THE DYNAMIC STIFFNESS MATRIX OF THE FINITE ANNULAR PLATE ELEMENT

The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in closed form and checked by the direct stiffness method. The paper has given wide convcrage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters at s separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response compulation.

Analysis of the hull girder vibration by dynamic stiffness matrix method

Dynamic stiffness matrix method is applied to compute vibration of hull girder in this paper. This method can not only simplify the computational model, but also get much higher frequencies and responses accurately. The analytical expressions of dynamic stiffness matrix of a Timoshenko beam for transverse vibration are presented in this paper. All effects of rotatory inertia and shear deformation are taken into account in the formulation. The resulting dynamic stiffness matrix combined with the Wittrick-Williams algorithm is used to compute natural frequencies and mode shapes of the 299,500 DWT VLCC, and then the vibrational responses are solved by the mode superposition method. The computational results are compared with those obtained from other approximate methods and experiment, and it indicates that the method is accurate and efficient.

Gershgorin and Rayleigh Bounds on the Eigenvalues of the Finite-Element Global Matrices via Optimal Similarity Transformations

The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenvalue bounding theorem to this matrix inherently fails to foresee its positive definiteness, predictably, and routinely failing to produce a nontrivial lower bound on the least eigenvalue of this, theoretically assured to be positive definite, matrix. Considered here are practical methods for producing an optimal similarity transformation for the finite-elements global stiffness matrix, following which non trivial, realistic, lower bounds on the least eigenvalue can be located, then further improved. The technique is restricted here to the common case of a global stiffness matrix having only non-positive off-diagonal entries. For such a matrix application of the Gershgorin bounding method may be carried out by a mere matrix vector multiplication.

Dynamic stiffness matrix of a poroelastic multi-layered site and its Green's functions

Few studies of wave propagation in layered saturated soils have been reported in the literature.In this paper,a general solution of the equation of wave motion in saturated soils,based on one kind of practical Blot's equation, was deduced by introducing wave potentials.Then exact dynamic-stiffness matrices for a poroelastic soil layer and half- space were derived,which extended Wolf's theory for an elastic layered site to the case of poroelasticity,thus resolving a fundamental problem in the field of wave propagation and soil-structure interaction in a poroelastic layered soil site.By using the integral transform method,Green's functions of horizontal and vertical uniformly distributed loads in a poroelastic layered soil site were given.Finally,the theory was verified by numerical examples and dynamic responses by comparing three different soil sites.This study has the following advantages:all parameters in the dynamic-stiffness matrices have explicitly physical meanings and the thickness of the sub-layers does not affect the precision of the calculation which is very convenient for engineering applications.The present theory can degenerate into Wolf's theory and yields numerical results approaching those for an ideal elastic layered site when porosity tends to zero.

Analysis of Vibration of the Euler-Bernoulli Pipe Conveying Fluid by Dynamic Stiffness Method and Transfer Matrix

The dynamic stiffness method and Transfer method is applied to study the vibration characteristics of the Euler-Bernoulli pipe conveying fluid in this paper. According to the dynamics equation of the pipe conveying fluid, the element dynamic stiffness is established. The vibration characteristic of the single-span pipe is analyzed under two kinds of boundary conditions. The results compared with the literature, which has a good consistency. Based on this method, natural frequency and the critical speed of the two types of multi-span pipe are deserved. This paper shows that the dynamic stiffness method and transfer matrix is an effective method to deal with the vibration problem of pipe conveying fluid.

Finite element model for arch bridge vibration dynamics considering effect of suspender length adjustment on geometry stiffness matrix

In this paper, we established a finite element (FEM) model to analyze the dynamic characteristics of arch bridges. In this model, the effects of adjustment to the length of a suspender on its geometry stiffness matrix are stressed. The FEM equations of mechanics characteristics, natural frequency and main mode are set up based on the first order matrix perturbation theory. Applicantion of the proposed model to analyze a real arch bridge proved the improvement in the simulation precision of dynamical characteristics of the arch bridge by considering the effects of suspender length variation.

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.

Dynamic Behaviour of Cast A356/Al₂O₃Aluminum Metal Matrix Nanocomposites

The present work includes the study of the dynamic properties of the nanocomposites specimens. The dynamic properties of A356/Al2O3 nanocomposites were investigated through different fabrication conditions. The A356/Al2O3 nanocomposites specimens were fabricated using a combination between the rheocasting and squeeze casting routes. The composites were reinforced with Al2O3 particulates of 60 and 200 nm and different volume fractions up to 5 vol.%. The dynamic properties of the A356/Al2O3 nanocomposites were investigated through measuring the dynamic properties of specimens. Free vibration method is used to measure frequency response (fn ), and damping factor (ξ). The viscoelastic properties such as loss factor η, storage modulus (E'), and loss modulus (E") were obtained. The results concluded that, the dynamic properties of nanocomposites were improved by increasing the volume fractions of nanoparticulates and decreasing the nanoparticulates size. The results indicated also that, the damping factor, and the related parameters (η, E' and E") was strongly affected by increasing both volume fraction and the particulates.

