字典乘积图的Euler性

人们在实践中发现,网络拓扑结构的一些性质能够在某种程度上衡量一个网络的性能如何,网络的可靠性便是其中的一个重要性能指标.分析现实世界中已有网络,如计算机网络、电网以及通讯网络等的可靠性具有重要的理论意义和应用价值.图的字典乘积利用已有规模较小的网络来构建规模较大的网络,且所得大网络的特征值完全由小网络的拓扑结构参数来刻画,并具有良好的性能,而图的欧拉回路与欧拉迹亦在此领域有着广泛的应用.乘积因子图的拓扑结构影响着字典乘积图的拓扑结构.本文主要研究字典乘积图的Euler回路问题和Euler迹问题,利用组合理论和极值构造方法,给出了两图的字典乘积图为Euler回路和Euler迹的一些充分必要条件.     

Euler梁有限差分模型的振动逆问题

本文用变步长的二阶差分格式建立了Euler 梁的离散模型,并找出了与之等价的弹簧-质点-刚杆系统。在此基础上,研究了Euler 梁离散模型频谱的性质,讨论了由全频谱数据构造Euler 梁截面参数的问题,简化了已有的算法,并用这一算法计算了数值算例,对结果作了初步分析。     

压电型Euler—Bernoulli梁的有限元分析方法

本文运用微分方程等效积分形式导出的虚位移原理和智能压电材料的压电效应提出了一种表面粘贴有ＰＶＤＦ压电薄膜的Ｅｕｌｅｒ－Ｂｅｒｎｏｕｌｌｉ梁单元模型；由有限单元法给出了运动微分方程，通过数值计算，将所得结果与有关文献进行了对比分析和研究。     

On Euler’s stretching formula in continuum mechanics

The Lie time-derivative of the material metric tensor field along the motion is the proper mathematical definition of the physical notion of strain rate or stretching. Its expression, as symmetric part of the velocity gradient in Euclid space, is provided by a celebrated formula conceived by the genius of Leonhard Euler around the middle of the eighteenth century and since then reproduced in articles, books and treatises on continuum mechanics. We present here a formulation, in the proper geometric context of the four-dimensional space-time manifold endowed with an arbitrary linear connection and referring to a material body of arbitrary dimensionality. The expression involves the material time-derivative of the metric field and torsion-form and gradient of the velocity field, according to the connection induced on the trajectory. As an application, the expressions of the Gram matrix of the stretching in natural and in normalized (or engineering) reference systems induced by orthogonal polar coordinates are provided.     

探索Euler生成子图边数的一种方法

关于超欧拉图的欧拉生成子图(spanning eulerian subgraph)的边数问题,P,A．Catlin、HongJian Lai、Zhi-Hong Chen等人提出若干问题。本文给出了探索超欧拉图的欧拉生成子图边数的一种方法。     

Euler梁的模态和频谱的一些定性性质

本文讨论了Euler梁的离散模型在任意边界支承(固支、铰支、滑支和自由)下的固有频率和模态的定性性质。文中指出梁的非零频率是分离的,并给出了梁的单个非刚体模态满足的充要条件。     

基于Euler Bernoulli理论的压电系统集中参数模型修正

摘要： 针对压电俘能系统悬臂梁结构集中参数模型的局限性,引入Euler Bernoulli梁振动模型。通过分析两模型在振动时相对位移传递率发现,集中参数模型在基础激励情况下,传递率峰值存在较大偏差。理论分析了Euler Bernoulli及集中参数模型在一阶模态附近位移传递率函数,对集中参数模型进行了修正。仿真结果表明修正后的集中参数模型相对位移传递率峰值与Euler Bernoulli模型在低阶模态吻合良好。     

基于Euler Bernoulli理论的压电系统集中参数模型修正

针对压电俘能系统悬臂梁结构集中参数模型的局限性,引入Euler Bernoulli梁振动模型。通过分析两模型在振动时相对位移传递率发现,集中参数模型在基础激励情况下,传递率峰值存在较大偏差。理论分析Euler Bernoulli及集中参数模型在1阶模态附近位移传递率函数,对集中参数模型进行修正。仿真及有限元结果表明修正后的集中参数模型相对位移传递率峰值与Euler Bernoulli模型在低阶模态吻合良好。     

Analysis of viscoelastic Bernoulli–Euler nanobeams incorporating nonlocal and microstructure effects

