Application of the flexibility influence function method in the dynamic analysis of composite beams

The flexibility influence function technique is validated as a method for calculating the displacements and the rotations of a laminated beam subjected to a dynamic load, using the first-order shear deformation laminate theory and comparing the results with those obtained by modal analysis and two finite element models (one-dimensional and three-dimensional). The movements (displacements and rotations) were calculated from a single-span beam subjected to a time-variable load with four boundary conditions: clamped-clamped, hinged-hinged, clamped-free, clamped-hinged. A carbon/epoxy cross-ply laminated beam was selected to avoid bending-torsion coupling. The maximum movements calculated by the flexibility influence function method differs very little from those calculated with the other two models accounted for by the first-order shear deformation laminate theory: modal analysis and the one-dimensional numerical model. The differences in the rotations between the three-dimensional numerical model and the flexibility influence function method are slightly bigger, and could be due to the warping of the cross-section of the beam, which is not included in the first-order shear deformation laminate theory.     

弹性曲梁在机械和热载荷共同作用下的几何非线性模型及其数值解

基于Euler-Bernoulli梁的几何非线性理论,建立了弹性曲梁在任意分布机械载荷和热载荷共同作用下的几何非线性静平衡控制方程。该模型不仅计及了轴线伸长,同时也精确地考虑了梁的初始曲率对变形的影响以及轴向变形与弯曲变形之间的相互耦合效应。应用打靶法数值求解了半圆形曲梁在横向均匀升温作用下的非线性弯曲问题,数值比较了轴向伸长对曲梁变形的影响。     

拼接式组合扁梁受弯性能分析

本文提出了一种拼接式组合扁梁,对其进行了受弯性能分析．组合扁梁属于内嵌式组合梁,其组成部分较为复杂,传统承载力计算公式偏保守．为便于此类梁的设计,本文在等效应力法的基础上使用等效矩形应力图法,对拼接式组合扁梁的正截面抗弯承载力公式进行推导．使用ABAQUS有限元软件对组合方法公式的准确性进行验证,并与等效应力法公式进行对比,结果表明组合公式得到的数值更为精准．在相同截面高度和用钢量下设计了一个深肋组合扁梁和一个拼接式组合扁梁,并进行了受弯性能对比;同时对不同钢强度和翼缘厚度影响下的拼接式组合扁梁抗弯承载性能进行分析．使用换算截面法对其进行了弹性刚度的计算,并和有限元进行了对比,二者吻合较好,研究结果为拼接式组合扁梁的设计和优化提供了一定参考依据．     

旋转中心刚体-FGM梁刚柔热耦合动力学特性研究

对旋转中心刚体-功能梯度材料(functionally graded material,FGM)梁刚柔热耦合动力学特性进行研究.FGM梁为物理性能参数沿厚度方向呈幂律分布的欧拉伯努利梁.考虑柔性梁的横向弯曲变形和轴向拉伸变形, 并计入横向弯曲变形引起的纵向缩短,即非线性耦合变形量.考虑变截面空心梁在外部高温、内冷通道冷却情况下的热力耦合对系统动力学特性的影响,求解得到FGM梁沿厚度方向分布的温度场, 进而在本构关系中计入热应变.采用假设模态法对柔性梁变形场进行离散,运用第二类拉格朗日方程推导得到系统的刚柔热耦合动力学方程,并编制动力学仿真软件, 然后通过仿真算例对系统的动力学问题进行研究.结果表明:不同截面梁动力学响应差异较大, 因此需对实际系统合理建模;大范围运动已知时, 考虑热冲击载荷的FGM梁将有效抑制横向弯曲变形,而大范围运动恒定时随热冲击的叠加会出现高频振荡; 大范围运动未知时,外力矩和热冲击载荷相互作用产生热力耦合效应, 导致系统呈现高频振荡,同时与中心刚体大范围旋转运动产生刚柔热耦合效应.      

