Winkler地基上裂纹Timoshenko梁的弯曲解析解

将梁中裂纹等效为无质量线性扭转弹簧,研究了温克勒(Winkler)基础上具有任意开裂纹数目Timoshenko梁的弯曲变形．利用Delta广义函数和Heaviside函数以及Laplace变换,给出了Winkler基础上具有任意裂纹数目Timoshenko梁弯曲变形的解析通解．在此基础上,研究了Winkler基础上受均布荷载作用简支裂纹Timoshenko梁的弯曲变形,数值分析了裂纹数目和位置以及深度、梁剪切刚度和基础反力系数等对裂纹Timoshenko梁弯曲变形的影响．结果表明：在裂纹处,梁挠度存在尖点,转角存在跳跃;梁挠度随着裂纹深度和数目的增加而增加,但横截面弯矩和转角减小;随着基础反力系数的增加,梁挠度、弯矩和转角减小;随着剪切刚度的增加,梁挠度减少,弯矩和转角增大．     

考虑界面滑移效应的组合裂纹梁弯曲解析解

将上部子梁的裂纹等效为线性扭转弹簧,考虑组合梁连接面的滑移位移,建立了以组合裂纹梁挠度和滑移位移为基本未知量的组合裂纹梁弯曲变形一维数学模型．利用Laplace变换及其逆变换,给出了组合裂纹梁弯曲变形一维数学模型的解析通解．在此基础上,研究了均布载荷作用下简支组合裂纹梁的弯曲变形问题,数值分析了连接面剪切刚度、裂纹深度、数目和位置等参数对组合裂纹梁弯曲变形的影响,结果表明：在裂纹处,组合裂纹梁挠度曲线存在尖点,而横截面转角曲线存在跳跃,且随着裂纹数目和深度的增加,挠度和横截面转角跳跃值增大;随着连接面剪切刚度的增加,挠度和横截面转角减小,并最终趋于定值．并且,随着组合梁跨高比的增加,连接面剪切刚度对梁挠度影响逐渐减弱．     

考虑轴力二阶效应悬臂梁的支承及裂纹参数识别

建立了轴向压力作用下悬臂裂纹梁边界支承和裂纹损伤程度识别方法．首先,将悬臂梁边界非完整支承等效为竖向和扭转弹簧、梁中开裂纹等效为内部扭转弹簧,利用Laplace变换,得到了边界弹性支承、考虑轴向压力二阶效应、具有任意裂纹数目Euler-Bernoulli悬臂梁弯曲挠度的解析解．其次,提出了边界弹性支承弹簧柔度和裂纹等效扭转弹簧柔度的识别方法．最后,通过数值试验,考察了轴向压力,裂纹深度以及测量误差等对识别结果的影响,说明了本文考虑轴向压力二阶效应的悬臂梁边界支承弹簧柔度及裂纹等效扭转弹簧柔度识别方法的适用性和可靠性,结果表明：相比于应变测量误差,挠度测量误差对裂纹损伤程度识别结果影响更加敏感,且轴向压力对裂纹损伤程度识别影响较小,因此,应严格控制挠度的测量误差．同时,边界支承扭转弹簧柔度的识别误差大于其竖向弹簧柔度识别误差．这些结果为实际工程中边界非完整支承悬臂裂纹梁的参数识别提供了指导．     

Pasternak地基上连续裂纹Euler梁的弯曲

基于梁中开裂纹的等效线性扭转弹簧模型,并将梁跨内支座约束解除,代之以未知约束反力,给出了Pasternak地基上具有任意裂纹数目的多跨连续梁静力弯曲的解析通解．在此基础上,利用梁边界条件及跨内支座处挠度约束条件,得到了Pasternak地基上两等跨简支连续裂纹梁的弯曲挠度,数值考察了地基反力系数、裂纹数目、深度和位置等参数对连续裂纹梁弯曲变形的影响,结果表明：在裂纹处,Pasternak地基上连续裂纹Euler梁挠度存在尖点,而横截面转角存在跳跃,并且随着裂纹深度的增加和地基反力系数的减小,裂纹梁挠度和转角增加;当裂纹深度较小时,裂纹位置对连续地基裂纹梁挠度的影响有限,但随着裂纹深度的增加,裂纹位置对连续地基裂纹梁挠度影响逐渐显著．这些结论对地基梁健康检测和安全评估具有一定指导意义．     

纤维增强聚合物加固黏弹性Timoshenko木梁的弯曲变形

假定木梁和纤维增强聚合物(FRP)布分别服从标准线性固体黏弹性本构和弹性本构,且FRP布与木梁紧密粘贴,建立了FRP布加固黏弹性矩形截面Timoshenko木梁弯曲变形的控制方程.在此基础上,利用Laplace变换及其逆变换,给出了突加集中和均布载荷作用下FRP布加固简支黏弹性Timoshenko木梁弯曲变形的轴向位移、转角和挠度解析表达式.根据花旗松(DF)木材标准线性固体本构的材料参数,数值分析了芳纶纤维聚合物(AFRP)含量和梁跨高比对AFRP布加固黏弹性Timoshenko DF梁弯曲蠕变行为的影响.结果表明:Timoshenko DF梁的弯曲蠕变效应显著,AFRP布加固可有效减小Timoshenko DF梁的蠕变挠度;随着DF梁跨高比减小或AFRP含量的提高,AFRP布加固Timoshenko DF梁的最大压应力和最大拉应力减小.     

