基于小波分析的裂纹梁的损伤识别

阐述了一种基于小波变换的含裂纹梁的损伤识别方法,利用含裂纹梁的一阶模态阵型作为小波分析的力学特征信号,识别损伤的位置和大小.利用小波分析系数的模极大值随分析尺度的传播定位损伤的位置,计算针对于损伤频率信号的能量判断损伤的大小.与以前的小波分析方法相比,此方法确定损伤位置的可靠性高,能识别微小的损伤.利用能量守恒定理和小波分析频段细化的能力,裂纹的定量分辨率高.     

简支梁中裂纹参数的识别

结构中的裂纹对系统振动特性将产生一定的影响 ,一般来讲 ,裂纹参数与振动特性的改变之间很难有直接的函数关系 ,通过振动参数的改变来识别裂纹有一定的困难 ,本文经过计算证明 :对于受弯的两端简支梁 ,当裂纹较小时 ,梁的自振频率的变化率与裂纹参数之间存在明确的函数关系 ,利用这一函数关系 ,梁中的裂纹深度与裂纹位置可由自振频率的变化率计算得出。同时证明 :对于简支梁而言 ,单纯利用自振频率无法唯一地确定裂纹位置 ,只能唯一地确定裂纹的深度     

基于压电增益特性进行梁中缺陷的识别

驱动元件PZT片和传感元件PVDF膜粘贴于自由梁表面 ,通过测试压电增益 ,试验获取梁中不同缺陷尺寸下的固有频率。根据固有频率的变化 ,实现缺陷的识别。梁中的缺陷采用等效线性弹簧模拟 ,描绘出不同模态下刚度与缺陷可能位置曲线。根据曲线的交点 ,得出缺陷位置与尺寸。相比于实际的缺陷位置与尺寸 ,自由梁弯曲激振下识别的结果满足一定的精度     

基于压电增益特性进行梁中缺陷的识别

驱动元件PZT片和传感元件PVDF膜粘贴于自由梁表面,通过测试压电增益,试验获取梁中不同缺陷尺寸下的固有频率,根据固有频率的变化,实现缺陷的识别,梁中的缺陷采用等效线性弹簧模拟,描绘出不同模态下刚度与缺陷可能位置曲线,根据曲线的交点,得出缺陷位置与尺寸,相比于实际的缺陷位置与尺寸,自由梁弯曲激振下识别的结果满足一定的精度。     

连续小波变换在梁结构损伤诊断中的应用研究

为了检测出梁中的裂缝或因刚度降低引起的损伤,对有损伤简支梁的振型曲线进行连续小波变换．从小波系数出现模极大值有效地识别损伤的存在以及裂缝位置和刚度下降段的位置。基本振型是用小波变换识别裂缝的最佳振型．用损伤位置处振幅较大的振型曲线来识别最清楚,对有噪声影响的振型曲线同样可以用本文方法进行识别。通过分析和计算获得满意结果．在梁结构损伤诊断中具有较高的应用价值。     

基于裂缝梁动力特性和自振频率的参数敏感性

基于Bernoulli-Euler理论,将开口裂缝梁视为变截面梁,利用模态摄动方法建立了一种求解带任意数量开口裂缝简支梁和连续梁动力特性的半解析分析方法。在等截面无损梁的模态子空间内将裂缝梁的变系数微分方程的求解转化为非线性代数方程组的求解;利用无损梁的自振频率和振型函数摄动求解裂缝梁的模态参数;通过矩形开口裂缝简支梁和两跨连续梁的动力试验验证了笔者方法的准确性;最后,利用开口裂缝梁动力特性的半解析解研究了简支梁和两跨连续梁的自振频率对裂缝尺寸和位置的敏感性。     