The present study introduces an analytical–computational model to simulate the effects of different simultaneous aspects on the behavior of nanobeams. The first one deals with the space nonlocality interaction and taking into account the microstructure effects, which has been formulated by using the nonlocal couple-stress elasticity. The second factor deals with the memory-dependent effect and has been investigated in the framework of linear viscoelasticity theory. It is the first time to apply the coupled effects of the microstructure and long-range interactions between the particles, to reflect the size-dependency of viscoelastic structures. Bernoulli–Euler nanobeam is taken as a vehicle to present the details of the proposed model. Eringen nonlocal elasticity and the modified couple-stress theory are used to formulate the two phenomena of long-range cohesive interaction and the microstructure local rotation effects, respectively. Boltzmann superposition viscoelastic model, endowed by Wiechert series, is used to simulate the linear behavior of isotropic, homogeneous and non-aging viscoelastic materials. The extended Hamilton’s principle is applied to formulate the analytical model of mechanical behavior of the nonlocal couple-stress nanobeam. The model has been verified and some results are compared with those published in the literature and a good agreement has been obtained. It is shown that the material-length scale parameter, nonlocal parameter, viscoelastic relaxation time and length-to-thickness ratio have a significant effect on the bending response of viscoelastic nanobeams with various boundary conditions.     

A Lagrange‐Euler‐assumed modes approach to modeling flexible robotic manipulators

Abstract

This paper presents a general Lagrange‐Euler‐assumed modes dynamics formulation for lightweight flexible manipulators. The proposed explicit form formulation, not yet available in the existing literature, can be viewed as an extended version of the Lagrange‐Euler formulation for rigid manipulators. The deformation of a link from its rigid body position is modeled by a homogeneous 4×4 transformation matrix composed of summations of assumed link modes. The number of modes can be arbitrarily selected. The joint flexibility is modeled by a linear torsionai spring with known characteristics. The methodology presented can be easily used to derive the full nonlinear dynamic equations of flexible manipulators by computing only the dynamic coefficients using computer algebra such as MACSYMA. The resulting nonlinear dynamic equations are in a closed form and are especially suitable for advanced nonlinear control strategy synthesis. Taken as an illustrative example, a two‐link flexible manipulator is studied to demonstrate the effectiveness of the formulation.     

颗粒流体系统Euler/Lagrange模型中自适应三角网格的生成

针对二维颗粒流体系统Euler／Lagrange模型的有限元模拟,建立了三角网格生成的自适应算法。该算法能够根据颗粒分布与颗粒大小自适应地调整网格的疏密程度,使其网格密度在系统边界附近及颗粒边缘附近较大,而在其它地方较小。与此同时,网格的光滑化也提高了网格质量, 从而为颗粒流体系统介观尺度的有限元模拟奠定了基础。     

A note on the integrability of a remarkable static Euler–Bernoulli beam equation

It has recently been shown that the fourth-order static Euler–Bernoulli ordinary differential equation, where the elastic modulus and the area moment of inertia are constants and the applied load is a function of the normal displacement, in the maximal case has three symmetries. This corresponds to the negative fractional power law y ^?5/3, and the equation has the nonsolvable algebra ${sl(2, \mathbb{R})}$ . We obtain new two- and three-parameter families of exact solutions when the equation has this symmetry algebra. This is studied via the symmetry classification of the three-parameter family of second-order ordinary differential equations that arises from the relationship among the Noether integrals. In addition, we present a complete symmetry classification of the second-order family of equations. Hence the admittance of ${sl(2, \mathbb{R})}$ remarkably allows for a three-parameter family of exact solutions for the static beam equation with load a fractional power law y ^?5/3.     

基于Euler方程的B型和C型嗡鸣特性数值研究

运用非定常Eu ler方程求解气动力,耦合结构运动方程,采用改进的四步龙格-库塔推进方法,在时间域内研究了音速附近发生的单自由颤振问题。其中气动力模块采用非结构网格技术进行空间离散,运用线性弹簧方法实现非结构网格的运动。空间上采用Jam son中心格式的有限体积法,时间上采用双时间推进方法。从无量纲化的结构方程出发,把M数、音速、密度、舵面刚度、转动惯量、弦长等一系列气动、结构参数对嗡鸣特性的影响归结为三个无量纲参数的影响。通过研究发现,运用非定常Eu ler方程可以模拟B型和C型嗡鸣,但不能模拟因激波附面层干扰而产生的A型嗡鸣。C型嗡鸣比B型嗡鸣发展缓慢,提高系统阻尼对于排除C型嗡鸣更有效。     

基于样条有限点法的变截面Euler梁横向自由振动分析

基于Bernoulli-Euler梁理论,采用样条有限点法建立考虑截面高宽度沿轴线性变化的变截面Euler梁振动分析的计算模型,通过沿梁轴线设置一定数量的样条节点对变截面梁样条离散化,采用三次B样条函数对梁的位移场进行插值,基于Hamilton原理导出变截面Euler梁的振动方程,推导考虑截面尺寸变化效应的总刚度和总质量矩阵的表达式,并编制计算程序,算例分析表明,模型的变截面梁的横向自振频率解答与文献解答吻合良好,计算精度和计算效率高,且模型边界处理简单,取样条离散节点数为15时,模型可以取得较高精度且解答趋于稳定。模型可适用于不同边界、不同截面变化率和不同截面类型的变截面Euler梁的自由振动分析。     

