用下结构的动态响应。结果表明:结构振动信号可以反映塔壳结构局部不同程度损伤的影响,裂纹损伤对固有频率影响较小,最大20%损伤对固有频率的减小约为7%~8%;对模态振型影响较大,尤其在高阶(如15阶频率)上可能出现新的振型;对位移响应、动应力影响最为明显。     

The displacement discontinuity method in the analysis of open cracks

The application of the displacement discontinuity numerical technique to the solution of some problems of fracture mechanics is demonstrated in the hypothesis of homogeneous and elastic material. The fracture is supposed to be free from traction and is represented by a set of constant displacement discontinuity elements, except for two parabolic elements, located at each crack tip, in order to simulate the singularity of the solution near the crack tips. On the basis of the stress and displacement field determined by the displacement discontinuity method, the stress intensity factors for mode I and II are computed according to the method of the displacements. Three examples are provided to verify the validity of the formulation.

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Sommario Lo scopo del presente lavore è di illustrare l'applicazione del metodo numerico della Displacement Discontinuity alla soluzione di alcuni problemi di meccanica della frattura, nell'ipotesi di materiale omogeneo ed elastico. La frattura è supposta aperta ed è rappresentata da una linea di elementi a discontinuità di spostamento costante, con l'eccezione di due speciali elementi parabolici, ubicati agli apici, al fine di simulare la singolarita' del campo tensionale. Sulla base del campo degli sforzi e degli spostamenti cosi determinati, vengono ricavati i fattori di concentrazione degli sforzi in modo I e II mediante il metodo degli spostamenti. Vengono inoltre riportati tre esempi di calcolo, effettuati al fine di verificare la validità del procedimento proposto.

     

Experimental investigation on the propagation of fatigue cracks emanating from sharp notches

The effect of notch geometry on the propagation of fatigue cracks emanating from sharp V-shaped notches is investigated by means of an experimental campaign performed on Al-7075-T651 specimens carrying notches with opening angles of 45°, 90°, and 135°. The samples were tested using a servohydraulic machine under different loading directions and at several loading levels. The crack deflection induced by the variation in loading direction was determined my measuring the kinking angle and by studying the crack propagation plane through fractographic analysis. A linear elastic fracture mechanics approach was adopted for the analysis of experimental results. Stress intensity factors were calculated using an appropriate weight function set up for studying inclined edge cracks emanating from sharp V-notches. The influence of K _II on the crack propagation was discussed on the basis of theoretical and semi empirical models.