Stability of curvilinear Euler-Bernoulli beams in temperature fields

In this work, stability of thin flexible Bernoulli-Euler beams is investigated taking into account the geometric non-linearity as well as a type and intensity of the temperature field. The applied temperature field T(x,z) is yielded by a solution to the 2D Laplace equation solved for five kinds of thermal boundary conditions, and there are no restrictions put on the temperature distribution along the beam thickness. Action of the temperature field on the beam dynamics is studied with the help of the Duhamel theory, whereas the motion of the beam subjected to the thermal load is yielded employing the variational principles.The heat transfer (Laplace equation) is solved with the use of the finite difference method (FDM) of the third-order accuracy, while the integrals along the beam thickness defining the thermal stress and moments are computed using Simpson's method. Partial differential equations governing the beam motion are reduced to the Cauchy problem by means of application of FDM of the second-order accuracy. The obtained ordinary differential equations are solved with the use of the fourth-order Runge-Kutta method.The problem of numerical results convergence versus a number of beam partitions is investigated. A static solution for a flexible Bernoulli-Euler beam is obtained using the dynamic approach based on employment of the relaxation/set-up method.Novel stability loss phenomena of a beam under the thermal field are reported for different beam geometric parameters, boundary conditions, and the temperature intensity. In particular, it has been shown that stability of the flexible beam during heating the beam surface essentially depends on the beam thickness.     

Vibration of beams with piezoelectric inclusions

A mathematical model for the vibration of beams with piezoelectric inclusions is presented. The piezoelectric inclusion in a non-piezoelectric matrix (host beam) is analyzed as two inhomogeneous inclusion problems, elastic and dielectric, by using Eshelby’s equivalent inclusion method. The natural frequency of the beam is determined from the variational principle in Rayleigh quotient form, which is expressed as functions of the elastic strain energy and dielectric energy of the piezoelectric inclusion. The Euler–Bernoulli beam theory and Rayleigh–Ritz approximation technique are used in the present analysis. In addition, a parametric study is conducted to investigate the influence of the energies due to piezoelectric coupling on the natural frequency of the beam.     

基于修正压力场理论的再生混凝土梁抗剪承载力计算方法研究

基于修正压力场理论分析有腹筋再生混凝土梁的剪切破坏机理,建立了更接近有腹筋再生混凝土梁实际受力的抗剪模型,并通过考虑再生骨料有效粒径和受箍筋作用下的裂缝宽度与构件裂缝处应力的联系,分析了再生骨料咬合力对梁斜截面抗剪性能的影响,提出了再生混凝土梁极限抗剪承载力的计算方法.此外,本文将理论结果与课题组自制的6根再生混凝土梁...     

变截面耦合微悬臂双梁的基本振动特性

本文研究了连接部件的几何参数对变截面耦合微悬臂双梁振动特性的影响．首先，利用集总参数法建立了等效的两自由度系统耦合振动的解析模型；其次，利用分离变量法获得了耦合双梁自由振动的固有频率、振幅比和强迫振动的反共振频率；最后，通过比对解析解、有限元数值结果和实验数据，验证了解析预测的可靠性．研究结果表明，连接部件的宽度和初始偏转角的变化会对耦合双梁振动的特性产生较大的影响．     

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.     

具有非线性支撑和弹性边界约束的轴向载荷梁结构动力学行为研究

弹性梁结构作为一种基本单元被广泛于建筑、航空、航天、船舶等工程领域. 为有效降低弹性梁结构的振动水平, 深刻理解其振动特性、动力学行为显得尤为重要. 本文建立了具有非线性支撑和弹性边界约束的轴向载荷梁结构动力学分析模型, 并采用伽辽金截断法预报梁结构的动力学响应. 在伽辽金截断法的求解过程中, 选取具有弹性边界约束的轴向载荷梁结构的模态振型函数作为伽辽金截断法的试函数与权函数. 首先, 研究截断数对伽辽金截断法稳定性的影响, 并采用谐波平衡法研究伽辽金截断法的可靠性. 在此基础上, 研究谐波激励扫频方向、非线性支撑参数对具有非线性支撑和弹性边界约束的轴向载荷梁结构动力学响应的影响规律. 研究结果表明, 具有非线性支撑和弹性边界约束的轴向载荷梁结构的动力学响应具有初值敏感性且非线性支撑参数对梁结构动力学响应的影响显著. 相关非线性支撑参数使得梁结构出现复杂动力学行为. 合适的非线性支撑参数能够抑制具有非线性支撑和弹性边界约束的轴向载荷梁结构的复杂动力学行为并对梁结构边界处的减振具有有益效果.      

