含轴向运动效应的裂纹梁横向振动频率研究

针对含轴向运动效应开口裂纹梁,借助裂纹梁连续等效刚度模型,将裂纹效应引入轴向运动梁的横向振动方程.应用传递矩阵法推导了求解其振动频率的特征方程,计算得到裂纹和运动参数连续变化情况下梁的一阶和二阶固有频率数值解.对裂纹和轴向运动参数对梁的振动频率的联合影响机理进行了分析,研究表明,对于梁的一阶和二阶固有频率,轴向运动速度和裂纹深度具有耦合作用效应.裂纹加深使得由轴向速度带来的频率衰减加速;同时,速度提升导致由裂纹引起的频率衰减变得更加剧烈.相较于二阶频率,耦合作用效应对于一阶频率表现得更加显著.     

含旋转运动效应裂纹梁横向振动特性的研究

针对开口裂纹作用下旋转运动欧拉-伯努力梁的振动特性进行了研究。文中使用裂纹梁连续等效刚度模型模拟裂纹效应,将含裂纹旋转运动梁视为弯曲刚度沿梁长度方向连续变化的梁,并应用传递矩阵法推导了求解其振动特性的特征方程。考虑不同裂纹深度和位置、不同旋转速度,分析了梁的一阶和二阶固有频率的变化情况。研究结果表明:旋转运动效应和裂纹效应并非独立影响梁的固有频率,两者间具有耦合作用效应;转速提升使由裂纹导致的频率衰减幅度变小,同时裂纹加深使得由速度升高带来的阶频提升更加显著;相比于二阶频率,耦合作用效应对于一阶频率更加显著。     

含多处裂纹梁的振动分析

基于传递矩阵方法,提出了一种计算含有任意处裂纹梁固有频率的新方法。将梁内裂纹模拟为无质量的弯曲弹簧,得到了梁的解析特征方程。通过数值模拟计算,讨论了裂纹数量,以及裂纹位置和裂纹深度对梁的固有频率的影响。通过与文献[4]的计算结果比较,验证了本文方法的有效性。     

传递矩阵法分析约束悬臂裂纹管道失稳临界流速

研究了自由端受线性弹簧支承和扭转弹簧约束的悬臂输流管道在含有圆周非贯穿裂纹时的失稳临界流速;根据梁模型模态函数的一般表达式和裂纹处的关联式以及传递矩阵法推导出含裂纹梁的模态函数;根据特征方程具体分析了裂纹位置、裂纹深度、裂纹圆周角等参数对系统失稳临界流速的影响,并进行了数值仿真分析。结果表明:由于裂纹的存在,系统的失稳临界流速下降,动态失稳临界流速下降的速率和幅值均比静态失稳临界流速下的大;临界流速与裂纹位置、深度和裂纹圆周角等参数密切相关,特别是对颤振失稳临界流速的影响更明显,在裂纹位置、裂纹非贯穿圆周角、裂纹深度等参数影响下,管道的失稳形态将从屈曲失稳转变为颤振失稳。     

含裂纹梁非线性静动力特性及简化动力学建模Static and dynamic behaviour of cracked beam and simplified dynamic model

主要研究裂纹对梁结构动力特性的影响规律,进而为含裂纹梁结构状态监测提供理论依据。首先,对裂纹影响区域进行分析,建立含裂纹梁二维接触非线性有限元模型,阐明含裂纹梁具有拉压不同刚度的静力特性;其次,通过对机理模型的分析,指出拉压不同刚度会引起轴向与弯曲的耦合振动;然后,通过非线性动力学分析方法研究其动力特性,观察到含裂纹梁在冲击荷载下会产生轴向与弯曲的耦合振动现象,并指出这种轴向与弯曲耦合振动的一个重要特征是轴向振动频谱图中含有弯曲振动基频的两倍频成分;最后,通过引入非线性弹簧建立一种新颖的含裂纹梁简化动力学模型,通过与精细有限元分析对比,验证了模型的合理性。该简化动力学模型将接触非线性问题转换为材料非线性问题,避免了费时的接触非线性动力学求解过程。     