移动列车荷载作用于单层Euler梁上时地基土的变形分析

以弹性波动理论及分层法为基础,提出一种计算车辆-轨道-地基土耦合体系动力响应的方法,其中将列车荷载分别简化为移动荷载、单自由度移动质量块及双自由度移动体系,轨道模拟为单层的Euler梁.考虑车辆-轨道-地基土的协同工作,计算地基土的变形.计算分析表明:1)地基土变形最大值出现在荷载作用点附近;2)将列车荷载仅仅简化为移动荷载是不合理的;3)车辆重量对地基土变形影响较大;4)车辆与轨道结构本身均有一定的减振功能.同时,与同类研究方法相比,该方法有计算量小的优点.研究成果可为研究由列车振动荷载引起的环境振动分析和评价提供参考.     

Banach空间中复合刚性Volterra泛函微分方程隐显Euler方法的稳定性分析

刚性泛函微分方程数值方法的研究大多是在内积空间中基于单边Lipschitz常数具有适度大小的条件下进行;然而对于某些刚性问题,其单边Lipschitz常数却不可避免地取非常巨大的正值。因此有必要突破内积空间和单边Lipschitz常数的限制,直接在Banach空间中探讨相应的数值方法。针对Banach空间中的非线性复合刚性Volterra泛函微分方程,对其非刚性部分采用显式Euler方法求解,刚性部分采用隐式Euler方法求解,得到了求解该问题的隐显Euler方法,论证了方法的稳定性和渐近稳定性。数值试验结果验证了所获理论的正确性。     

Semi-analytical solution for free transverse vibrations of Euler–Bernoulli nanobeams with manifold concentrated masses

In the present study, transverse vibrations of nanobeams with manifold concentrated masses, resting on Winkler elastic foundations, are investigated. The model is based on the theory of nonlocal elasticity in the presence of concentrated masses applied to Euler–Bernoulli beams. A closed-form expression for the transverse vibration modes of Euler–Bernoulli beams is presented. The proposed expressions are provided explicitly as the function of two integrated constants, which are determined by the standard boundary conditions. The utilization of the boundary conditions leads to definite terms of natural frequency equations. The natural frequencies and vibration modes of the concerned nanobeams with different numbers of concentrated masses in different positions under some typical boundary conditions (simply supported, cantilevered, and clamped–clamped) have been analyzed by means of the proposed closed–form expressions in order to show their efficiency. It is worth mentioning that the effect of various nonlocal length parameters and Winkler modulus on natural frequencies and vibration modes are also discussed. Finally, the results are compared with those corresponding to a classical local model.     

A Hermite DRK interpolation-based collocation method for the analyses of Bernoulli–Euler beams and Kirchhoff–Love plates

A Hermite differential reproducing kernel (DRK) interpolation-based collocation method is developed for solving fourth-order differential equations where the field variable and its first-order derivatives are regarded as the primary variables. The novelty of this method is that we construct a set of differential reproducing conditions to determine the shape functions of derivatives of the Hermite DRK interpolation, without directly differentiating it. In addition, the shape function of this interpolation at each sampling node is separated into a primitive function possessing Kronecker delta properties and an enrichment function constituting reproducing conditions, so that the nodal interpolation properties are satisfied for the field variable and its first-order derivatives. A weighted least-squares collocation method based on this interpolation is developed for the static analyses of classical beams and plates with fully simple and clamped supports, in which its accuracy and convergence rate are examined, and some guidance for using this method is suggested.     

Applications of dual MRM for determining the natural frequencies and natural modes of an Euler–Bernoulli beam using the singular value decomposition method

In this paper, a dual multiple reciprocity method (MRM) is employed to solve the natural frequencies and natural modes for an Euler–Bernoulli beam. It is found that the conventional MRM using an essential integral equation results in spurious eigenvalues and modes. By using the natural integral equation of dual MRM, the spurious eigendata can be filtered out. Four numerical examples are given to verify the validity of the present formulation. In one of these four examples, fixed–fixed supported beam, it is found that the boundary eigenvector cannot be determined by either the essential or natural integral equation alone since the rank of the corresponding leading coefficient matrix is insufficient. The singular value decomposition method is then used to solve the eigenproblem after combining the essential and natural integral equations. This method can avoid the spurious eigenvalue problem and possible indeterminancy of boundary eigenvectors at the same time.