Modeling and analysis of sliding joints with clearances in flexible multibody systems

The modeling of the sliding joint with clearance between a flexible beam and a rigid hole is investigated in this paper. The flexible beam is discretized using the three-dimensional curved Euler–Bernoulli beam element of the Absolute Nodal Coordinate Formulation, while the motion of the rigid hole is described by the Cartesian coordinates. Moreover, the cross sections of both the flexible beam and the rigid hole are assumed to be circular. The existing joints with clearances are mainly rigid joints with small clearances, and the contact detection algorithm adopted can solve only one pair of potential contact points within one section. In order to model the contact problem in the sliding joint with clearance, a new contact detection method based on the intersection of the rigid hole’s cross section and the flexible beam is proposed, which yields a two-dimensional contact detection problem. Based on the common-normal concept, the ellipse–circle contact detection problem within the hole’s cross section can be solved. The potential contact point on the hole’s cross section will be determined, and the closest point projection on the beam’s neutral axis can be defined further. The proposed contact detection method can deal with the sliding joint with large clearance and the multiple-point contact problem within one section. In addition, the penalty method is adopted to model the frictionless contact between the flexible beam and the rigid hole. Finally, two numerical examples about sliding joints with clearances, one with an initially curved beam under gravity and the other with a straight beam under zero gravity, are presented to demonstrate the influence of the clearance of sliding joint on the dynamic performance of flexible multibody systems.     

刚构连续梁桥墩梁固节点结构的光弹性试验及有限元分析

某铁路特大桥的主桥部分采用预应力混凝土刚构连续梁桥,本文采用光弹性模型冻结应力法对该刚构连续梁桥墩梁固节点结构进行了应力分析,给出了结构边界应力分布和主应力迹线。应用ANSYS软件对墩梁固节点实际结构进行了有限元计算。将实验与有限元分析结果进行了比较,结果表明,实验应力分析法与有限元数值法吻合较好。在有限元分析中,对墩梁固节点结构梁端加载边界的影响区进行了研究,通过合理选择梁的长度可以有效减小局部应力。模型实验和有限元计算的结果为结构的优化设计提供了重要的依据。     

考虑剪切效应的旋转FGM楔形梁刚柔耦合动力学建模与仿真

本文对一类中心刚体-柔性梁系统在大范围转动下的刚柔耦合动力学问题进行了研究. 柔性梁为功能梯度材料(functionally graded materials, FGM)楔形变截面梁,材料体积分数在梁轴向呈幂律分布变化. 以弧长坐标来描述柔性FGM梁的几何位移关系,分别使用倾角和拉伸应变变量描述柔性梁的横向弯曲和纵向拉伸变形,并计及剪切效应. 采用假设模态法离散变形场,运用第二类拉格朗日方程进行方程推导,得到系统考虑剪切效应的刚柔耦合动力学模型. 基于全新的刚柔耦合动力学建模理论,研究不同轴向材料梯度分布的FGM楔形梁,通过数值仿真计算,分析讨论不同的转速、梯度分布规律以及变截面参数对系统动力学特性的影响. 结果表明,剪切效应对大高跨比的FGM楔形梁的变形影响较为明显,不容忽略;材料梯度分布规律和截面参数的选取均会对旋转FGM楔形梁的动力学响应和频率产生较大影响. 本文提出的考虑剪切效应的倾角刚柔耦合动力学模型是对以往非剪切模型的进一步完善,可应用于工程中的 Timoshenko梁结构的动力学问题求解.      

基于近场动力学的梁结构振动特性分析方法研究

基于欧拉梁理论推导了两自由度梁的常规态型近场动力学(Peridynamics,PD)模型,并提出一种新的自由边界条件施加方法,对不同边界条件的PD梁进行了模态分析,与局部梁的有限元结果进行了对比,验证了模型的收敛性,分析了PD非局部参数对固有频率的影响.结果表明,当近场作用域内物质点密度较小时,PD梁模型非局部性较弱,...     

考虑温度效应的索梁面内动力学建模及特性分析

根据增量热场理论,温度变化影响下索梁结构会形成新的热应力平衡状态．因此基于已有的索梁结构非线性动力学模型,结合与斜拉索张拉力和垂度相关的无量纲参数,重新建立考虑温度变化影响下索梁结构面内振动的动力学模型,并推导其面内非线性运动方程．接着开展特征值分析,得到包含温度效应的索梁结构面内振动频率的超越方程及模态振型函数．通过算例研究温度变化对不同刚度比的索梁结构影响,得到其前四阶面内振动的模态频率与温度变化的关系曲线．研究结果表明：面内模态频率受温度变化影响明显,其影响程度与刚度比大小和模态的阶数密切相关,温度变化对低阶模态频率的影响比对高阶模态频率影响更为复杂;升温和降温对索梁结构面内振动特性的影响不对称;此外温度变化会导致频率偏转点的位置发生漂移．     

Wave propagation in a porous composite beam: Porosity determination,location and quantification

