含裂纹体蠕变断裂理论及其应用研究

评介了蠕变断裂力学研究概况．着重论述含裂纹材料与结构的蠕变断裂、蠕变损伤、蠕变疲劳裂纹扩展和寿命预估等方面研究的近期进展．从中介绍蠕变断裂力学的研究途径、方法及其广阔的工程应用前景      

含双裂纹圆截面悬臂梁的损伤识别研究

裂纹的萌生和扩展直接影响构件的振动响应,对构件的安全可靠性具有重要影响.本文以圆截面悬臂梁为对象,结合转角模态振型和模态频率等高线,研究了一种双裂纹识别技术.首先,基于应力强度因子和卡氏定理推导了无裂纹梁单元和含裂纹梁单元的刚度矩阵;在此基础上,建立了含裂纹圆截面悬臂梁的有限元动力学方程;然后,结合裂纹对梁转角模态振型和模态频率的影响,提出了双裂纹识别策略.最后,通过算例讨论了双裂纹识别策略的可行性.结果表明,圆截面悬臂梁的模态转角在裂纹位置出现突变,裂纹深度越大转角突变值越大;将识别出的裂纹位置作为已知参数,通过模态频率等高线法,可以准确地识别出双裂纹的深度.     

端头带有质量块的悬臂梁在冲击载荷下的剪切失效

以飞射物撞击构件引起破坏为工程背景,研究端头带有质量块的悬臂梁受到冲击载荷作用后发生剪切失效的可能性。分析表明:在初始速度间断面上是否发生失效取决于无量纲初始动能和质量块尺寸与梁厚之比,而与梁的长度无关;质量块的转动惯量对于剪切失效具有不可忽略的影响。     

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。     

弹性非保守系统的拟固有频率变分原理及其应用

本文在文献[1]的基础上,进一步考虑系统的运动性态,提出并证明了弹性非保守系统自激振动的拟固有频率变分原理,然后利用这些变分原理计算了几个典型的非保守系统的稳定性问题.结果表明本文提出的变分原理不仅是分析非保守系统颤振问题的一个强有力的工具,而且还为建立一些近似方法提供了理论依据.     

耦合故障转子系统中裂纹信息的诊断

旋转机械中,当裂纹与其他故障并存形成耦合故障时,裂纹信息往往被其他故障的信息所掩盖,从而难以从信号特征上诊断出裂纹故障。利用裂纹故障引起的等效外加弯矩特性,采用基于模型的故障诊断方法,可以诊断出耦合故障中的裂纹故障信息。以两种最常见的耦合故障—裂纹碰摩耦合故障、裂纹松动耦合故障为例,采用基于模型的诊断方法诊断耦合故障中的裂纹信息,取得了比较好的效果,并进行试验来验证理论结果。     

耦合离散流体理论的差分格式及其应用

求解Navier-Stokes方程组,一直是粘性流动计算的主导途径。但在计算中,都是在一定的网格单元上进行离散,而对不同的离散单元,流动的特征并不相同。本文通过离散单元上网格雷诺数的变化分析,采用耦合离散流体理论（CDFT）差分格式,对向后台阶底部超声速流动问题进行数值模拟,得到了满意的结果。     

双悬臂梁结构的应用研究

分析了双悬臂梁结构的工作特性，利用其端部在小位移下近似发生平动的特点，研制出了双悬臂结构应变测量传感器，并给出了该传感器与应变片的对比试验结果，其最大误差小于1．7％，该传感器可广泛应用于各种建筑结构试验时的应变测量。     

任意斜裂纹转子的耦合振动研究

对包含不同类型裂纹(横裂纹、横-斜裂纹以及任意斜裂纹)的转子的耦合振动进行研究,以揭示裂纹转子在不同方向上刚度参数的变化规律及其交叉耦合机理,特别是由此引发的振动特征.对于包含不同类型裂纹的转子轴段,采用六自由度Timoshenko梁单元模型对其进行单元建模,并基于应变能理论推导计算柔度参数和刚度矩阵.在此基础上,采用纽马克-β数值算法求解裂纹转子的运动方程,获得裂纹转子在单故障或多故障激励(不平衡激励、扭转激励或不平衡激励加扭转激励)作用下的耦合振动响应,进而分析耦合振动谱特征.与横裂纹和横-斜裂纹相比,任意斜裂纹使转子刚度矩阵的交叉耦合效应更显著,导致转子发生更强烈的弯-扭耦合甚至是纵-弯-扭耦合振动.无论是在不平衡激励还是扭转激励作用下,弯曲振动与扭转振动幅度都更大.而且,包含不同类型裂纹的转子的耦合振动特征频率,例如旋转基频与二倍频、扭转激励频率及其边带成分的幅值,对裂纹面方向角具有不同的敏感性.所得的这些研究结果,可以为转子裂纹的特征参数辨识与诊断提供理论依据.     

