Perturbation of symmetries for super-long elastic slender rods

This paper analyses perturbations of Noether symmetry, Lie symmetry, and form invariance for super-long elastic slender rod systems. Criterion and structure equations of the symmetries after disturbance are proposed. Considering perturbation of all infinitesimal generators, three types of adiabatic invariants induced by perturbation of symmetries for the system are obtained.

Structure properties and Noether symmetries for super-long elastic slender rod

DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. This paper studies the structural properties of a super-long elastic slender rod as a structural model of DNA by using Kirchhoff＇s analogue technique and presents the Noether symmetries of the model by using the method of infinitesimal transformation. Baaed on Kirchhoff＇s analogue it analyses the generalized Hamilton canonical equations. The infinitesimal transfornaationa with rcspect to the radial coordinnte, the gonarnlizod coordinates, and the Cluasi-momenta of 5he model are introduced. The Noether gymmetries and conserved qugntities of the model are obtained.

Dynamic Response Study of Steel Catenary Riser Based on Slender Rod Model

A numerical model of the steel catenary riser(SCR) is built based on the slender rod model. The slender rod model,which describes the behavior of the slender riser in terms of the center line position, can solve the geometrical nonlinearity effectively. In a marine environment, the SCR is under the combined internal flow and external loads,such as wave and current. A general analysis considers only the inertial force and the drag force caused by the wave and current. However, the internal flow has an effect on the SCR; it is essential to explore the dynamic response of the SCR with the internal flow. The SCR also suffers the lift force and the fluctuating drag force because of the current. Finite element method is utilized to solve the motion equations. The effects of the internal flow, wave and current on the dynamic response of the SCR are considered. The results indicate that the increase of the internal flow density leads to the decrease of the displacement of the SCR, while the internal flow velocity has little effect on the SCR. The displacement of the SCR increases with the increase of the wave height and period. And the increasing wave period results in an increase in the vibration period of the SCR. The current velocity changes the displacements of the SCR in x-and z-directions. The vibration frequency of the SCR in y-direction increases with the increase of the current velocity.

Singularity Theory on Buckling of Compressible Slender Rods with Deformation of Cross Section

他们的不稳定性上的杆的压缩的可能性的关键效果是经由奇特理论表明的使用新方法。可压缩的杆的批评负担总是比一 Euler 杆，和一个代用品大，这被显示出批评草耙分叉，不能为 Euler 杆发生，可以为可压缩的杆发生。可压缩的杆的一张整个分叉图如下；什么时候可压缩的杆的原来的苗条海角比率， S_0，比小(1 +upsilon/3 ) 3X3 ^(1/2 ) Xpi/2，杆不弄弯；当 S_0 暗示了由时[(1+upsilon/3 ) 3X3 ^(1/2 ) pi/2，(1+upsilon/5 ) 5X5 ^(1/2 ) Xpi/4 ] ，杆可以经历 subcriticalpitchfork 分叉，倒塌可以发生；当 S_0 暗示了由时[(1 +upsilon/5 ) 5X5 ^(1/2 ) Xpi/4， +infinity ] ，杆可以经历超级批评草耙分叉。原因有点分叉转移的杆的生气的节的变丑指向到相应于更大的苗条海角比率的。

Determination of complex Young's modulus of viscoelastic bars using forced longitudinal vibration of slender rods

A method to identify complex Young＇s modulus of viscoelastic materials using forced longitudinal vibration of slender rods is proposed. The method differs from the beam one. Experimental tests were carried out at room temperature with different lengths in 108 mm, 100 mm, 90 ram, 83.5 mm, 80 ram, 74.5 mm, 70 mm for the polycarbonate bars, and the curves of ratios A2/A1 between two ends of a viscoelastic bar versus frequencies are obtained, furthermore, the corresponding 3 dB bandwidth and the storage and loss modulus can be calculated. Sufficient number of obtained complex Young＇s modulus at different frequency allows us to calculate other ones using the least square method. If the step of the tested frequency is 5 Hz, the maximum error of results can be less than 6%. By comparison with the measurement methods which the previous literature mentioned, this new method simplifies the calculation, and the physical meaning appears apparently and clearly.

考虑轴向大拉伸下弹性模量对聚酯系泊动态响应的影响

Owing to the particularity of a polyester fiber material,the polyester mooring undergoes large axial tensile deformation over long-term use.Large axial tensile deformation significantly impacts the dynamic response of the mooring system.In addition,the degrees of large axial tension caused by different elastic moduli are also different,and the force on the mooring line is also different.Therefore,it is of great significance to study the influence of elastic modulus on the dynamic results of the mooring systems under large axial tension.Conventional numerical software fails to consider the axial tension deformation of the mooring.Based on the theory of slender rods,this paper derives the formula for large axial tension using the method of overall coordinates and overall slope coordinates and provides the calculation programs.Considering a polyester mooring system as an example,the calculation program and numerical software are used to calculate and compare the static and dynamic analyses to verify the reliability of the calculation program.To make the force change of the mooring obvious,the elastic moduli of three different orders of magnitude are compared and analyzed,and the dynamic response results after large axial tension are compared.This study concludes that the change in the elastic modulus of the polyester mooring changes the result of the vertex tension by generating an axial tension.The smaller the elastic modulus,the larger the forced oscillation motion amplitude of the top point of the mooring line,the more obvious the axial tension phenomenon,and the smaller the force on the top of the polyester mooring.

