一类多孔固体的等效偶应力动力学梁模型

一维多孔固体结构可采用等效连续介质梁模型来研究其动力学行为. 当类梁结构的高度尺寸和多孔固体单胞结构尺寸相近时,等效模型的力学行为会产生尺寸效应现象. 等效经典模型由于不包含尺度参数而无法描述尺寸相关特点,而广义连续介质力学模型则可以准确地考虑尺寸效应的影响. 基于偶应力理论,对一类单胞含有圆形孔洞的周期性多孔固体类梁结构,给出了分析其横向自由振动的等效连续介质铁木辛柯梁模型. 通过对单胞分析,在应变能等价和几何平均的意义下,定义了等效偶应力介质的材料常数. 利用已有的材料常数,推导了等效铁木辛柯梁的动力学微分方程. 将实际多孔固体结构进行完全的动力学有限元离散计算,所获得的解作为精确解以检验等效梁模型所获得的频率和振型的精度. 振型的比较借助于模态置信准则矩阵方法. 大量算例表明,等效偶应力铁木辛柯梁模型在频率和振型两方面均具有较高的计算精度. 重点研究了单胞孔径的相对大小、类梁结构高度与单胞尺寸比以及类梁结构长高比对等效梁模型精度的影响. 在此基础上,偏保守地建议了多孔固体类梁结构自振分析方法.      

Identification of multiple open and fatigue cracks in beam-like structures using wavelets on deflection signals

A novel method for damage detection of multi-cracked beam-like structures by analyzing the static deflection is presented. The damage incurred produces a change in the stiffness of the beam. This causes a localized singularity which can be identified by a wavelet analysis of the displacement response. The existence and location of the cracks can be revealed by positions of the peaks in the continuous wavelet transform (CWT). To achieve this, the static profile of beams is analyzed with Gauss2 wavelet to identify the cracks. Beams under some ideal boundary and prescribed load conditions are considered. The deflected shape of the beam with open and fatigue cracks has been simulated under static loading using lumped crack models adopted from fracture mechanics and involving various degrees of complexity. The deflection of cracked beam in closed form for several cases of loads, crack sizes, and crack locations is calculated, and an explicit expression for the damage index (DI), based on CWT, is developed; it is demonstrated that the proposed damage index does not depend on mechanical properties of a homogeneous beam, and that the DI of one crack does not depend on the size and location of other cracks in a multiple cracked beam. Hence, the obtained expression for the DI can be used to find the size of each crack independently. Numerical results show that the method can detect cracks of small depth and is also applicable under the presence of measurement noise.     

Tikhonov's regularization approach in mode shape curvature analysis applied to damage detection

In this paper an on-going research effort aimed at detecting and localizing damage in plate-like structures by using mode shape curvature based damage detection algorithm is described. The proposed damage index uses exclusively mode shape curvature data from the damaged structure. This method was originally developed for beam-like structures. In this paper, the method is generalized to plate-like structures which are characterized by two-dimensional mode shape curvature. To calculate mode shape curvatures from the measured mode shapes, three approaches are proposed: the first one is the well-known central difference approximation, the other two are classical approaches based on Tikhonov's regularization technique with smoothing functional. The applicability and effectiveness of the proposed damage detection algorithms are demonstrated experimentally on an aluminium plate containing mill-cut damage. The validity of the method is assessed by comparing the identification results of the experimental test case to the results obtained from the simulated test case. The modal frequencies and the corresponding mode shapes of the aluminium plate are obtained via finite element models for numerical simulations and by using a scanning laser vibrometer (SLV) for the experimental study.     

AN APPROXIMATE ANALYSIS OF FREQUENCY RESPONSE OF A CRACKED HINGEDHINGED BEAM

A new method based on a modified line-spring model is developed forevaluating the natural frequencies of vibration of a cracked beam.This model inconjunction with the Euler-Bernoulli beam theory,modal analysis and linear elasticfracture mechanics is applied to obtain an approximate characteristic equation of acracked hinged-hinged beam.By solving this equation the natural frequencies aredetermined for different crack lengths in different positions.The results show goodagreement with the solutions through finite element analysis.The present method maybe extended to analyze other cracked complicated structures with various boundaryconditions.     