饱和多孔弹性Timoshenko梁的大挠度分析

基于微观不可压饱和多孔介质理论和弹性梁的大挠度变形假设,考虑梁剪切变形效应,在梁轴线不可伸长和孔隙流体仅沿轴向扩散的限定下,建立了饱和多孔弹性Timoshenko梁大挠度弯曲变形的非线性数学模型.在此基础上,利用Galerkin截断法,研究了两端可渗透简支饱和多孔Timoshenko梁在突加均布横向载荷作用下的拟静态弯曲,给出了饱和多孔 Timoshenko梁弯曲变形时固相挠度、弯矩和孔隙流体压力等效力偶等随时间的响应.比较了饱和多孔Timoshenko梁非线性大挠度和线性小挠度理论以及饱和多孔 Euler-Bernoulli梁非线性大挠度理论的结果,揭示了他们间的差异,指出当无量纲载荷参数q＞l0时,应采用饱和多孔Timoshenko梁或Euler-Bernoulli梁的大挠度数学模型进行分析,特别的,当梁长细比λ＜30时,应采用饱和多孔Timoshenko梁大挠度数学模型进行分析.     

基于裂纹诱导弦挠度的简支外伸梁裂纹损伤识别

基于梁横向开裂纹的线性扭转弹簧模型,给出了具有任意裂纹数目的简支外伸梁弯曲挠度的显式解析解,研究了集中载荷作用下简支外伸梁裂纹诱导弦挠度函数的性质,给出了裂纹位置和裂纹等效扭转弹簧柔度的近似表达式,从而实现了梁横向裂纹位置及裂纹损伤程度的识别．在此基础上,为利用裂纹梁的测量挠度识别裂纹损伤,提出了分段线性函数的最佳拟合法,实现了简支外伸梁裂纹的损伤参数识别．通过数值试验验证了该识别方法的适用性和可靠性,考察了识别结果对梁挠度测量误差和裂纹深度的敏感性,结果表明随着挠度测量误差的增大,裂纹损伤参数识别误差增大,但裂纹损伤识别方法具有较强的鲁棒性,在工程实际中具有一定的应用性．     

基于裂纹扭转弹簧模型的Timoshenko裂纹梁动力特性分析

忽略裂纹对梁剪切变形的影响,基于开裂纹的等效扭转弹簧模型,建立了Timoshenko裂纹梁动力弯曲的控制方程,得到了一种新的裂纹梁动力弯曲控制方程的求解方法,得出了具有任意条裂纹Timoshenko梁自振模态的统一显式表达式。数值分析了简支、悬臂、两端固支Timoshenko裂纹梁的自振频率和振动模态,考察了裂纹数目和裂纹深度等因素对裂纹梁动力特性的影响。结果表明:随着裂纹数目和深度的增加,裂纹梁的自振频率减小,且当裂纹较深时,裂纹深度对自振频率的影响显著;裂纹梁的挠度模态曲线和转角模态曲线在裂纹处分别呈现尖点和跳跃现象,且尖点效应和转角跳跃随裂纹深度的增加而愈加明显。另外,当裂纹处的弯矩为零时,裂纹对梁的自振频率和振动模态没有影响。这些结果可对梁的安全性评估及裂纹损伤检测提供理论指导。     

悬臂梁中开闭裂纹的损伤识别

利用裂纹诱导弦挠度函数,建立了悬臂Euler-Bernoulli中开闭裂纹位置、深度、初始张开角等损伤参数的识别方法.为此,首先将梁中开闭裂纹等效为单向扭转弹簧,给出了考虑裂纹缝隙效应的裂纹梁等效抗弯刚度,并得到悬臂Euler-Bernoulli开闭裂纹梁弯曲挠度的显式闭合解及裂纹诱导弦挠度函数,证明了裂纹诱导弦挠度的...     