用于夹层梁静动力及屈曲分析的新型组合结构单元

推导出新型组合结构单元,用于考虑界面滑移的3层部分作用夹层组合梁的静动力及屈曲特性分析.基于铁木辛柯梁理论,建立考虑夹层梁部分作用效应的能量原理.针对其受力特性,在节点位移、横截面转角和界面滑移插值时均采用含内部自由度的高阶插值函数,以解决含界面有限元数值分析中常遇到的“滑移锁定”现象.通过变分原理得到夹层梁的刚度矩阵、质量矩阵以及几何刚度矩阵的显示表达式.基于MATLAB编译相应夹层结构的有限元程序并验证其准确性.对不同截面3层夹层组合梁进行不同荷载条件和边界条件下的静动力及屈曲特性分析,并探讨不同夹层组合梁跨高比和不同界面抗剪连接刚度下的计算结果及其误差的变化规律.所推导的显示表达式新型组合结构单元计算效率高,并便于推广应用于其他有限元程序或商业软件子程序中.

全装配RC楼盖结构振动台试验与平面内刚度分析

为研究采用分布式连接全装配RC楼盖(DCPCD)结构抗震性能,依据一致相似律设计制作了缩尺比例为1/4的单跨两开间四层全装配RC楼盖框架-剪力墙结构振动台试验模型。建立了考虑DCPCD平面内弹性变形的等效梁、连接件模型和现浇结构对比模型,分析了三种模型的动力特性与地震响应。进行了模型结构在水平地震激励下的振动台试验。结果表明:欠人工质量模型是合理可行的,模型重力效应可达到应有重力效应的63%以上,减小了重力失真效应对试验结果的不利影响;等效梁模型与连接件模型两种分析方法能较好地模拟DCPCD结构的地震响应;水平地震作用下DCPCD发生了较大的平面内变形,使地震响应与现浇结构存在较大差异;DCPCD不满足国内外规范对刚性楼盖的规定,建议抗震设计时考虑楼盖的平面内变形对地震作用计算和抗震分析的影响。

基于改进MSET的一次风机故障预警及诊断方法

针对电站风机故障预警和故障点追溯等问题,基于改进多元状态估计技术(MSET)模型和误差分量,提出了一次风机故障预警和诊断方法。首先,介绍了多元状态估计技术的概念;选取了建模变量,并进行了数据预处理,通过构建改进动态记忆矩阵D,进行了MSET模型有效性的验证;然后,使用相似度函数作为故障预警依据,并利用滑动窗口法降低了噪音干扰,采用两种动态记忆矩阵构建方法,分别建立了模型,并进行了模型的有效性验证;最后,采用人为增加扰动的方式,模拟了温度、振动故障数据,进行了故障预警模拟,并通过计算各参数的误差分量进行了故障点追溯。研究结果表明:改进的动态记忆矩阵建模方法具有更高的准确度和更强的抗干扰能力;改进MSET和误差分量模型可成功实现故障的提前预警和故障点追溯功能。该模型能够为电站设备故障预警和检修提供借鉴。

控制力矩陀螺微振动时的固有频率波动机理研究

为了解控制力矩陀螺(CMG)与蜂窝板的共振机理从而指导微振动地面试验,建立了一个蜂窝板上CMG的等效动力学模型。通过等效板理论和薄板理论推导蜂窝板刚度矩阵的半解析解;结合随框架角变化的CMG惯量矩阵和陀螺矩阵获得CMG固有频率及其波动的变化规律。并提出控制力矩陀螺的设计建议,以期为CMG的地面试验设计提供理论支撑和指导意见,解决CMG与蜂窝板的共振问题。

基于节点相似性的并行启发式网络拓扑结构发现算法

针对网络社区发现算法的低精确度与高复杂度问题,在节点相似性的基础上提出了一种适用于复杂网络的社区发现算法。利用邻接矩阵和经典决策规则,制定具有较高可靠性和准确性的相似性判定准则,实现网络拓扑中相邻节点之间关系的量化与计算。通过引入具有较少冲突的哈希表,提出具有并行运算结构的启发式社区发现算法,完成对复杂网络拓扑结构的高质量检测。仿真测试结果表明,与经典的Jaccard准则发现算法相比,基于节点相似性的发现算法具有更高的发现精确度及时间效率。

基于谱聚类的社交网络动态社区发现算法

动态社区发现研究是社交网络分析(SNA)的重要研究领域。随着节点加入或离开社交网络,节点间的关系也随之建立或消失,进而影响着社区结构的变化。针对社交网络静态社区发现算法缺少必要的社区节点历史信息而导致的网络结构分析、聚类信息不足和计算开销过大的问题,基于社区网络演化事件的划分并根据主要社区事件的分析,提出一种基于谱聚类的动态社区发现算法(SC-DCDA)。首先,根据实验观察使用谱映射的方法将高维数据降维,并采用改进的模糊C-均值聚类(FCM)算法确定动态社交网络中的节点与待发现社区的关联度;其次,根据演化相似度矩阵分析社区结构。通过使用真实网络数据集以及模块度得分、轮廓系数等社区发现算法衡量指标,评估所提算法的效果。实验结果表明,SC-DCDA的计算开销相较于传统谱聚类降低了8.37%,在所有数据集上的平均模块度得分是0.49,其他衡量指标的定性分析结果也较好,验证了所提算法在信息交互、聚类效果和精确度上表现较好。

