基于绝对节点坐标法的变截面拱面外弯扭振动分析

基于绝对节点坐标法(absolute nodal coordinate formulation,ANCF)研究了均质变截面Euler-Bernoulli拱的面外弯扭振动的振动特性。建立了考虑面外弯曲和扭转的均质的振动模型,在总体惯性坐标系下,将它划分为若干个变截面拱单元,给出单元的动能、应变能以及外力势能的表达式,得到了单元质量矩阵和刚度矩阵,进而获得了拱的总体的质量矩阵和刚度矩阵。应用Lagrange方程建立了拱的弯扭振动微分方程。数值计算了两端固定的等截面圆弧拱和变截面圆弧拱的前三阶频率,画出了相应的振型图,分析了变截面圆弧拱的中心角、半径、高宽比以及均布径向载荷对其振动特性的影响规律;数值计算了两端固定的等截面和变截面抛物线型非圆弧拱的前三阶频率,画出了相应的振型图。     

变截面梁横向振动特性的半解析法

提出一种计算变截面梁横向振动特性的半解析法。基于欧拉-伯努利梁理论给出的弯曲刚度、质量分布沿梁轴线连续或非连续变化的变截面梁横向振动方程;将该变截面梁等效为多段均匀梁,并基于相邻两段连接处的位移(位移、转角)和力(弯矩、剪力)的连续条件,建立了两相邻均匀段之间模态函数的关系;针对简支边界条件给出了计算变截面梁横向振动固有频率的特征方程和模态函数,并用Newton-Raphson方法计算其固有频率。通过与有限元法的数值结果比较说明半解析解的高精度和有效性。     

初应力位形上小的变形问题

论文研究初应力杆的小变形问题。用初应力作为参数,提出初应力位形上小变形问题的位移变分原理;针对直杆的几何特点,提出了用数值参数描写直杆初应力,用所提出的变分原理建立了初应力杆的小变形位移分量的定解问题。所得的方程中包含了初应力的数值参数。分析表明,初应力的不同的数值参数可以对相关的刚度、压杆的临界力以及基本变形的耦合与固有频率产生显著的影响。     

考虑面外振动的轮胎三维环模型

提出了包含面外扭转和面外弯曲振动的三维环模型,并应用于卡车子午线轮胎振动模态分析。在综述轮胎环模型发展的基础上,考虑了大变形应变和非线性应变项、面内面外弯曲和面外扭转三维位移模式,修正文献中的轮胎初始应力和气压功表达式,利用Hamilton变分原理首次建立了三维轮胎环模型的动力学控制方程,并利用模态展开技术得到了三维环模型面内和面外振动固有频率的解析解。该解析解首次建立了轮胎物理参数和轮胎三维振动固有频率之间的解析表达式,为轮胎的动态设计提供了理论指导。为验证三维环模型的准确性,对比了环模型分析、有限元模型和实验模态分析的结果,发现三者之间吻合良好,这证明文中建立的轮胎三维环模型的可靠性和准确性,能抓住子午线轮胎振动的本质规律。     

变截面粱横向振动特性半解析法

提出一种计算变截面梁横向振动特性的半解析法.基于欧拉-伯努利梁理论给出的弯曲刚度、质量分布沿梁轴线连续或非连续变化的变截面梁横向振动方程;将该变截面梁等效为多段均匀梁,并基于相邻两段连接处的位移(位移、转角)和力(弯矩、剪力)的连续条件,建立了两相邻均匀段之间模态函数的关系;针对简支边界条件给出了计算变截面梁横向振动固有频率的特征方程和模态函数,并用Newton-Raphson方法计算其固有频率.通过与有限元法的数值结果比较说明半解析解的高精度和有效性.     

锥形纳米管纵向振动固有频率

研究变截面锥形纳米管/棒的纵向振动问题。由于其控制方程涉及变系数微分方程,提出适用范围广、简单精确的积分方程方法求解该问题,基于经典弹性杆理论与非局部弹性杆理论分别给出几种边界条件下的固有频率计算。对一端固定一端附加集中质量的碳纳米管的纵向振动,给出共振基频的近似简单表达式。与其它方法所得数值结果对比表明该方法有效。     

变曲率FGM拱的面内自由振动分析EI北大核心CSCD

基于Euler-Bernoulli曲梁理论,考虑材料沿拱厚度方向呈梯度分布时中性层的改变,将变曲率功能梯度材料(Functionally Graded Materials,FGM)拱在弧线方向离散成多个曲拱单元。视每个曲拱单元为半径一定的圆弧拱单元,根据Hamilton变分原理推导出FGM圆弧拱单元的面内自由振动方程,进而求得了单元传递矩阵。利用传递矩阵法(Transfer Matrix Method,TMM)推导出变曲率FGM拱的面内自由振动特征方程,求解两端固定边界条件下变曲率FGM拱面内自由振动的固有频率,并将得到结果与现有文献作了比较,证明TMM对求解该问题的有效性。分析了曲率变化系数和材料体积分数变化系数对变曲率FGM拱的面内自由振动频率的影响。     