任意斜裂纹转子的耦合振动研究

对包含不同类型裂纹(横裂纹、横-斜裂纹以及任意斜裂纹)的转子的耦合振动进行研究,以揭示裂纹转子在不同方向上刚度参数的变化规律及其交叉耦合机理,特别是由此引发的振动特征.对于包含不同类型裂纹的转子轴段,采用六自由度Timoshenko梁单元模型对其进行单元建模,并基于应变能理论推导计算柔度参数和刚度矩阵.在此基础上,采用纽马克-β数值算法求解裂纹转子的运动方程,获得裂纹转子在单故障或多故障激励(不平衡激励、扭转激励或不平衡激励加扭转激励)作用下的耦合振动响应,进而分析耦合振动谱特征.与横裂纹和横-斜裂纹相比,任意斜裂纹使转子刚度矩阵的交叉耦合效应更显著,导致转子发生更强烈的弯-扭耦合甚至是纵-弯-扭耦合振动.无论是在不平衡激励还是扭转激励作用下,弯曲振动与扭转振动幅度都更大.而且,包含不同类型裂纹的转子的耦合振动特征频率,例如旋转基频与二倍频、扭转激励频率及其边带成分的幅值,对裂纹面方向角具有不同的敏感性.所得的这些研究结果,可以为转子裂纹的特征参数辨识与诊断提供理论依据.     

Non-linear dynamics of a cracked cantilever beam under harmonic excitation

The presence of cracks in a structure is usually detected by adopting a linear approach through the monitoring of changes in its dynamic response features, such as natural frequencies and mode shapes. But these linear vibration procedures do not always come up to practical results because of their inherently low sensitivity to defects. Since a crack introduces non-linearities in the system, their use in damage detection merits to be investigated. With this aim the present paper is devoted to analysing the peculiar features of the non-linear response of a cracked beam.The problem of a cantilever beam with an asymmetric edge crack subjected to a harmonic forcing at the tip is considered as a plane problem and is solved by using two-dimensional finite elements; the behaviour of the breathing crack is simulated as a frictionless contact problem. The modification of the response with respect to the linear one is outlined: in particular, excitation of sub- and super-harmonics, period doubling, and quasi-impulsive behaviour at crack interfaces are the main achievements. These response characteristics, strictly due to the presence of a crack, can be used in non-linear techniques of crack identification.     

Non-linear vibrations of cantilever beams with feedback delays

A comprehensive investigation of the effect of feedback delays on the non-linear vibrations of a piezoelectrically actuated cantilever beam is presented. In the first part of this work, we examine the linear and non-linear free responses of a beam subjected to a delayed-acceleration feedback. We show that the trivial solution loses stability via a Hopf bifurcation leading to limit-cycle oscillations. We analyze the stability of the dynamic response in the postbifurcation, close to the stability boundaries by examining the nature of the Hopf bifurcation and away from the stability boundaries by using the method of harmonic balance and Floquet theory. We find that, increasing the gain for certain feedback delays may culminate in quasiperiodic and chaotic oscillations of the beam.In the second part, we analyze the effect of feedback delays on a beam subjected to a harmonic base excitations. We find that the nature of the forced response is largely defined by the stability of the trivial solutions of the unforced response. For stable trivial solutions (i.e., inside the stability boundaries of the trivial solutions), the homogeneous response emanating from the feedback diminishes, leaving only the particular solution resulting from the external excitation. In this case, delayed feedback acts as a vibration absorber. On the other hand, for unstable trivial solutions, the response contains two co-existing frequencies. Depending on the excitation amplitude and the commensurability of the delayed-response frequency to the excitation frequency, the response is either periodic or quasiperiodic.     