Waveform fractal dimension for mode shape-based damage identification of beam-type structures

Mode shape-based structural damage identification has been a research focus during the last couple of decades. Most of the existing methods need a numerical or measured baseline mode shape serving as a reference to identify damage, and this requirement extremely limits the practicability of the methods. Recently, waveform fractal dimension such as Katz’s waveform fractal dimension (KWD) has been explored and applied to mode shape for crack identification without a baseline requirement. In this study, different from the popular KWD, an approximate waveform capacity dimension (AWCD) is formulated first, from which an AWCD-based modal abnormality algorithm (AWCD-MAA) is systematically established. Then, the basic characteristics of AWCD-MAA on abnormality detection of mode shapes, e.g., crack localization, crack quantification, noise immunity, etc., are investigated based on an analytical crack model of cantilever beams using linear elastic fracture mechanics. In particular, from the perspective of isomorphism, a mathematical solution on the use of applying waveform fractal dimension to higher mode shapes for crack identification is originally proposed, from which the inherent deficiency of waveform fractal dimension to identify crack when implemented to higher mode shapes is overcome. The applicability and effectiveness of the AWCD-MAA is validated by an experimental program on damage identification of a cracked composite cantilever beam using smart piezoelectric sensors/actuators (i.e., Piezoelectric lead–zirconate–titanate (PZT) and polyvinylidene fluoride (PVDF)). The proposed AWCD-MAA provides a novel, viable method for crack identification of beam-type structures without baseline requirement, and it largely expands the scope of fractal in structural health monitoring applications.     

Crack parameter estimation in structures using finite element modeling

This paper addresses the problem of linear crack quantification, crack depth estimation and localization, in structures. An optimization technique based on a finite element model for cracked structural elements is employed in the estimation of crack parameters for beam, truss and two-dimensional frame structures. The modal data for the cracked structures are obtained by solving the corresponding eigenvalue problem. The error in the modal data is simulated by an additive noise that follows the normal distribution. The simulated reduced modal data is expanded using the eigenvector projection method. Numerical examples showed that this technique gives good results for cracks with high depth ratio. The accuracy of the estimated crack parameters depends on (1) the number of modes used, (2) the error level in the cracked structure modal data and (3) the number of measured degrees of freedom in the case of reduced modal data.     

AN IMPEDANCE ANALYSIS FOR CRACK DETECTION IN THE TIMOSHENKO BEAM BASED ON THE ANTI-RESONANCE TECHNIQUE

An alternative technique for crack detection in a Timoshenko beam based on the first anti-resonant frequency is presented in this paper.Unlike the natural frequency,the anti-resonant frequency is a local parameter rather than a global parameter of structures,thus the proposed technique can be used to locate the structural defects.An impedance analysis of a cracked beam stimulated by a harmonic force based on the Timoshenko beam formulation is investigated.In order to characterize the local discontinuity due to cracks,a rotational spring model based on fracture mechanics is proposed to model the crack.Subsequently,the proposed method is verified by a numerical example of a simply-supported beam with a crack.The effect of the crack size on the anti-resonant frequency is investigated.The position of the crack of the simply-supported beam is also determined by the anti-resonance technique.The proposed technique is further applied to the"contaminated"anti-resonant frequency to detect crack damage,which is obtained by adding 1-3% noise to the calculated data.It is found that the proposed technique is effective and free from the environment noise.Finally,an experimental study is performed,which further verifies the validity of the proposed crack identification technique.     

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.     

基于均匀荷载面曲率的简支裂纹梁损伤识别

为了采用模态参数对结构裂纹进行定位与定量,基于集中柔度模型,采用无质量的扭转弹簧模拟裂纹,建立简支裂纹梁的振动微分方程。针对现有柔度曲率指标仅能判断裂纹的大致范围,基于线性插值理论,建立裂纹位置与相邻测点均匀荷载面曲率差的关系,提出裂纹进一步定位公式,实现裂纹位置的精确定位。针对现有大多数损伤识别方法无法实现裂纹的损伤定量,基于位移曲率与结构刚度和弯矩的关系,理论推导了均匀荷载面曲率的结构刚度损伤程度识别方法,基于弹簧串联原理和线刚度思想,首次提出串联等效线刚度模型,建立裂纹深度与均匀荷载面曲率的关系,实现裂纹深度的定量。通过简支裂纹梁数值算例,考虑多裂纹的损伤情况,验证了新方法对裂纹定位与定量的有效性。     

Nondestructive evaluation of damage in composite structures using modal parameters

The problem of using measured modal parameters to detect and locate damage in structures made of fiberreinforced composites is investigated. Recent work in this area using modal sensitivity equations is used in conjunction with internal-state variable constitutive theory to derive a set of damage-detection equations which are used to predict, from changes in measured modal parameters, the current value of the internal-state variables in each finite element. The value of the internal-state variable determines the extent of damage at a given location. Numerical examples involving damaged composite beams are used to demonstrate the capability of the theory to predict the exact location and the severity of damage. To provide experimental evidence to support the theory, mechanical and modal tests are performed on a [0,90₃] _s laminated composite beam in the undamaged state and in three additional states of progressive damage. At each stage of damage, edge replications are taken to determine the crack density along the length of the beam. The predicted values of the internal-state variables, obtained from the modalsensitivity equations using measured modal information, are compared with the values of the internal-state variables obtained from crack-density measurements along the length of the beam. Good agreement between the predicted and the measured values is found.     

