基于修正偶应力和高阶剪切变形理论的变截面微梁的自由振动

基于修正偶应力和高阶剪切理论建立了仅含有一个尺度参数的Reddy变截面微梁的自由振动模型,研究了变截面微梁自由振动问题的尺度效应和横向剪切变形对自振频率计算的影响。基于哈密顿原理推导了动力学方程与边界条件,并采用微分求积法求解了各种边界条件下的自振频率。算例结果表明,基于偶应力理论预测的变截面微梁的自振频率均大于经典梁理论的预测结果,即捕捉到了尺度效应。另外,梁的几何尺寸与尺度参数越接近,尺度效应就越明显,而梁的长细比越小,横向剪切变形对自振频率的影响就越明显。     

Timoshenko固端梁特征值问题近似计算方法

利用模态摄动法将Timoshenko梁特征值问题的求解转化为一组非线性代数方程组的求解，不仅可以简化计算过程，而且计算结果具有较高的精度，对同一类问题具有适用性。通过算例，计算了在不同长细比条件下，剪切变形和转动惯量对固端梁的各阶主频率的影响。     

弹性地基梁振动特性的近似分析方法

文中介绍了用模态摄动法分析复杂情况下弹性地基梁动力特性的近似方法。这一方法中可考虑纵向钢筋以及变地基弹性系数对弹性地基梁振动特性的影响，通过算例说明了这一方法的有效性。     

精确频率约束下框架结构的尺寸优化

本文研究受到频率约束的框架结构优化设计问题,采用基于Bernoulli-Euler梁的动力刚度法求解框架结构的自振频率,采用W-W算法精确求解自振频率及频率对设计变量的灵敏度.分析比较了将框架结构的杆件按普通静刚度梁单元和动力刚度梁单元分别建立计算模型时得到的频率分析结果.以杆件面积为设计变量,以结构重量为优化目标,对基频约束下的框架结构进行了尺寸优化,比较了节点集中质量对优化结果的影响.通过2个数值算例,验证了动力刚度阵法在框架结构频率性能分析与优化设计中的适用性,并具有较高的计算精度.     

预应力混凝土梁桥在移动荷载作用下的动力响应分析

建立预应力钢筋混凝土等直梁强迫振动的运动微分方程,分析了梁在预应力钢筋作用下的横向振动问题.将运动微分方程解耦,得到梁在预应力作用下自振频率的解析解以及梁振动时的动力响应.分析了梁的自振频率与预应力和偏心距的关系.通过实例计算,得到了关于不同速度移动荷载车辆作用下梁的动力挠度曲线,并给出了考虑预应力和不考虑预应力时梁的动力效应比较.结果表明:随着车辆荷载移动速度的增大,梁的动力挠度随之增大;考虑预应力时梁的动力效应略有降低.     

基于单弹簧联结单元法的钢筋混凝土梁损伤模拟

钢筋混凝土梁的损伤模拟的重难点在于描述两种材料非线性的本构关系以及钢筋混凝土粘结滑移关系非线性的描述,采用单弹簧联结单元法模拟钢筋和混凝土相互作用,结合混凝土四参数损伤模型,模拟钢筋混凝土结构多轴应力状态下从开始加载到结构破坏的全过程。数值算例不仅体现该方法的有效性,也具有重要的工程实践意义。     

电学开路挠曲电悬臂梁自振频率分析

挠曲电效应是一种新兴的机电耦合效应,在微纳米尺度的传感器、致动器和俘能器方面有广阔的应用前景．本文基于挠曲电材料的变分原理和电吉布斯自由能,推导了表面覆盖电极的挠曲电悬臂梁在电学开路条件下的机电耦合动力学控制方程和相应的力电边界条件．进一步获得了求解电学开路条件下挠曲电悬臂梁自振频率的超越方程．以聚偏氟乙烯(PVDF)材料为算例,讨论了挠曲电系数、末端质量块和梁尺寸对结构自振频率和电学开路/短路条件下结构自振频率有效频移的影响．计算结果表明,挠曲电系数的增大会提高梁的自振频率;末端质量的增大可以降低梁的自振频率,并且末端质量块的转动效应对悬臂梁自振频率的影响很小;悬臂梁结构的有效频移随着结构尺寸减小而增加,并在某一厚度尺寸趋于饱和值．     