细长竹木圆棒双激光对射自动检测系统设计

针对细长竹木圆棒胚体存在的表面凹坑、开裂等外观缺陷,设计了一种双激光对射式自动检测系统。机械结构采用载物链条使细长竹木圆棒整体平移并在弹性压板下滚动,由对称布置的双激光斜入射至压板和圆棒贴合部位,实现对竹木圆棒表面的双螺旋扫描和空隙检测;控制部分以西门子S7-200 Smart PLC为主体,设计了与实体链条同步的数字链条进行并行控制。测试结果表明,系统相对于人工检测漏检率为0,具有成本低、效率高、可靠性高、易于使用等特点,可有效解决细长竹木圆棒胚体表面质量初筛问题。

超细长拉紧杆车槽夹具的设计

针对拉紧杆零件的结构特点及空刀槽的加工问题,设计了拉紧杆车槽夹具。介绍了拉紧杆车槽夹具的结构组成及重要部件的详细结构特征,给出了车槽夹具安装、使用方法。应用拉紧杆车槽夹具,可以提高拉紧杆零件表面质量和加工精度,在生产中具有良好的实用性。

一种航空涡轮发动机传动零件轴转子的加工方法研究

某航空涡轮发动机传动零件轴转子在加工过程中让刀现象严重,刀具磨损过快,叶片加工尺寸不稳定,叶片表面容易形成振纹。为了解决这一问题,介绍了一种加工工艺,并给出了合适的刀具选择。

考虑轴向均布荷载的细长压杆临界荷载近似解析解

计算细长压杆临界荷载时,若考虑轴向均布荷载,则只能求得数值解,不能得到解析解。为获得近似解析解,建立了细长压杆屈曲时的势能函数,由势能驻值原理导出稳定方程进行求解。受既有3种细长压杆的傅里叶级数型挠曲线的启发,探索另外6种既满足位移边界条件又满足内力边界条件的傅里叶级数型挠曲线,求得9种细长压杆临界荷载的近似解析解。结果表明:临界荷载与轴向均布荷载成线性或准线性关系。若在所得解答中令轴向均布荷载为零,则可得细长压杆的欧拉临界荷载;若令上端中心轴向荷载为零,则可得细长压杆的均布临界荷载。若考虑轴向均布荷载,支座位置互换后临界荷载一般会有特别显著的变化。比较所得解答与有限元数值解发现:大多数细长压杆的两种解较一致,即所得解答能满足预期要求。

套管加固法加固轴压钢管柱力学性能研究

套管加固法加固轴压钢管柱是一种能有效抑制轴压钢管柱屈曲失稳的加固方法,具有理论清晰、构造简单、安全可靠、技术合理、经济适用等显著优点。本文基于ABAQUS软件模拟分析内杆长细比及套管内杆长度比对杆件在轴向压力作用下的破坏机理及极限承载力的影响,选取4种不同套管内杆长度比和6组内杆长细比不同的杆件进行有限元模拟分析,得出套管内杆长度比及内杆长细比对杆件轴压极限承载力的影响规律,为套管加固法在工程中的应用提供一定的设计依据。

不同因素对于深海系泊系统动张力的影响分析

研究了流作用下的初始位置、缆长和预张力对于深海系泊缆动张力的影响.考虑深水系缆的拉伸和弯曲变形,以及缆变形的几何非线性和水动力影响,取正交坐标和切向量描述任意结点的6个广义位移,基于细长杆理论推导缆索的单元刚度矩阵,引入单元内张力一致假设,得到12×12的非线性刚度矩阵,实现了本文单元与有限元软件的调用对接.同时计算了不同初始位置、缆长和预张力条件下系泊系统的动张力,给出了不同因素对于动张力的影响规律.