基于等效弹簧模型的裂纹Euler-Bernoulli梁弯曲变形分析

考虑裂纹的缝隙效应,研究了开闭裂纹Euler-Bernoulli梁的弯曲变形．首先,将裂纹等效为内部旋转弹簧,利用广义函数,给出了考虑裂纹缝隙影响的Euler-Bernoulli梁的等效抗弯刚度,推导了具有任意数目开闭裂纹梁弯曲变形的显式通解．在此基础上,研究了均布载荷作用下上侧单裂纹简支梁以及裂纹处承受集中力和集中力偶共同作用的固支梁的弯曲变形,分析了梁长细比、裂纹深度和位置以及载荷等对裂纹开闭状态和梁弯曲变形的影响。结果表明：梁挠度分布在裂纹处存在尖点,而转角分布存在跳跃;梁挠度与载荷的响应关系一般为双折线形式,分别对应于裂纹的张开和闭合状态;且裂纹张开时,裂纹梁的柔度随着梁长细比的增加和裂纹深度的减小而减小。这些结果对梁裂纹无损检测具有指导意义．     

Bending of Timoshenko beam with effect of crack gap based on equivalent spring model

Considering the effect of crack gap,the bending deformation of the Timoshenko beam with switching cracks is studied.To represent a crack with gap as a nonlinear unidirectional rotational spring,the equivalent flexural rigidity of the cracked beam is derived with the generalized Dirac delta function.A closed-form general solution is obtained for bending of a Timoshenko beam with an arbitrary number of switching cracks.Three examples of bending of the Timoshenko beam are presented.The influence of the beam’s slenderness ratio,the crack’s depth,and the external load on the crack state and bending performances of the cracked beam is analyzed.It is revealed that a cusp exists on the deflection curve,and a jump on the rotation angle curve occurs at a crack location.The relation between the beam’s deflection and load is bilinear,each part corresponding to an open or closed state of crack,respectively.When the crack is open,flexibility of the cracked beam decreases with the increase of the beam’s slenderness ratio and the decrease of the crack depth.The results are useful in identifying non-destructive cracks on a beam.     

Nonlinear dynamic response of an edge-cracked functionally graded Timoshenko beam under parametric excitation

This paper investigates the nonlinear flexural dynamic behavior of a clamped Timoshenko beam made of functionally graded materials (FGMs) with an open edge crack under an axial parametric excitation which is a combination of a static compressive force and a harmonic excitation force. Theoretical formulations are based on Timoshenko shear deformable beam theory, von Karman type geometric nonlinearity, and rotational spring model. Hamilton’s principle is used to derive the nonlinear partial differential equations which are transformed into nonlinear ordinary differential equation by using the Least Squares method and Galerkin technique. The nonlinear natural frequencies, steady state response, and excitation frequency-amplitude response curves are obtained by employing the Runge–Kutta method and multiple scale method, respectively. A parametric study is conducted to study the effects of material property distribution, crack depth, crack location, excitation frequency, and slenderness ratio on the nonlinear dynamic characteristics of parametrically excited, cracked FGM Timoshenko beams.     

基于裂纹附加模态Timoshenko梁的裂纹损伤识别

将梁中横向裂纹等效为无质量扭转弹簧，并忽略其对梁剪切变形的影响，得到的具有任意裂纹数目Timoshenko 梁自振模态的统一显示解析表达式．将裂纹梁的自振模态分为基本模态和裂纹附加模态，利用最小二乘拟合，建立了利用裂纹附加模态函数的梁裂纹损伤识别方法．通过数值模拟开展了简支单裂纹梁以及悬臂和固支双裂纹梁等的裂纹损伤识别，考察了测量误差对损伤识别的影响，数值结果表明本文所提出的裂纹损伤识别方法对裂纹位置的识别精度高于对裂纹损伤程度的识别精度；随着测量误差的增加，裂纹位置及裂纹损伤程度的识别误差增加，但仍在可接受的范围内，故该裂纹损伤识别方法在实际工程中具有一定的应用价值．     

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.     

纤维增强聚合物布加固裂纹木梁的稳定性

梁中横向裂纹等效为无质量内部转动弹簧，假定纤维增强聚合物(FRP)布与梁表面紧密粘贴，建立了考虑轴向压力二阶效应FRP 布加固裂纹梁线性弯曲的控制方程，并得到其显式解析通解．在此基础上，研究了FRP加固简支裂纹木梁的稳定性，通过数值求解方程，分析了纤维增强聚合物(CFRP)布含量、裂纹深度和位置以及数量等因素对CFRP 布加固简支裂纹杉木梁临界载荷的影响，结果表明：CFRP 加固可明显减小裂纹深度和数量等对裂纹杉木梁临界载荷的影响，且裂纹处弯矩较大或裂纹较深时加固效应愈加显著；CFRP 加固裂纹木梁临界载荷随CFRP 布加固层含量的增加而增加，但当CFRP 布含量达到一定值后，进一步增加CFRP 含量对CFRP加固裂纹梁临界载荷提高并不明显．     

Detection of crack location using cracked beam element method for structural analysis

The local flexibility introduced by cracks changes the dynamic behavior of the structure and, by examining this change, crack position and magnitude can be identified. In order to model the structure for FEM analysis, a special finite element for a cracked Timoshenko beam is developed. Shape functions for rotational and translational displacements are used to obtain the consistent mass matrix for the cracked beam element. Effect of the crack on the stiffness matrix and consistent mass matrix is investigated. Proposed is a procedure for identifying cracks in structures using modal test data.     

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.