经典理论与一阶理论之间简支梁特征值的解析关系

利用Euler-Bernoulli梁理论(EBT)和Timoshenko梁理论(一阶理论,TBT)之间,梁的特征值问题在数学上的相似性,研究了不同梁理论之间特征值的关系。将特征值问题的求解转化为一个代数方程的求解,并导出了不同梁理论之间梁的特征值之间的精确解析关系。因此,只要已知梁的经典结果(临界载荷和固有频率),便很容易从这些关系中获得一阶梁理论下的相应结果。这些解析结果清楚地显示了横向剪切变形对经典结果影响的本质特点。另外,从这些关系中获得的含有剪切变形影响的结果,可以用于检验一阶理论下梁特征值数值结果的有效性、收敛性以及精确性等问题。     

钢筋混凝土开孔深梁有限元分析与设计研究Finite element analysis of RC deep beams with openings and researching of the design method

钢筋混凝土深梁受力不同于浅梁,梁腹开孔后受力更趋复杂。现有的设计方法对深梁行为的解释不够完备,设计结果的适用性难以判断,设计规范也没有给出开孔深梁的设计条文。为研究深梁设计方法的有效性,本文采用了非线性有限元分析方法,引入适合混凝土结构非线性分析的断裂塑性模型,并考虑钢筋粘结滑移效应,对一系列开双孔或偏孔钢筋混凝土深梁试验进行仿真分析,所得结果与试验结果吻合良好,能够准确预测深梁在裂缝、破坏形态及承载力等方面的受力特征。研究表明现有的深梁设计方法中,压拉杆模型方法相较内力法和应力图形法更加经济有效。在仿真分析的基础上,提出了一种对开孔深梁具有普遍适用性的非线性设计方法,其设计结果具有高承载力、较好延性、经济的配筋量和充分的材料利用率的优点。     

用加权残数法分析纤维增强复合材料层合板的屈曲及自振频率

纤维增强复合材料层合板的屈曲及自振频率,用加权残数法分析,属于二次特征值的问题,迄今尚未有解。本文通过转换,把二次特征值的问题变化为标准一次特征值问题,从而获得解。通过四边简支矩形特殊正交各向异性层合板承受面内轴压的屈曲及横向自振频率的算例,所得结果与解析解吻合较好。     

The perturbation finite element method for solving the plane problem in consideration of linear creep

In this paper, a method (PFMC) for solving plane problem of linear creep is presented by using perturbation finite element. It can be used in plane problem in consideration of creep, such as reinforced concrete beam, presiressed concrete beam, reinforced concrete cylinder and reinforced concrete tunnel in elastic or visco-elastic medium, as well as underground building and so on.In the presented method, the assumption made in the general increment method that variables remain constant in a divided time interval is not taken. The accuracy is improved and the length of time step becomes larger. The computer storage can be reduced and the calculating efficiency can be increased.Perturbation finite element formulae for four-node quadrilateral isoparametric element including reinforcement are established and five numerical examples are given. As contrasted with the analytical solution, the accuracy is satisfactory.     

复合纤维增强混凝土阻尼测试装置开发与试验研究

纤维与聚合物的掺入可以明显改善混凝土材料的阻尼性能。本文首先给出了正弦交变激励下粘弹性材料三点弯曲梁阻尼特性关系,其次首次自主开发了大尺寸材料的阻尼性能测试装置,然后利用开发的装置在频率(0.5~2.0Hz)条件下测定了6种不同配比复合纤维增强阻尼混凝土的损耗因子与储存模量,最后对纤维的阻尼增强机理进行了初步探讨。试验结果表明:复合纤维增强阻尼混凝土与素混凝土相比,提高了混凝土的损耗因子80%~200%。主要原因是聚合物分子在外力作用下的内耗增加了普通混凝土的阻尼能力,而纤维的阻尼增强机理在于纤维的掺入增加了纤维与水泥基材的界面摩擦力。     

钢筋混凝土靶侵彻的可压缩弹-塑性动态空腔膨胀阻力模型

在Forrestal素混凝土靶侵彻的可压缩弹-塑性球形动态空腔膨胀理论模型基础上,考虑粉碎区以内钢筋对混凝土的环向约束作用,提出了一个适用于刚性弹侵彻钢筋混凝土靶的阻力模型。论文通过体积配筋率的引入,获得了钢筋混凝土靶空腔表面径向应力的理论解,并讨论了配筋率对空腔壁面径向应力及各分区大小的影响。结果表明:钢筋对混凝土的环向约束效应影响了空腔膨胀过程中混凝土各区域的大小分布,并提高了空腔表面的径向应力。     

Dynamic analysis of beam-cable coupled systems using Chebyshev spectral element method

The dynamic characteristics of a beam–cable coupled system are investigated using an improved Chebyshev spectral element method in order to observe the effects of adding cables on the beam. The system is modeled as a double Timoshenko beam system interconnected by discrete springs. Utilizing Chebyshev series expansion and meshing the system according to the locations of its connections,numerical results of the natural frequencies and mode shapes are obtained using only a few elements, and the results are validated by comparing them with the results of a finiteelement method. Then the effects of the cable parameters and layout of connections on the natural frequencies and mode shapes of a fixed-pinned beam are studied. The results show that the modes of a beam–cable coupled system can be classified into two types, beam mode and cable mode, according to the dominant deformation. To avoid undesirable vibrations of the cable, its parameters should be controlled in a reasonable range, or the layout of the connections should be optimized.     