Effect of matrix cracking in cross-ply ceramic matrix composite beams on their mechanical properties and natural frequencies

The present paper illustrates the effect of matrix cracks in longitudinal and transverse layers of cross-ply ceramic matrix composite (CMC) beams on their mechanical properties and vibration frequencies. Even in a geometrically linear problem considered in the paper, the physical non-linearity is introduced by matrix cracks and interfacial fiber-matrix friction in longitudinal layers. A closed-form solution for mechanical properties of a cross-ply CMC beam with matrix cracks is developed in the paper. The frequency of free vibrations of a simply supported beam is derived as a function of the amplitude, accounting for the effect of matrix cracks. As shown in the paper, the prediction of the natural frequencies of cross-ply CMC beams with matrix cracks in both longitudinal and transverse layers is possible using simple, yet accurate, approximate equations.     

An evolutionary search technique to determine natural frequencies and mode shapes of composite Timoshenko beams

Natural frequencies and mode shapes of composite Timoshenko beams are determined by a diversity guided evolutionary algorithm (DGEA) with different boundary conditions. After applying boundary conditions, frequency equation is obtained in determinant form. Then, natural frequencies and consequently mode shapes are obtained using DGEA where the absolute value of determinant is the subject of optimization. Advantages of employing DGEA are: first, all natural frequencies are produced in a simple run, second, its simplicity for implementation and third, the procedure is not computationally prohibitive. Results clearly show the applicability of the proposed method for obtaining natural frequencies and mode shapes.     

Vibration control of a transversely excited cantilever beam with tip mass

The problem of controlling the vibration of a transversely excited cantilever beam with tip mass is analyzed within the framework of the Euler–Bernoulli beam theory. A sinusoidally varying transverse excitation is applied at the left end of the cantilever beam, while a payload is attached to the free end of the beam. An active control of the transverse vibration based on cubic velocity is studied. Here, cubic velocity feedback law is proposed as a devise to suppress the vibration of the system subjected to primary and subharmonic resonance conditions. Method of multiple scales as one of the perturbation technique is used to reduce the second-order temporal equation into a set of two first-order differential equations that govern the time variation of the amplitude and phase of the response. Then the stability and bifurcation of the system is investigated. Frequency–response curves are obtained numerically for primary and subharmonic resonance conditions for different values of controller gain. The numerical results portrayed that a significant amount of vibration reduction can be obtained actively by using a suitable value of controller gain. The response obtained using method of multiple scales is compared with those obtained by numerically solving the temporal equation of motion and are found to be in good agreement. Numerical simulation for amplitude is also obtained by integrating the equation of motion in the frequency range between 1 and 3. The developed results can be extensively used to suppress the vibration of a transversely excited cantilever beam with tip mass or similar systems actively.     

Improved natural frequencies for plates with a free edge

A simple correction formula is developed for the square of natural frequencies of plates with a free edge. The theory is applied to torsional vibrations of a long plate strip and to vibrations of a circular plate with a free edge and a number of nodal diameters. The paper concludes with the remark that the theory may be extended mutatis mutandis to vibrations of shells with a free edge.     

A Simplified Quadrature Element Method to compute the natural frequencies of multispan beams and frame structures

In this paper a new version of the Modified Quadrature Element Method (MQEM) is proposed. Like MQEM, the proposed method overcomes the drawback of the distance δ of the Quadrature Element Method (QEM) without introducing further degrees of freedom at the ends of the element as in the Differential Quadrature Element Method (DQEM), but it makes the computational cost of the stiffness matrix (and the mass matrix) lighter and uses a general procedure to generate the sampling points distribution. The method here presented has been applied to compute the fundamental frequencies of some structures.     

Transient vibrations of a fractional Zener viscoelastic cantilever beam with a tip mass

Meccanica - The presented work concerns the kinematically excited transient vibrations of a cantilever beam with a mass element fixed to its free end. The Euler–Bernoulli beam theory and the...     

Calculation of higher natural frequencies of simply supported elastic composite beams using Riccati matrix method

A composite beam is composed of an upper slab and a lower beam connected at the interface by shear transmitting studs. In this paper, an improved and efficient numerical model for the calculation of higher natural frequencies of an elastic composite beam is presented. The numerical model uses the Riccati transfer matrix method. First, the exact field transfer matrix for an element of the beam is represented using the combination of the Analog Beam Method and the transfer matrix method. Second, applying Riccati method to the beam system, the natural frequencies can be easily calculated. The advantage of the present model is to overcome the numerical instabilities of the ordinary transfer matrix method, especially when calculating the higher natural frequencies of structures. A numerical example is given to illustrate and compare the results with those available from other methods. Finally, a parametric study is given to examine the effect of various parameters of the elastic composite beam on its free vibration behavior.