基于并联谐振匹配的超声电机阻抗特性

针对目前对超声电机及其驱动系统的阻抗特性测试均局限于单定子和低电压的现状,提出了超声电机及驱动器组成的并联等效电路整体模型,通过电学仿真得到机电系统的阻抗特性。通过傅里叶分解的方法对电机驱动电压和驱动电流信号进行处理,得到超声电机实际工作中的阻抗特性。通过仿真分析和实验可知:机电系统随着驱动频率的降低,阻抗呈单调增大的趋势,同时电机负载扭矩(小于额定扭矩)越大,系统阻抗越小;机电系统谐振匹配频率越小,系统阻抗越小,同时谐振匹配点越靠近电机共振频率,系统阻抗模随着驱动频率的减小,增大得越快。最后,通过机电系统阻抗特性提出超声电机实际工作的理想频率和驱动器的谐振匹配频率均应略大于电机共振频率的频率点。     

含垂直裂纹的简支梁自由振动分析

裂纹将改变梁结构局部刚度,导致其结构模态参数变化,影响结构工作特性。针对这个问题,以简支梁为研究对象,采用有限元分析方法,建立含垂直内部裂纹的简支梁有限元模型,研究垂直内部裂纹的长度和位置对简支梁的固有频率和振型的影响规律。讨论垂直内部裂纹简支梁振动曲率与裂纹长度和位置的关系。结果表明,随着裂纹长度的增加,简支梁的固有频率减小,裂纹简支梁与健康简支梁之间的差异逐渐增加;垂直内部裂纹将导致简支梁在裂纹所在截面附件的局部刚度发生变化,且裂纹的影响区域随着裂纹长度的增加而增加;振型的曲率可以用于识别简支梁垂直内部裂纹位置。     

工字截面梁轨结构裂纹损伤的小波有限元定量诊断

研究工字截面梁轨结构裂纹定量识别中的正反问题,即通过裂纹位置和深度求解结构的固有频率以及利用结构的固有频率,识别裂纹位置和深度.裂纹被看作为一扭转线弹簧,利用工字梁裂纹应力强度因子推导出线弹簧刚度,构造出结构的小波有限元刚度矩阵和质量矩阵,从而获得裂纹结构的前3阶固有频率.通过行列式变换,将反问题求解简化为只含线弹簧刚度一个未知数的一元二次方程求根问题,分别做出以不同固有频率作为输入值时裂纹位置与裂纹深度之间的解曲线,曲线交点预测出裂纹的位置与深度,试验结果验证算法的有效性.     

固贴式薄膜体声波传感器的仿真分析

针对布拉格反射栅的特点,选用ta-C作为高声阻抗材料,Al N作为低声阻抗材料。利用COMSOL Multiphysics对布拉格反射栅薄膜体声波传感器(BAW-SMR)建模并对建立的模型进行固体力学和静电学的有限元仿真分析,得到了传感器的谐振频率、不同布拉格反射栅对数下传感器的导纳特性曲线、阻抗特性曲线以及形变位移图。通过对比分析得出当前条件下布拉格反射栅对数为4对时,传感器的阻抗特性曲线平滑,谐振频率为3. 258 GHz;当布拉格反射栅对数为3对或5对时,阻抗特性曲线存在寄生谐振。针对存在寄生谐振的传感器,选取具有3对布拉格反射栅的传感器进行优化,通过改变传感器上电极的尺寸和厚度来消除寄生谐振,实现了对寄生谐振峰的有效抑制,为进一步的研究提供了理论依据。     

Free vibration analysis of Euler-Bernoulli beam with double cracks

In this paper, the influence of two open cracks on the dynamic behavior of a double cracked simply supported beam is investigated both analytically and experimentally. The equation of motion is derived by using the Hamilton’s principle and analyzed by numerical method. The simply supported beam is modeled by the Euler-Bemoulli beam theory. The crack sections are represented by a local flexibility matrix connecting three undamaged beam segments. The influences of the crack depth and the position of each crack on the vibration mode and the natural frequencies of a simply supported beam are analytically clarified for the single and double cracked simply supported beam. The theoretical results are also validated by a comparison with experimental measurements.     