Monitoring structural damage of components using an effective modulus approach

This paper describes a novel nondestructive damage detection method that was developed to study the influence of a crack on the dynamic properties of a cantilever beam subjected to bending. Experimental measurements of transfer functions for the cracked cantilever beam revealed a change in the natural frequency with increasing crack length. A finite element model of a cracked element was created to compute the influence of severity and location of damage on the structural stiffness. The proposed model is based on the response of the cracked beam element under a static load. The change in beam deflection as a result of the crack is used to calculate the reduction in the global component stiffness. The reduction of the beam stiffness is then used to determine its dynamic response employing a modal analysis computational model. Euler–Bernoulli and Timoshenko beam theories are used to quantify the elastic stiffness matrix of a finite element. The transfer functions from both theories compare well with the experimental results. The experimental and computational natural frequencies decreased with increasing crack length. Furthermore the Euler–Bernoulli and Timoshenko beam theories resulted in approximately the same decrease in the natural frequency with increasing crack length as experimentally measured.     

Operational modal filter and its applications

In the paper, the procedure for the estimation of modal filter coefficients from output-only data is presented. The basic concept of the procedure consists in frequency response functions synthesis based on the knowledge of an operational modal model. A method of operational mode shapes scaling is described. The method is then compared with the classical modal filter and with modal filtration of responses spectra, which is sometimes used as a solution for modal filtration based on the output-only data. Each solution is applied to load identification and damage detection. The study shows the method verification on data obtained from laboratory experiment.     

Best achievable modal eigenvectors in structural damage detection

This paper reports a modal formulation of the original method presented by Lim and Kashangaky, based on the use of the best achievable eigenvectors in damage detection problems. The method requires the measurement of both frequencies and mode shapes. The structural damage is located by computing the Euclidean distances between the measured mode shapes and the best achievable modal eigenvectors. The method is able to detect loss of both stiffness and mass properties, even though in this paper only the loss of stiffness will be analyzed. A simple numerical example is reported to investigate the applicability of the modal formulation. Finally, an experimental validation is included using a 10-bay truss laboratory structure.     

On irregularity-based damage detection method for cracked beams

A new damage detection technique using irregularity profile of a structural mode shape is proposed in this paper. The mode-shape of a cracked beam is first obtained analytically by using a general function. Its irregularity profile is then extracted from the mode shape by a numerical filter. The location and size of the crack in the beam can be determined by the peak value appearing on the irregularity profile. Two types of numerical filters, i.e., triangular and Gaussian, are examined. It has been found that the former filter is more effective in damage detection than the latter one. Numerical simulations suggest that the irregularity-based method requires a relatively low measurement resolution. Noise stress tests are carried out to demonstrate the effectiveness and robustness of this method under the influence of noise. As a validation, the proposed method is applied to detect crack damage in an E-glass/epoxy laminated composite beam. The successful detection of the crack in the composite beam demonstrates that the irregularity-based method is capable of assessing both the location and size of the crack and can be used efficiently and effectively in damage identification and health monitoring of beam-type structures.     

A 2-D continuous wavelet transform of mode shape data for damage detection of plate structures

A two-dimensional (2-D) continuous wavelet transform (CWT)-based damage detection algorithm using “Dergauss2d” wavelet for plate-type structures is presented. The 2-D CWT considered in this study is based on the formulation by Antoine et al. (2004). A concept of isosurface of 2-D wavelet coefficients is proposed, and it is generated to indicate the location and approximate shape or area of the damage. The proposed algorithm is a response-based damage detection technique which only requires the mode shapes of the damaged plates. This algorithm is applied to the numerical vibration mode shapes of a cantilever plate with different types of damage to illustrate its effectiveness and viability. A comparative study with other two 2-D damage detection algorithms, i.e., 2-D gapped smoothing method (GSM) and 2-D strain energy method (SEM), is performed, and it demonstrates that the proposed 2-D CWT-based algorithm is superior in noise immunity and robust with limited sensor data. The algorithm is further implemented in an experimental modal test to detect impact damage in an FRP composite plate using smart piezoelectric actuators and sensors, demonstrating its applicability to the experimental mode shapes. The present 2-D CWT-based algorithm is among a few limited studies in the literature to explore the application of 2-D wavelets in damage detection, and as demonstrated in this study, it can be used as a viable and effective technique for damage identification of plate- or shell-type structures.     