Coupled bending and torsional vibration of nonsymmetrical axially loaded thin-walled Bernoulli–Euler beams

The dynamic transfer matrix is formulated for a straight uniform and axially loaded thin-walled Bernoulli–Euler beam element whose elastic and inertia axes are not coincident by directly solving the governing differential equations of motion of the beam element. Bernoulli–Euler beam theory is used, and the cross section of the beam does not have any symmetrical axes. The bending vibrations in two perpendicular directions are coupled with torsional vibration and the effect of warping stiffness is included. The dynamic transfer matrix method is used for calculation of exact natural frequencies and mode shapes of the nonsymmetrical thin-walled beams. Numerical results are given for a specific example of thin-walled beam under a variety of end conditions, and exact numerical solutions are tabulated for natural frequencies and solutions calculated by the other method are also tabulated for comparison. The effects of axial force and warping stiffness are also discussed.     

锈蚀钢筋混凝土双筋矩形梁抗弯承载力分析

钢筋锈蚀是钢筋混凝土桥梁的主要病害之一。在锈蚀钢筋混凝土双筋矩形截面梁中,钢筋锈蚀易造成结构性能退化,并引起钢筋和混凝土相对滑移,导致结构的承载力降低,受拉区的钢筋与混凝土变形不协调。通过构造新的几何条件,推导了锈蚀钢筋混凝土双筋矩形梁正截面极限抗弯承载力计算公式。对室内快速锈蚀双筋矩形梁进行正截面抗弯承载力实验,结果表明推导的锈后双筋矩形梁正截面抗弯承载力公式的计算值与实验值吻合较好。上述工作为进一步进行工程实践奠定了基础。     

基于正交设计的冲击荷载下型钢混凝土梁动力性能有限元分析

为研究冲击荷载下型钢混凝土梁的动力性能,取试验结果验证模型有效性后,使用有限元软件ABAQUS建立了型钢混凝土梁落锤冲击模型．在对比了型钢混凝土梁与钢筋混凝土梁的动力性能后,分析了落锤速度对型钢混凝土梁的冲击位移、冲击力、冲击力位移曲线、惯性效应、塑性耗能等性能的影响,然后基于正交设计,研究了落锤质量、落锤速度、混凝土强度等参数对型钢混凝土梁动力性能的影响．研究结果表明：型钢混凝土梁的抗冲击性能较好;落锤速度是影响构件动力性能的主要参数,落锤质量对动力性能的影响较大,提高混凝土强度有助于增强构件的抗冲击性能．     

爆炸载荷下RC单向简支板的能量法优化设计

由钢筋混凝土(RC)板的抗力-位移(R-y)曲线特性可知,曲线下方面积代表板 在爆炸载荷作用下可能吸收的能量. 对爆炸载荷作用下RC板的R-y曲线采用双折线模型,计 算不同配筋率的R-y曲线下方面积,面积最大时的配筋率即可定义为相应设计的最佳配筋率. 考虑材料非线性及高应变率对混凝土和钢筋强度的影响,采用分层法迭代求解抗 力-挠度(R-y)曲线. 研究结果可供受爆炸载荷的RC板优化设计借鉴.     

Dynamic stiffness method for free vibration of an axially moving beam with generalized boundary conditions

Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discussed for the first time. The beam is supported by torsional springs and vertical springs at both ends. By modifying the stiffness of the springs, generalized boundaries can replace those classical boundaries.Dynamic stiffness matrices are, respectively, established for axially moving Timoshenko beams and Euler-Bernoulli(EB) beams with generalized boundaries. In order to verify the applicability of the EB model, the natural frequencies of the axially moving Timoshenko beam and EB beam are compared. Furthermore, the effects of constrained spring stiffness on the vibration frequencies of the axially moving beam are studied. Interestingly, it can be found that the critical speed of the axially moving beam does not change with the vertical spring stiffness. In addition, both the moving speed and elastic boundaries make the Timoshenko beam theory more needed. The validity of the dynamic stiffness method is demonstrated by using numerical simulation.