Closed-form solutions for crack detection problem of Timoshenko beams with various boundary conditions

An analytical approach for crack identification procedure in uniform beams with an open edge crack, based on bending vibration measurements, is developed in this research. The cracked beam is modeled as two segments connected by a rotational mass-less linear elastic spring with sectional flexibility, and each segment of the continuous beam is assumed to obey Timoshenko beam theory. The method is based on the assumption that the equivalent spring stiffness does not depend on the frequency of vibration, and may be obtained from fracture mechanics. Six various boundary conditions (i.e., simply supported, simple–clamped, clamped–clamped, simple–free shear, clamped–free shear, and cantilever beam) are considered in this research. Considering appropriate compatibility requirements at the cracked section and the corresponding boundary conditions, closed-form expressions for the characteristic equation of each of the six cracked beams are reached. The results provide simple expressions for the characteristic equations, which are functions of circular natural frequencies, crack location, and crack depth. Methods for solving forward solutions (i.e., determination of natural frequencies of beams knowing the crack parameters) are discussed and verified through a large number of finite-element analyses. By knowing the natural frequencies in bending vibrations, it is possible to study the inverse problem in which the crack location and the sectional flexibility may be determined using the characteristic equation. The crack depth is then computed using the relationship between the sectional flexibility and the crack depth. The proposed analytical method is also validated using numerical studies on cracked beam examples with different boundary conditions. There is quite encouraging agreement between the results of the present study and those numerically obtained by the finite-element method.     

Crack detection in simply supported beams without baseline modal parameters by stationary wavelet transform

There are significant changes in the vibration responses of cracked structures when the crack depth is significant in comparison to the depth of the structure. This fact enables the identification of cracks in structures from their vibration response data. However when the crack is relatively small, it is difficult to identify the presence of the crack by a mere observation of the vibration response data. A new approach for crack detection in beam-like structures is presented and applied to cracked simply supported beams in this paper. The approach is based on finding the difference between two sets of detail coefficients obtained by the use of the stationary wavelet transform (SWT) of two sets of mode shape data of the beam-like structure. These two sets of mode shape data, which constitute two new signal series, are obtained and reconstructed from the modal displacement data of a cracked simply supported beam. They represent the left half and the modified right half of the modal data of the simply supported beam. SWT is a redundant transform that doubles the number of input samples at each iteration. It provides a more accurate estimate of the variances at each scale and facilitates the identification of salient features in a signal, especially for recognising noise or signal rupture. It is well known that the mode shape of a beam containing a small crack is apparently a single smooth curve like that of an uncracked beam. However, the mode shape of the cracked beam actually exhibits a local peak or discontinuity in the region of damage. Therefore, the mode shape ‘signal’ of a cracked beam can be approximately considered as that of the uncracked beam contaminated by ‘noise’, which consists of response noise and the additional response due to the crack. Thus, the modal data can be decomposed by SWT into a smooth curve, called the approximation coefficient, and a detail coefficient. The difference of the detail coefficients of the two new signal series includes crack information that is useful for damage detection. The modal responses of the damaged simply supported beams used are computed using the finite element method. For real cases, mode shape data are affected by experimental noise. Therefore, mode shape data with a normally distributed random noise are also studied. The results show that the proposed method has great potential in crack detection of beam-like structures as it does not require the modal parameters of an uncracked beam as a baseline for crack detection. The effects of crack size, depth and location, and the effects of sampling interval are examined.     

局部柔度变化在管道裂纹定量识别中的应用

局部柔度可描述结构上出现的裂纹,结构的模态参数将随着裂纹的扩展而改变,利用这一变化可辨识出裂纹发生的位置和深度。由此,建立了一种基于局部柔度变化的管道裂纹定量识别方法。该方法通过将管道结构沿径向离散为一系列依次嵌套的薄壁环,从而求得裂纹引起的局部柔度的变化规律,进而获得局部柔度与管道固有频率的特征关系,绘制裂纹管道的各阶固有频率曲面。采用实测前3阶固有频率去截取相应的固有频率曲面,获得各阶频率等高线,利用其交点定量诊断裂纹的位置与深度。实验结果验证了该方法的有效性。     