基于改进残余力向量法的桁架结构损伤诊断

提出一种基于改进残余力向量法的桁架结构损伤诊断方法. 先由灵敏度分析, 求出结构刚度联系矩阵,再由刚度联系矩阵将损伤后的刚度摄动矩阵展开成对角矩阵,代入 残余力向量方程,得到由刚度联系矩阵表示的新的残余力向量方程,此方程可以直接求解, 即可诊断出桁架结构的损伤杆件及其损伤程度. 对于实测中难以获得完备振型的情况,采用 模态扩阶的方法来获得完备的测试振型. 最后以一桁架结构进行数值仿真分析,证实了该方 法的有效性.     

Closed-loop based detection of debonding of piezoelectric actuator patches in controlled beams

A practical closed loop control based damage detection scheme is presented aiming at detecting small damage in controlled structures. In this detection method, a deliberately designed sensitive control system is used to augment small frequency shifts caused by small structural damage. Since a small frequency change can destabilize such a sensitive control system, it can be easily observed and thus the small damage can be detected. To perform active control of structures, a modal velocity observer (MVO) is designed by combining two observers, which can be used for multi-mode control. By properly choosing the parameters in the MVO, it can be made very sensitive to the frequency shift suitable for small damage detection. To demonstrate this method in detecting small debonding of piezoelectric patches on a smart beam, a detailed model of beam with partly debonded piezoelectric patches is established based on the Timoshenko’s beam theory, in which both transverse and longitudinal vibrations are modeled, and a characteristic equation is also derived to examine the effect of the debonding on the control performance. Both the model and the control law are validated by an active vibration control experiment. Finally, an example is given to illustrate application of the method in piezoelectric actuator debonding detection. The results show that even a small edge debonding in a piezoelectric actuator patch can make the sensitive control system unstable, and therefore can be detected.     

基于柔度的桁架结构损伤定位方法

建立了一种基于模态柔度的桁架结构损伤定位方法。从结构柔度矩阵与刚度矩阵的正交关系出发,将损伤结构在观测模态下的节点误差作为损伤定位的动力指纹,通过采用模态参数的一阶矩阵摄动技术,以近似解析的方式推导了本文方法的损伤定位原理。并且通过对一个典型桁架结构的数值模拟研究,验证了本文损伤定位方法的有效性和鲁棒性。研究结果表明,本文基于柔度的损伤定位方法能够在实际观测条件下,准确地识别桁架结构的损伤单元位置。     

Structural damage localization and evaluation based on modal data via a new evolutionary algorithm

This paper is intended to present a method for the localization and evaluation of damage in plates based on the changes in natural frequencies and mode shapes of the damaged plate using an optimization approach. The colonial competitive algorithm is employed to detect damage (or damages) in plates by optimizing a damage function. The performance of the proposed method is demonstrated by implementing the technique to two examples; a shear wall and a four-fixed supported plate with and without modal data noise including one or a large number of damages. The results confirm the applicability and efficiency of the presented method in detecting damage localization and quantification in the shear walls. Furthermore, the proposed method is implemented to the four-fixed supported plate aimed at demonstrating the high sensitivity of the proposed method in quantitative estimation of damaged plate structures. Finally, the reliability of the presented method is explored through the comparison of the obtained results and those of the other methods. It is concluded that the proposed method can be viewed as a powerful and robust method for structural damage detection in plate structures.     

On the use of non-linear vibrations and the anti-resonances of Higher-Order Frequency Response Functions for crack detection in pipeline beam

The identification of new scientific challenges, as well as the increasing high-performance computing support, indicates that the benefits of applying novel nonlinear techniques for crack detection will continue to grow. So, significant effort has been invested in recent years to develop effective techniques to detect crack in mechanical structures. The objective of this paper is to discuss and propose a robust diagnostic of damage based on non-linear vibrational measurements with particular regard to the Higher-Order Frequency Response Functions. An important observation is that the appearances of the non-linear harmonic components and the emerging anti-resonances in Higher-Order Frequency Response Functions can provide useful information on the presence of cracks and may be used on an on-line crack monitoring system for small levels of damage. Efficiency of the proposed methodology is illustrated through numerical examples for a pipeline beam including a breathing crack.