单轴对称截面圆弧拱平面外稳定性研究

根据变分原理推导了任意开口薄壁截面曲梁的稳定平衡方程。单轴对称截面圆弧拱在均布径向荷载(均匀受压)或两端作用大小相等、方向相反的端弯矩(均匀弯曲)作用下,平衡方程中曲率平面内的变形和曲率平面外的变形相互独立,故要么发生曲率平面内弯曲失稳,要么发生曲率平面外的弯扭失稳。给出单轴对称截面圆弧拱在这两种受力情况下平面外屈曲荷载的理论解答。通过一些无碍结果的近似使所得公式形式简洁,便于在工程中应用。最后给出了计算实例,与已有的文献进行比较,并使用通用有限元软件ANSYS 进行了模拟,分析结果与该文计算结果吻合,证明了所得公式的正确性。     

变曲率FGM拱的面内自由振动分析

基于Euler-Bernoulli曲梁理论,考虑材料沿拱厚度方向呈梯度分布时中性层的改变,将变曲率功能梯度材料(Functionally Graded Materials,FGM)拱在弧线方向离散成多个曲拱单元。视每个曲拱单元为半径一定的圆弧拱单元,根据Hamilton变分原理推导出FGM圆弧拱单元的面内自由振动方程,进而求得了单元传递矩阵。利用传递矩阵法(Transfer Matrix Method,TMM)推导出变曲率FGM拱的面内自由振动特征方程,求解两端固定边界条件下变曲率FGM拱面内自由振动的固有频率,并将得到结果与现有文献作了比较,证明TMM对求解该问题的有效性。分析了曲率变化系数和材料体积分数变化系数对变曲率FGM拱的面内自由振动频率的影响。     

基础竖向多频参数激励下圆弧拱平面内动力失稳研究

地震波、冲击波、环境振动激励会通过地基基础传递到拱上,致使拱发生动力失稳失去承载能力。为深入研究拱在基础竖向激励下的动力稳定性,该文基于能量法,建立了基础竖向激励下圆弧拱平面内动力稳定能量方程,利用哈密顿原理得到了拱面内径向和切向振动的耦合控制方程,求解了圆弧拱平面内失稳前的动轴力与动弯矩解析解。引入拱轴线不可压缩假设,解决了圆弧拱平面内动力控制方程的解耦问题。利用伽辽金法建立了基础竖向多频激励下圆弧拱平面内二阶常微分动力稳定方程,运用多尺度法推导了基础竖向多频激励下圆弧拱平面内动力失稳的临界激励频率解析公式,得到了圆弧拱同时发生一阶反对称参数共振和二阶正对称共振失稳的动力不稳定域,并利用有限元数值分析验证了理论解析解的正确性。进一步分析了拱矢跨比、长细比和圆心角对动力不稳定域的影响。     

Vibration and stability of an initially stressed laminated plate based on a higher-order deformation theory

Equations of motion for a laminated plate in a general state of nonuniform initial stress where the higher-order shear deformation terms are included are derived. The equations are derived by using the average stress method. The natural frequencies and buckling loads of cross-ply laminated plates subjected to initial stress are investigated. The initial stress is taken to be a combination of uniaxial pure bending and extensional stresses in the plane of the plate. The results obtained from the present higher-order theory are compared with first-order theory and other higher-order theory results. In addition, the effects of various parameters on the natural frequencies and buckling loads are studied.     

点支撑预应力中厚矩形板的横向振动

基于Reissner-Mindlin一阶剪切变形板理论,讨论在预加面内机械荷载或温度场作用下,点支撑中厚矩形板的横向振动。温度场假定沿板表面为均布,沿板厚方向为线性分布的。利用考虑剪切变形影响的Timoshenko梁函数,采用Rayleigh-Ritz法给出不同边界条件下点支撑中厚板的自振频率。结果表明,温度升高与预加面内压力将使板的自振频率下降,支撑点位置的变化、边界约束条件和横向剪切变形效应都对板的自振频率有显著影响。     

Nonlocal elasticity effect on vibration of in-plane loaded double-walled carbon nano-tubes

Summary Vibration and buckling of in-plane loaded simply supported double-walled carbon nanotubes were investigated using the nonlocal Timoshenko-beam theory. The influence of in-plane loads on the natural frequencies was determined. The results show that while the natural frequencies decrease with increasing compressive in-plane loads, an increase in frequencies is observed for tension type of in-plane loads. Effects of in-plane loads are more pronounced for lower modes, and some mode changes are observed at critical in-plane loads. A comparison of nonlocal elasticity solutions with local elasticity solutions indicates that the nonlocal effects should be considered for higher modes of vibration of double-walled carbon nanotubes.     

The dynamic analysis of a flat plate under a moving load by the finite element method

The object of this paper is to analyse by the finite element method the dynamic responses of a flat plate subjected to various moving loads. First of all the actual continuous flat plate was replaced by a discrete system composed of isoparametric rectangular plate elements. And then the elementary and overall stiffness and mass matrices were determined and the natural frequencies and mode shapes of the flat plate were solved. Next, the Newmark direct integration method was used to find the dynamic responses of the flat plate. The effects of eccentricity, acceleration and initial velocity of the moving load, and the effect of span length were the key points of study. The dynamic behaviour of a multi-span flat plate supported by the beam members of rigid plane frames and subjected to the action of a series of moving loads (in identical or opposite directions) were also investigated.     