考虑内流作用的钢悬链线立管动力特性分析

考虑内流的作用,研究钢悬链线立管动力特性。采用细长柔性杆模型,建立内流作用下钢悬链线立管运动方程,运用有限元法进行离散,通过求解动力特性方程得到立管的固有频率和模态,基于Matlab平台编写相应计算程序,探讨内流流速、顶张力和顶端压强对钢悬链线立管动力特性的影响。结果表明:随着内流流速的增加,立管的固有频率降低,高阶模态的反转点向立管底端移动;随着顶张力的增加,立管的固有频率增加,高阶模态的反转点向立管顶部移动;随着管内顶端压强的增加,立管的固有频率降低。

振动采气管柱应力强度分析

为了给采气管柱疲劳寿命分析和完整性分析提供依据,考虑管柱自重及内、外压沿深度的线性变化,用有限元软件分析振动采气管柱的应力强度。将采气管柱看作是内空的细长杆,用有限元法对管柱进行离散化处理,再用拉格朗日方程得到采气管柱动力学微分方程。采用二维轴对称模型进行建模,采用4节点平面单元Plane42进行分析。分析结果表明,采用ANSYS中轴对称单元Plane42建立采气管柱有限元模型,进行振动采气管柱的应力强度分析是一种有效的方法;井口管柱应力最大,是应力危险点;振动载荷作用下,管柱内壁所受应力大于外壁所受应力。

轴向拉伸细长杆的非线性力学模型

聚酯系泊缆是深海工程中具备一定抗弯刚度、易拉伸变形的细长杆件结构.聚酯缆的轴向变形属大拉伸范畴,分析中应当区分变形前后状态,特别是缆索长度的改变使得基于小拉伸假设的细长杆模型需要予以改进.因此,基于Garrett细长杆模型,应用总体坐标和斜率取代Euler-Bernoulli(欧拉-伯努利)梁元的转角,解决缆索在空间中大转动变形的几何非线性问题;使用轴向拉伸变形前后物质点对应的方法,借助单元两个节点和一个中点,以及3个二次多项式形函数描述轴向拉伸变形下细长杆元的运动微分方程.通过与轴向拉伸悬臂梁的对比分析,验证了该拉伸杆元的收敛性和准确性.

深海系泊浮体物面非线性时域耦合动力分析

文章基于三维时域势流理论和弹性细长杆理论,研究并提出了深海系泊浮体物面非线性时域耦合动力分析方法。该方法采用时域物面非线性理论方法在瞬态位置直接时域模拟系泊浮体所需水动力,结合有限元方法计算系泊缆索的动力响应,利用异步耦合方法实现浮体和系泊缆索的时域耦合动力求解。既满足系泊浮体时域水动力耦合,又满足系泊浮体和系泊缆索动力耦合。通过对二阶非线性不规则波作用下深海系泊半潜式平台的时域耦合响应特性进行研究,将不同海况下物面非线性时域耦合静力响应和动力响应与间接时域耦合动力响应的三种方法计算结果进行比较。研究结果表明,系泊缆索动力响应明显,平台瞬态空间位置对垂荡低频运动影响较大,有必要在平台瞬时湿表面采用动力响应方法进行深海系泊浮体时域耦合响应分析。

细长杆与圆孔孔壁接触碰撞问题的动力间隙元法

本文通过在任意曲率的细长杆节点和圆孔孔壁之间构造一种虚拟单元——动力间隙元,将任意曲率的细长杆与圆孔孔壁连接起来,使其间的接触碰撞问题转化为平衡方程问题。文中针对石油工程中钻柱这类典型的细长杆与圆形井壁的接触碰撞问题进行了求解。结果表明,动力间隙元能较好地解决细长杆(如钻柱)与圆孔孔壁(如井壁)的接触碰撞问题。

轴向车铣细长杆的动力学分析

根据弹性体动力学理论,建立轴向车铣细长杆的动力学模型,得到了各阶固有频率和主振型的计算公式,分析了在简谐激励下细长杆强迫振动的动力学响应。利用ANSYS对40Cr细长杆的车铣加工进行了模态分析和谐响应分析,得到了细长杆振动峰值的频率和幅值,且与理论计算的结果一致。研究结果表明,在细长杆的车铣加工中,应合理选择铣刀转速和齿数,可使切削频率避开共振区间,有利于得到更好的加工质量。

细长杆多腔模不平衡注塑工艺优化

分析了细长杆多腔模平衡布局的不平衡原因,把径向方向Y的变形作为平衡优化的指标,提出优化成型工艺达到降低不平衡的思想,运用响应面建立拟合模型对4个成型工艺参数进行优化,分析结果证明,优化后Y方向的变形值降低了20.4%,充分证明优化方法的有效性。

深海系缆动张力的超谐动力响应

文章考虑深水系缆的拉伸和弯曲变形,取正交坐标和切向量描述任意结点的6个广义位移,考虑缆变形的几何非线性和水动力影响,基于细长杆理论推导缆索的单元刚度矩阵,引入单元内张力一致假设,推导出12×12的非线性刚度矩阵,并与有限元软件对接。针对1800m水深平台的系缆,考虑系缆端点垂荡运动,以及端点垂荡、横荡和海流作用两种状态下系泊系统的动力响应。计算结果表明,端点运动和海流作用,引起系缆系统的二倍超谐动力响应,并且随着流速增大,系缆超谐动力响应增大,系缆的超谐动张力分量对于缆索疲劳累积损伤具有重要影响,在系缆疲劳分析时应该予以考虑。