上土下岩地层中柱面SH波的传播特性分析

为了研究爆破地震波在上土下岩地层中传播的曲率对地表振动的影响,选取爆破地震波中的柱面SH波作为研究对象,基于弹性地震波理论与积分变换方法,建立了单层、多层层状地层的刚度矩阵和动力平衡方程。并以武汉宝通寺地铁站爆破开挖为工程背景,分析了地表速度与土岩地层界面速度的比值(|v_(0)/v_(1)|)与土层厚度和震源深度等参数的关系。结果表明:上土下岩地层中,当入射波频率大于30 Hz时,土层对距震距200 m处的地表振动速度具有明显的放大作用,土层越厚,土层的放大效应越小;而随着震中距的增加,土层呈现出过滤高频波的作用;随着震源深度增加,土层的放大效应逐渐减小;当震源深度在10~15 m时,可把柱面SH波简化为平面波作用。

基于正交试验的机床结合部动刚度优化配置

机床中结合部分布众多且不同接触条件下其动刚度值不同,优化分析时很难研究每个动刚度值对机床动态性能的影响。针对此类问题,提出一种基于正交试验的机床结合部动刚度优化配置方法。该方法通过模态柔度与弹性能分布理论判定机床的薄弱模态和薄弱结合部,建立以薄弱结合部的动刚度为设计变量,各阶薄弱模态的最小模态柔度为目标的多目标优化模型。为提高优化效率,采用正交试验方法规划试验方案,并在试验结果分析中引入相似优先比法对结合部动刚度进行协同优化配置。以某型立式加工中心为例,采用优化配置方法确定其结合部动刚度的最优配置方案。仿真结果显示该方案下薄弱模态的模态柔度明显降低,整机动态性能提高,验证了该方法的可行性。

轴承-转子系统中滚动球轴承的动力学相似设计

针对轴承-转子系统缩尺模型中轴承的动力学相似设计问题,基于量纲分析法和相似π定理,建立了轴承-转子系统中滚动球轴承模型的动力相似准则,获得了滚动球轴承模型与原型各动力参数的相似关系.在此基础上根据滚动球轴承刚度计算公式得出刚度与基本参数之间的相似关系,并进行了滚动球轴承接触变形和最小油膜厚度的数值验证.最后通过设计实例说明了所建立的相似关系在实际轴承-转子模型设计中的有效性和实用性.

一系螺旋弹簧动刚度对车辆-轨道耦合振动影响分析

建立准确表征一系悬挂轴箱螺旋弹簧波动特性的力学模型,运用动刚度矩阵法求解,研究其对悬挂系统隔振性能影响。结合基于格林函数法的车辆-轨道耦合动力学模型,引入弹簧刚度频变特性,对比分析考虑一系螺旋弹簧频变刚度前后车辆动力学性能之间的差异。结果表明,动刚度矩阵法可以精确求解螺旋弹簧随频率变化的动刚度特性,在一阶模态振动频率后弹簧刚度值呈现103等级的剧烈变化,该结果与有限元模型结果一致;一系螺旋弹簧的动态频率特性导致轮轨激励由车轮至构架的振动位移传递率提高到接近于1,而对车体的振动传递率提高到了10-3左右;在整车车辆-轨道动力学计算中,其对轮轨振动影响较小,但车体与构架出现了较高的高频振动能量峰值。包含一系悬挂动刚度的车辆模型更接近实际,为了降低车辆振动,应尽量提高一系螺旋弹簧自振频率并降低动刚度变化幅值。

非线性多自由度转子系统精细数值积分

针对非线性动力学问题中的刚度病态或奇异的问题,在某些高精度算法失效的情况下,经过恒等变换,抑制了刚度奇异和病态,然后通过哈密顿体系的常用方法将原方程转化为一阶微分方程,并利用求解非线性动力学方程的分段直接积分法进行逐步积分计算,提出了处理刚性问题的一般方法。以动力学行为极其复杂的非线性油膜力支撑的多自由度转子系统为例,采用较大时间步长获得到了较为理想的计算结果。

句子相似度的动态规划求解及改进

基于例子的机器翻译,其很关键的步骤之一就是如何从语料库中找到待译句子的最佳相似句。论文针对这个问题提出了利用动态规划方法基于句子相似矩阵进行求解的方法。根据这个方法就可以从语料库中为待译句子找到最佳相似句,同时在求解过程中还做了一些改进:利用矩阵分块求解的方法保留了句子的连续相似块,保证了结果的质量,对提高EBMT系统的翻译质量起到了一定的促进作用。