含裂纹梁非线性静动力特性及简化动力学建模

主要研究裂纹对梁结构动力特性的影响规律,进而为含裂纹梁结构状态监测提供理论依据。首先,对裂纹影响区域进行分析,建立含裂纹梁二维接触非线性有限元模型,阐明含裂纹梁具有拉压不同刚度的静力特性;其次,通过对机理模型的分析,指出拉压不同刚度会引起轴向与弯曲的耦合振动;然后,通过非线性动力学分析方法研究其动力特性,观察到含裂纹梁在冲击荷载下会产生轴向与弯曲的耦合振动现象,并指出这种轴向与弯曲耦合振动的一个重要特征是轴向振动频谱图中含有弯曲振动基频的两倍频成分;最后,通过引入非线性弹簧建立一种新颖的含裂纹梁简化动力学模型,通过与精细有限元分析对比,验证了模型的合理性。该简化动力学模型将接触非线性问题转换为材料非线性问题,避免了费时的接触非线性动力学求解过程。     

不确定边界条件下悬臂梁裂纹参数识别方法研究

基于Bernoulli-Euler梁振动理论,以等效弹簧来模拟裂纹引起的局部软化效应和由非完全固支边界条件引起的转角效应。推导了悬臂梁在不确定边界条件下确定其振动频率的特征方程,直接利用该特征方程,提出一种有效估计裂纹参数的优化方法,通过计算测量频率和理论频率之间的误差目标函数最小化即可识别裂纹参数-裂纹位置和深度。最后,应用两个实例-理想固支边界条件下和非完全固支边界条件下的悬臂梁实验来说明本文方法的有效性。实验结果表明:只需梁结构前三阶频率即可识别裂纹位置和深度。对于理想边界条件下的裂纹参数识别,在测量频率存在小误差情况下,该方法仍能给出比较满意的结果,对于非完全固支边界条件下的裂纹参数识别,利用本文方法能得到比Narkis的方法更精确的裂纹位置识别结果。同时本文方法还能给出比较满意的裂纹深度识别结果。     

含裂纹梁参数的谐响应识别

主要研究含裂纹梁在简谐激励作用下的动力特性,提出一种依据幅值变化对裂纹参数进行识别的新方法。首先,在振动过程中考虑裂纹的呼吸特性,以悬臂梁为例建立含裂纹梁的二维有限元模型,指出在一般激励频率下,其对应的幅值均是明显信号,可用来描述裂纹梁的动力特性。其次,当激励频率分别取无裂纹梁一阶频率的1/4和二阶频率的1/4时,幅值随裂纹参数的变化明显不同,可依据响应幅值的变化对裂纹参数进行识别。然后,利用曲面拟合技术绘出幅值变化曲面,对未知参数的裂纹进行识别,验证了该方法的有效性,并归纳出利用幅值变化对任意裂纹参数进行识别的基本步骤。最后,针对无裂纹梁频率计算可能存在误差的情况,分析识别方法的鲁棒性,结果显示即使最大误差为10%,该方法也能对裂纹参数进行准确识别。     

基于连续抗弯刚度模型的裂纹梁动力指纹损伤识别

基于断裂力学的应变能概念,建立裂纹简支梁连续抗弯刚度模型,提出基于连续抗弯刚度模型的裂纹梁动力指纹损伤识别方法。借助有限差分方法、Mathematica软件编程求解裂纹梁动力指纹(固有频率、振型、振型曲率),通过与铰接法及FEM法对不同裂纹工况下裂纹梁固有频率的数值计算比较及误差分析,成功验证了方法的有效性,并探讨了裂纹参数对动力指纹的影响。算例分析表明:连续抗弯刚度模型对裂纹参数变化敏感,裂纹梁抗弯刚度在裂纹处呈现最小值,邻近区域抗弯刚度受裂纹影响明显;裂纹简支梁的动力指纹随裂纹参数的变化呈跨中对称变化;裂纹梁结构的固有频率与振型曲率耦合的识别方法可以较好地识别出梁结构裂纹参数,识别误差为2.23%,证实了基于动力指纹检测裂纹损伤的可行性。本文结果为梁结构裂纹的检测提供了重要的理论依据,有广泛的实用与理论研究前景。     

含裂纹一维欧拉梁的裂纹无效位置分析

基于集中柔度模型,建立了含裂纹一维欧拉梁的频率方程,以此为基础探讨了裂纹无效位置的求解方法。数值计算结果显示,裂纹无效位置和位移振型节点并不一致。进一步的理论推导证明裂纹无效位置就是曲率模态振型的零点位置,从曲率和力学性能基本参数的关系分析,这一结论是合理的。本文结论对于实验、测试方案设计有指导意义。     

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.     

