基于有限测点信息的结构损伤识别柔度法

利用有限测点获得结构的模态参数,提出了基于有限测点的结构损伤识别的柔度法。该方法是通过仅考虑结构柔度的灵敏度分析,以结构各自由度的损伤信息为条件,选择对结构柔度变化敏感的自由度为测点,并利用有限测点的信息提出了结构完备模态振型的重建技术。在此基础上,对柔度矩阵做关于结构物理参数变化量的一阶泰勒展开,来确定结构单元的损伤因子对结构进行损伤识别。从而实现利用结构有限测点的模态信息来识别结构的损伤,解决了测试结构的模态振型的不完整给结构的损伤诊断带来的困难。通过数值算例说明了该方法的有效性。     

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.     

Damage detection method in complicated beams with varying flexural stiffness

A damage detection method for complicated beam-like structures is proposed based on the subsection strain energy method (SSEM), and its applicability condition is introduced. For a beam with the continuously varying flexural stiffness and an edge crack, the SSEM is used to detect the crack location effectively by numerical modal shapes. As a complicated beam, the glass fiber-reinforced composite model of a wind turbine blade is studied based on an experimental modal analysis. The SSEM is used to calculate the damage index from the measured modal parameters and locate the damage position in the blade model successfully. The results indicate that the SSEM based on the modal shapes can be used to detect the damages in complicated beams or beam-like structures for engineering applications.     

基于应变模态和稀疏贝叶斯学习的网架结构损伤识别

传统稀疏贝叶斯学习算法进行损伤识别时需要对每个单元进行刚度损伤系数的迭代更新,当结构单元众多时,存在计算效率低和对振型的完备性要求高等问题.本文提出了损伤识别两步法,首先利用应变模态差指标进行疑似损伤单元的判断;接着以单元刚度损伤系数为目标参数,建立结构损伤识别的多层次稀疏贝叶斯学习模型,利用稀疏贝叶斯学习算法进一步识...     

High-order layerwise mechanics and finite element for the damped dynamic characteristics of sandwich composite beams

A high-order discrete-layer theory and a finite element are presented for predicting the damping of laminated composite sandwich beams. The new layerwise laminate theory involves quadratic and cubic terms for approximation of the in-plane displacement in each discrete layer, while interlaminar shear stress continuity is imposed through the thickness. Integrated damping mechanics are formulated and both laminate and structural stiffness, mass and damping matrices are formed. A finite element method and a beam element are further developed for predicting the free vibration response, including modal frequencies, modal loss factors and through-thickness mode shapes. Numerical results and evaluations of the present model are shown. Modal frequencies and damping of sandwich composite beams are measured and correlated with predicted values. Finally, parametric studies illustrate the effect of core thickness and face lamination on modal damping and frequency values.     

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.     

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.     

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.     

基于改进遗传算法主动柔性结构压电元件位置优化

基于改进的遗传算法提出了一种解决多压电片布置在柔性结构上以实现振动主动控制的有效方法.本文采用D优化设计准则,即把Fisher信息矩阵行列式最大值作为目标函数的一种优化方法.通过对结构模态振型和动力特性的研究,使用一种简单的方法将所选择的低阶模态振型转化为归一化形式,最后通过结构模态振型可确定压电片最优位置.为了达到更好的振动控制效果,压电片布置在结构模态应变最大位置处.当在结构不同位置上布置压电片时,结构各阶模态振型也将随之发生不同程度的变化.本文建立了ANSYS软件和遗传算法的接口来实现对结构的模态重分析,从而提取各阶模态振型.     

Single beam analysis of damaged beams verified using a strain energy based damage measure

Analytical expression of a new damage measure which relates the strain energy, to the damage location and magnitude, is presented in this paper. The strain energy expression is calculated using modes and natural frequencies of damaged beams that are derived based on single beam analysis considering both decrease in mass and stiffness. Decrease in mass and stiffness are a fallout of geometric discontinuity and no assumptions regarding the physical behavior of damage are made. The method is applicable to beams, with notch like non-propagating cracks, with arbitrary boundary conditions. The analytical expressions derived for mode shapes, curvature shapes, natural frequencies and an improved strain energy based damage measure, are verified using experiments. The improvement in the damage measure is that it is not assumed that the bending stiffness of the damaged beam is constant, and, equal to that of undamaged beam when calculating the strain energy of the entire beam. It is also not assumed that the bending stiffness of the element in which the damage is located is constant.     