A wave-based method is developed to quantify the defect due to porosity and also to locate the porous regions, in a composite beam-type structure. Wave propagation problem for a porous laminated composite beam is modeled using spectral finite element method (SFEM), based on the modified rule of mixture approach, which is used to include the effect of porosity on the stiffness and density of the composite beam structure. The material properties are obtained from the modified rule of mixture model, which are used in a conventional SFEM to develop a new model for solving wave propagation problems in porous laminated composite beam. The influence of the porosity content on the group speed and also the effect of variation in theses parameters on the time responses are studied first, in the forward problem. The change in the time responses with the change in the porosity of the structure is used as a parameter to find the porosity content in a composite beam. The actual measured response from a structure and the numerically obtained time responses are used for the estimation of porosity, by solving a nonlinear optimization problem. The effect of the length of the porous region (in the propagation direction), on the time responses, is studied. The damage force indicator technique is used to locate the porous region in a beam and also to find its length, using the measured wave propagation responses.     

Analysis of Cracks and Deformations in a Full Scale Reinforced Concrete Beam Using a Digital Image Correlation Technique

This paper deals with the use of a digital image correlation technique for the determination of the actual mechanical behaviour of a full scale reinforced concrete beam after 25 years of service in a severe industrial environment. The objective is to investigate the influence of the service conditions on the cracking process and the flexural behaviour of the beam. For this purpose, one beam is removed from the existing structure before being tested in four point bending in laboratory. Displacement fields derived from digital images captured during five loading cycles are analysed in terms of crack detection and measurement, beam deflection and curvature. Owing to its good resolution, the method proves suitable for early crack detection and measurement. A comparison between experimental results and theoretical values derived from Eurocode 2 design code in the serviceability state suggests the existence of a longitudinal compressive force in the beam. A complementary analysis confirms the validity of this hypothesis. It is concluded that the cracking and the flexural behaviour of the tested beam are significantly affected by the existence of an initial compressive stress, which is possibly resulting from a swelling of the concrete due to long term exposure to wet atmosphere and elevated temperature.     

Global and local behaviour based composite damping studies on thin-walled box structure

The local (plate)/global (beam) vibration and damping behavior of composite thin-walled box member subjected to vibratory environment are studied and presented in this paper. This investigation is carried out by the use of 3D beam and thin plate finite elements and the corresponding modal frequencies/damping values of composite box beam are predicted by modal strain energy method. Application examples illustrate the ability of the 3D beam and thin plate element to predict both local and global modal frequencies/damping of hollow box sections. The influence of L/h ratio, b/h ratio and ply angle on the frequency and loss factor of composite box beam is investigated. In addition, an attempt has also been made to investigate the effect of temperature on the composite damping characteristics of rectangular box type section.     

Error estimation of laser-Doppler anemometry measurements in fluids with spatial inhomogeneities of the refractive index

We report a combined experimental and theoretical investigation of the influence of spatial non-uniformities of the refractive index on the accuracy of laser Doppler anemometry (LDA) measurements in transparent fluids. One LDA beam is guided through heated air of a thermal boundary layer near a heated vertical flat plate. It is found that the hot air is deflecting the beam because of a modification of the refractive index n in the fluid. This deflection causes three effects: (1) spatial displacement of beam intersection, (2) waist mismatch in the measurement volume and (3) variation in interference fringe distance. With the help of a rotating disk calibration system the resulting displacement of the LDA measurement volume and the Doppler frequency variation is systematically studied at different temperatures. Using a simple model of beam propagation under the influence of well-defined temperature inhomogeneities, the displacement of measurement volume and change in Doppler frequency are calculated and are found to be in agreement with the experimental observations. The results provide a rational framework for an assessment of the accuracy of LDA data in arbitrary transparent fluids with non-uniform refractive index.     

六边形桥墩柔性抗船撞装置抗弯刚度

针对中国自主研发的桥梁柔性抗船撞装置,构建该装置模型:由两个相似的六边形梁为内外钢围以及均布且垂直于六边形各边的防撞圈构成。分析该模型得到在冲击载荷作用下六边形梁的控制方程及相应的初边值条件。利用Laplace变换和数值Laplace逆变换对该方程进行求解,揭示六边形梁在冲击载荷作用下的动态响应。并进一步分析外钢围等效抗弯刚度对抗船撞装置动态响应的影响,发现外刚围结构在冲击载荷作用下存在临界等效抗弯刚度。当外钢围等效抗弯刚度达到该临界值后,该外钢围在冲击载荷作用下可以近似为刚性。