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.     

Fourier and wavelet analyses for fatigue assessment of concrete beams

We investigate damage detection in a simply-supported pre-stressed beam. A crack was propagated by fatigue loads, which were applied up to two million cycles. Both fast Fourier transform (FFT) and continuous wavelet transform (CWT) are used in the analysis of the structural response to impulse loads. The acceleration response of the full-scale beam was measured each time a certain number of cycles of fatigue loads were applied. The results of this study show that both methods can clearly identify the crack growth induced by fatigue loads. The natural frequencies found by FFT are sensitive to the crack progression. The results from the CWT analysis show a clear difference in structural responses between the initial and damaged states of the structure. The response accelerations are de-noised by a soft-thresholding method before they are analyzed by CWT. In addition to the frequency components, the CWT shows the moment in time when particular frequencies occur. Therefore, wavelet analysis has the potential of becoming an effective tool for damage detection and health monitoring of structures for which the natural frequencies are irregularly changing. As the crack grows, the magnitude of ridges obtained by CWT analysis decreases significantly, which indicates the reduction in structural stiffness.     

辅助质量块—单裂纹悬臂梁耦合系统固有频率的理论研究及其应用

论文研究了辅助质量块—单裂纹悬臂梁耦合系统的固有频率,用无缺陷悬臂梁固有振型叠加一个多项式来近似拟合含单裂纹悬臂梁的振型,由动力学方法推导了辅助质量块—单裂纹悬臂梁系统的固有频率方程的解析形式,系统频率随着质量块在梁上位置改变而改变,即可得到固有频率曲线,此频率曲线包含了缺陷信息,因此可对固有频率曲线进行平稳小波变换来识别梁上的缺陷.同时用有限元计算结果对上述固有频率理论推导进行验证,有限元结果与论文理论推导结果相一致.最后论文数值计算了质量块大小、缺陷深度、位置等因素对系统固有频率的影响,也探讨了平稳小波变换用于识别损伤,结果验证了该理论推导的可靠性和损伤识别的准确性.     

带裂纹旋转柔性梁系统的刚柔耦合动力学研究

对具有刚柔耦合效应的带裂纹旋转柔性梁进行建模和动力学特性分析研究。采用晶格弹簧离散模型,利用无质量弹簧模拟梁上裂纹,通过考虑梁变形的二阶耦合项建立了带裂纹旋转柔性梁系统的一次近似耦合动力学控制方程。数值计算结果表明,裂纹的存在会使旋转柔性梁的固有频率降低,并且随着梁转速的增大,这种降低效应呈减弱趋势;值得注意的是,裂纹梁的固有频率与裂纹处的弯矩具有正相关关系。此外,裂纹的存在不仅会使转速变化阶段梁的末端位移响应增大,还会对转速稳定后梁的末端振荡产生显著的影响。     

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.     

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.     

A NEW APPROACH TO FREE VIBRATION ANALYSIS OF A BEAM WITH A BREATHING CRACK BASED ON MECHANICAL ENERGY BALANCE METHOD

In this paper, a new approach to free vibration analysis of a cracked cantilever beam is proposed. By considering the effect of opening and closing the crack during the beam vibration, it is modeled as a fatigue crack. Also, local stiffness changes at the crack location are considered to be a nonlinear amplitude-dependent function and it is assumed that during one half a cycle, the frequencies and mode shapes of the beam vary continuously with time. In addition, by using the experimental tests, it is shown that the local stiffness at the crack location varies continuously between the two extreme values corresponding to the fully closed and the fully open cases of the crack. Then, by using the mechanical energy balance the dynamic response of the cracked beam is obtained at every time instant. The results show that for a specific crack depth, by approaching the crack location to the fixed end of the beam, more reduction in the fundamental frequency occurs. Furthermore, for a specific crack location, the fundamental frequency diminishes and the nonlinearity of the system increases by increasing the crack depth. In order to validate the results, the variations of the fundamental frequency ratio against the crack location are compared with experimental results.