Vibration analysis of rotating cantilever plates

A finite element technique is used to determine the natural frequencies and the mode shapes of a cantilever plate mounted on the periphery of a rotating disc. The plane of the plate is assumed to make any arbitrary angle with the plane of rotation of the disc. The distributed centrifugal force is resolved into two components—one acting in the plane of the plate and the other normal to the plate. The stresses produced in the middle surface of the plate due to the in-plane forces are first determined. The increase in the bending stiffness of the plate elements due to these in-plane stresses is obtained in a manner similar to that used in the stability analysis of plates. The component of the distributed centrifugal force normal to the plate surface is added to the inertia force. From the results of computations carried out for various values of the aspect ratio, the speed of rotation, the disc radius and the setting angle, empirical formulae are derived giving the effect of these parameters on the natural frequencies. These empirical formulae are observed to be in agreement with the corresponding known formulae for rotating cantilever beams, when the aspect ratio is high.     

水平弹性支承圆弧钢拱的弹性屈曲分析

钢拱常支承于其他结构上.拱脚受到弹性约束并出现水平位移,弹性约束会显著影响拱的力学行为.该文得到了水平弹性支承拱在沿弦长均匀分布的面内竖向荷载作用下的内力及位移的解析解,构造了一个无量纲化柔度系数.利用这个参数,对线性解进行分析,提出了计算跨中轴力和拱脚支座位移的理论公式.根据跨中轴力大小,提出了在线性计算范围内划分拱...     

非均布荷载作用下震后地下拱结构抗动载能力评估

为评估非均布荷载作用下震后地下防护结构的抗动载能力,针对震前震后三种结构型式,给出了动荷载动力系数的确定方法,推导出了非均布荷载作用下地下拱形结构的弯矩和拱脚推力的计算公式。针对工程实例,计算了不同损伤型式的拱结构承受非均布动载时的结构内力,从而给出了非均布荷载作用下震后结构的抗动载能力评估方法。研究表明:抗弯设计条件下震后拱结构抗非均布动载能力将降低约13%,而在抗剪设计条件下由于裂缝的穿透震后拱结构抗非均布动载能力将降低50%以上。     

Compact computation of natural frequencies and buckling loads for plane frames

Existing theory is assembled to give a method which needs only the core of a mini-computer to calculate the eigenvalues of large rigidly jointed plane frames with certainty, the eigenvalues being natural frequencies and critical load factors in free vibration and buckling problems, respectively. The method is illustrated by annotated listings of vibration and buckling programs, each involving under two hundred Fortran statements and with low number storage requirements (see Table I). The use of the programs as ‘black boxes’ is fully explained, with illustrative examples. The member theory used is the ‘exact’ classical Bernoulli-Euler uniform member theory. Possible applications include: evaluation of answers from approximate methods; calculation of critical loads for substitution in the modified Merchant-Rankine formula to estimate collapse loads of frames; and calculation of shifts in natural frequencies caused by structural damage, in connection with structural integrity monitoring of inaccessible structures.     

Free vibrations of shear‐flexible and compressible arches by FEM

The purpose of this paper is to analyse free vibrations of arches with influence of shear and axial forces taken into account. Arches with various depth of cross‐section and various types of supports are considered. In the calculations, the curved finite element elaborated by the authors is adopted. It is the plane two‐node, six‐degree‐of‐freedom arch element with constant curvature. Its application to the static analysis yields the exact results, coinciding with the analytical ones. This feature results from the use of the exact shape functions in derivation of the element stiffness matrix. In the free vibration analysis the consistent mass matrix is used. It is obtained on the base of the same functions. Their coefficients contain the influences of shear flexibility and compressibility of the arch. The numerical results are compared with the results obtained for the simple diagonal mass matrix representing the lumped mass model. The natural frequencies are also compared with the ones for the continuous arches for which the analytically determined frequencies are known. The advantage of the paper is a thorough analysis of selected examples, where the influences of shear forces, axial forces as well as the rotary and tangential inertia on the natural frequencies are examined. Copyright © 2001 John Wiley & Sons, Ltd.     

Buckling behavior of a central cracked thin plate under tension

The buckling characteristics of cracked plates subject to uniaxial tensile loads are analysed by the aid of the finite element method. Owing to the fact that crack buckling behavior is affected by the in-plane stress distribution around a crack, to get more accurate results, pre-buckling in-plane stress fields are analysed by the finite element method. For the critical loads calculation, the finite element approach adopted is based on Von Karman's linearize theory for buckling of plates subjected to pre-buckling state of plane stress. Several singular elements based on the Willian series are used in this plate bending approach. In this study, the effect of crack length, the effect of boundary condition, the effect of Poison's ratio and the effect of biaxial force on critical loads are analysed and discussed. Furthermore, the effect of initial imperfection is also discussed. There is a good agreement between other researcher's work and present results.