基于改进灰狼优化算法的结构损伤识别

结合模态柔度矩阵、广义模态柔度矩阵和振型三个识别精度较好的指标,构造新的目标函数求解损伤识别问题。通过Nelson方法求解得到的频率与振型的导数,得到对结构刚度发生变化时更具敏感性的位置,然后在这些位置布置传感器以提取结构信息。针对原有的灰狼算法虽然全局搜索能力强,但是存在局部搜索精度差的问题,本文从初始种群和收敛因子等方面着手,改善灰狼算法的局部搜索能力及收敛速度。最后利用提出的方法,通过识别梁模型及桁架模型中的损伤单元说明本文方法的有效性。     

Cyclo-symmetric modal synthesis of rotating bladed disc system

The natural mode analysis of bladed disc system at an arbitrary constant rotational speed is investigated in this paper and the large deformation effect caused by the pretorsion of the blades is considered. The computational method of group theory is employed in substructure technique and equilibrium position and stress distribution of the bladed disc system in centrifugal field are obtained through simultaneous iteration, furthermore, the initial stress stiffness matrix, the large deformation stiffness matrix and the corresponding rotating natural frequencies and modal shapes are determined. Because the large deformation effect of the blades is considered and all the interface degrees of freedom between the substructures can be eliminated in the present method, the computation work can be cut down remarkably under the precondition that the computational accuracy is ensured. This shows that, in general, the substructure simultaneous iteration method presented in this paper has a good convergency, thus greatly reducing the computation work.     

Mode identification of a rotating disk

A modal testing method permitting identification of the natural frequencies, the number of nodal diameters and wave motions in a rotating disk is presented in this paper. This method is applicable at arbitrary rotation speed without requiring a priori information about the vibration modes of the stationary disk. The influence of disk rotation speed on the prediction of mode shapes with this method is shown, and experimental predictions of modal parameters are presented for both axisymmetric and asymmetric disks.     

基于转角模态和小波神经网络的连续梁损伤识别研究

基于小波奇异性检测原理和神经网络非线性映射能力,结合结构基本模态参数,提出了一种结合小波神经网络与结构转角模态的损伤识别方法．首先,建立三跨连续梁的有限元模型获取结构模态参数,并对其进行Mexihat小波变换,通过系数图突变点判断结构损伤位置．然后,将小波系数模特征向量作为BP神经网络的输入,分别研究了该方法在单损伤和多损伤工况下的识别能力．最后将不同工况下神经网络预测值与结构实际损伤程度进行对比,得到单处损伤预测误差平均值为0.22%,多处损伤预测误差平均值分别为0.22%和0.18%,结果表明该方法在结构损伤识别方面的有较高有效性及精确度．     

Noise analysis for sensitivity-based structural damage detection

As vibration-based structural damage detection methods are easily affected by environmental noise, a new statistic-based noise analysis method is proposed together with the Monte Carlo technique to investigate the influence of experimental noise of modal data on sensitivity-based damage detection methods. Different from the commonly used random perturbation technique, the proposed technique is deduced directly by Moore-Penrose generalized inverse of the sensitivity matrix, which does not only make the analysis process more efficient but also can analyze the influence of noise on both frequencies and mode shapes for three commonly used sensitivity-based damage detection methods in a similar way. A one-story portal frame is adopted to evaluate the efficiency of the proposed noise analysis technique.     

Geometrically exact planar beams with initial pre-stress and large curvature: Static configurations,natural frequencies,and mode shapes

Within this paper, an analytical formulation is provided and used to determine the natural frequencies and mode shapes of a planar beam with initial pre-stress and large variable curvature. The static configuration, mode shapes, and natural frequencies of the pre-stressed beam are obtained by using geometrically exact, Euler–Bernoulli beam theory. The beam is assumed to be not shear deformable and inextensible because of its slenderness and uniform, closed cross-section, as well as the boundary conditions under consideration. The static configuration and the modal information are validated with experimental data and compared to results obtained from nonlinear finite-element analysis software. In addition to the modal analysis about general static configurations, special consideration is given to an initially straight beam that is deformed into semi-circular and circular static configurations. For these special circular cases, the partial differential equation of motion is reduced to a sixth-order differential equation with constant coefficients, and solutions of this system are examined. This work can serve as a basis for studying slender structures with large curvatures.     

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.     

转动盘一片系的循环对称模综

本文考察在任意恒定转速下叶片/轮盘系的固有模态分析,计及叶片预扭所引起的大变形效应.把群论算法用于子结构技术,通过联立迭代求出叶片/轮盘系在离心场中的平衡位置和应力分布,进而确定初应力刚度矩阵、大变形刚度矩阵,以及相应的动频模态.由于本方法考虑了叶片大变形的影响,且可消去子结构间的全体内连自由度。从而在确保精度的前提下,显著地压缩了计算的规模.实践证明本文提出的子结构联立迭代法有很好的收敛性,它使计算量有巨大的节省.     

Nonlinear Random Response of Cylindrical Panels to Acoustic Excitations Using Finite Element Modal Method

This paper investigates large amplitude multi-mode free vibration andrandom response of thin cylindrical panels of rectangular planform usinga finite element modal formulation. A thin laminated composite doublycurved element is developed. The system equation in structural nodal DOFis transformed into the modal coordinates by the using the modes of theunderlying linear system. The nonlinear stiffness matrices are alsotransformed into nonlinear modal stiffness matrices. Numericalintegration is employed to determine free vibration and random response.Single-mode free vibration results are compared with existing classicalanalytical solutions to validate the nonlinear modal formulation.Nonlinear random analysis results for cylindrical panels have shown thatthe root mean square of panel deflections could be larger than thoseobtained using the linear structure theory. Time histories, probabilitydistribution functions, power spectral densities, and phase plane plotsare also presented.