利用传递矩阵法对阶梯悬臂梁的裂纹参数识别

基于Bernoulli-Euler梁振动理论,以等效弹簧模拟裂纹引起的局部软化效应,利用传递矩阵法推导阶梯悬臂梁振动频率的特征方程,对于含多个裂纹以及复杂边界条件的阶梯梁,仅需求解4×4的行列式即可获得相应的频率特征方程。直接利用该特征方程,提出两种有效估计裂纹参数的方法———等值线法和目标函数最小化法,并应用两段阶梯悬臂梁的数值算例说明方法的有效性。算例结果表明,只需结构前三阶频率即可识别裂纹位置和深度。应用“零设置”可减小计算频率与理论频率不相等对识别结果的影响。等值线法可以直观给出裂纹位置和裂纹深度参数,目标函数最小化法可给出最优的裂纹参数结果,并且该方法可推广应用到含多个裂纹复杂梁(如非完全固支、弹性支撑等)结构的裂纹参数识别中。     

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.     

Four-beam model for vibration analysis of a cantilever beam with an embedded horizontal crack

As one of the main failure modes, embedded cracks occur in beam structures due to periodic loads. Hence it is useful to investigate the dynamic characteristics of a beam structure with an embedded crack for early crack detection and diagnosis. A new four-beam model with local flexibilities at crack tips is developed to investigate the transverse vibration of a cantilever beam with an embedded horizontal crack; two separate beam segments are used to model the crack region to allow opening of crack surfaces. Each beam segment is considered as an Euler-Bernoulli beam. The governing equations and the matching and boundary conditions of the four-beam model are derived using Hamilton's principle. The natural frequencies and mode shapes of the four-beam model are calculated using the transfer matrix method. The effects of the crack length, depth, and location on the first three natural frequencies and mode shapes of the cracked cantilever beam are investigated. A continuous wavelet transform method is used to analyze the mode shapes of the cracked cantilever beam. It is shown that sudden changes in spatial variations of the wavelet coefficients of the mode shapes can be used to identify the length and location of an embedded horizontal crack. The first three natural frequencies and mode shapes of a cantilever beam with an embedded crack from the finite element method and an experimental investigation are used to validate the proposed model. Local deformations in the vicinity of the crack tips can be described by the proposed four-beam model, which cannot be captured by previous methods.     

基于有限元位移模式的含裂纹梁结构动力学模型

针对裂纹的存在将降低梁的刚度的实际情形,首先根据断裂力学理论,引入裂纹梁因裂纹扩展而释放的应变能表达式,然后根据金属材料的特点,运用有限元位移法建立裂纹梁单元的动力学模型,再在梁单元模型的基础上应用有限元位移法建立裂纹梁结构的动力学方程。研究表明：基于有限元位移模式所建立的动力学方程较好地体现了裂纹梁动态性能与其结构参数和裂纹参数之间的内在关系,反映了裂纹的位置及长度对含裂纹梁结构动态性能的影响,为建立含裂纹梁结构动力学模型提供了一种新的有效方法。最后通过实例对理论分析结果进行了验证。     

Structural damage identification of a cantilever beam using excitation force level control

Most studies in damage identification so far have concentrated on comparing modal parameters of a structure with an open crack with those of an intact structure. In this study, a new damage identification method for beam-like structures with a fatigue crack is proposed, which does not require comparative measurement on an intact structure but several measurements at different level of excitation forces on the cracked structure. The idea comes from the fact that dynamic behavior of a structure with a fatigue crack changes with the level of the excitation force. In other words, a beam with a real fatigue crack would behave as an intact beam at low excitation forces due to the crack closure. The 2nd spatial derivatives of frequency response functions along the longitudinal direction of a beam are used as the sensitive indicator of crack existence. Then, weighting function is employed in the averaging process in frequency domain to account for the modal participation of the differences between the dynamic behavior of beam with a fatigue crack at the low excitation and one at the high excitation. Subsequently, a damage index is defined such that the location and level of the crack may be identified. Finally, it is shown that damage identification method using the proposed damage index is very successful through experiment and finite element analysis.