共查询到16条相似文献,搜索用时 156 毫秒
1.
研究受力螺旋作用的圆截面Kirchhoff弹性直杆在各种边界条件下的稳定性问题. 用直角坐标和Cardano角表示截面的形心位置和姿态. 由Kirchhoff方程得到弹性细杆的直线平衡特解,导出线性化扰动方程及其通解. 根据边界条件确定积分常数的非零解存在条件,讨论了各种边界条件,如两端铰支、两端固定、一端铰支一端固定以及一端固定一端自由的弹性细杆直线平衡状态的稳定性,导出了临界载荷的表达式,绘制了稳定域,将Greenhill公式推广到其他边界条件,并且使压杆的Euler 公式成为其特例.
关键词:
Kirchhoff弹性杆
稳定性
力螺旋
Greenhill公式 相似文献
2.
以脱氧核糖核酸和工程中的细长结构为背景, 大变形大范围运动的弹性杆动力学受到关注. 将分析力学方法运用到精确Cosserat弹性杆动力学, 旨在为前者拓展新的应用领域, 为后者提供新的研究方法. 基于平面截面假定, 在弯扭基础上再计及拉压和剪切变形形成精确Cosserat弹性杆模型. 用刚体运动的概念描述弹性杆的变形, 导出弹性杆变形和运动的几何关系; 在定义截面虚位移及其变分法则的基础上, 建立用矢量表达的d’Alembert-Lagrange原理, 在线性本构关系下化作分析力学形式, 并导出Lagrange方程和Nielsen方程, 定义正则变量后化作Hamilton正则方程; 对于只在端部受力的弹性杆静力学, 导出了将守恒量预先嵌入的Lagrange方程, 并讨论了其首次积分. 从弹性杆的d’Alembert-Lagrange原理导出积分变分原理, 在线性本构关系下化作Hamilton原理. 形成的分析力学方法使弹性杆的全部动力学方程具有统一的形式, 为弹性杆动力学的对称性和守恒量的研究及其数值计算铺平道路.
关键词:
精确Cosserat弹性杆
分析动力学方法
变分原理
Lagrange方程 相似文献
3.
基于弹性杆的Kirchhoff模型讨论受拉扭弹性细杆的超螺旋形态.导出细长螺旋杆的等效抗弯和抗扭刚度.分析受拉扭弹性细杆的稳定性和分岔,且利用等效刚度概念将弹性杆的稳定性条件应用于对细长螺旋杆稳定性的判断.在扭矩不变条件下增加拉力至极限值时,直杆平衡状态失稳转为螺旋杆状态.继续增加拉力,直螺旋杆平衡状态失稳卷绕为超螺旋杆.从而对Thompson/Champney实验中受拉扭弹性细杆形成超螺旋形态的多次卷绕现象作出定性的理论解释.
关键词:
弹性细杆
Kirchhoff动力学比拟
等效刚度
超螺旋形态 相似文献
4.
5.
讨论圆截面弹性细杆在黏性介质中的平面振动. 基于Kirchhoff理论,以杆中心线的Frenet坐标系为参考系,建立其动力学方程,杆中心线为任意平面曲线时,其扭转振动与弯曲振动解耦. 讨论两端固定条件下任意形状杆的平面扭转振动,以及无扭转的轴向受压直杆和圆环杆的平面弯曲振动,导出其自由振动频率和阻尼系数. 证明空间域内压杆的Lyapunov稳定性和欧拉稳定性条件为时域内渐近稳定性的充分必要条件,或无阻尼压杆的稳定性必要条件. 圆环杆平衡恒满足渐近稳定性条件.
关键词:
弹性细杆
黏性介质
扭转振动
弯曲振动 相似文献
6.
在动力学普遍原理中, 高斯最小拘束原理的特点是可通过寻求函数极值的变分方法直接得出运动规律, 而无须建立动力学微分方程. Kirchhoff动力学比拟方法以刚性截面的姿态表述弹性细杆的几何形态, 并发展为以弧坐标s和时间t为自变量的弹性杆分析力学. 由于截面姿态的局部微小改变沿弧坐标的积累不受限制, Kirchhoff模型适合描述弹性杆的超大变形. Cosserat弹性杆模型考虑了Kirchhoff模型忽略的截面剪切变形、中心线伸缩变形和分布力等因素, 是更符合实际弹性杆的动力学模型. 建立了基于高斯原理的Cosserat弹性杆的分析力学模型, 导出拘束函数的普遍形式, 以平面运动为例进行讨论. 关于弹性杆空间不可自相侵占的特殊问题, 给出相应的约束条件对可能运动施加限制, 以避免自相侵占情况发生. 相似文献
7.
作为DNA等一类生物大分子的力学模型,弹性细杆的非线性力学再次受到关注,形成一个力学与分子生物学的交叉学科.除了不受外界约束的自由弹性细杆外,受曲面约束的弹性细杆静力学具有重要的应用背景.在分析约束、约束方程和约束力的基础上建立了受曲面约束的圆截面弹性细杆的平衡微分方程,即曲面上的Kirchhoff方程,它是以截面主矢和截面姿态坐标以及中心线的Descartes坐标为变量的微分/代数方程.作为应用,讨论了约束是圆柱面的情形.此时平衡的无量纲方程仅含的物理参数是截面对形心的抗扭刚度和对主轴的抗弯刚度的比值,与几何参数无关.由此导出方程的螺旋杆特解.数值计算表明,对弹性细杆中心线的几何形状有显著影响的是截面主矢和姿态坐标及其导数的起始值,而不是物理参数.
关键词:
弹性细杆
DNA超螺旋
曲面约束
螺旋杆 相似文献
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根据Cosserat弹性杆的动力学普遍定理,讨论其守恒量问题. 因弹性杆的动力学方程是以截面为对象,并且是以弧坐标和时间为双自变量,其守恒量必定是以积分的形式给出,分别存在关于弧坐标或时间守恒的问题. 根据弹性杆的动量和动量矩方程,导出其动量守恒和动量矩守恒的存在条件及其表达,并讨论了关于沿中心线弧坐标的守恒问题;再分别根据弹性杆关于时间和弧坐标的能量方程导出了各自的关于时间和弧坐标的守恒量存在条件及其表达, 结果包括了弹性杆的机械能守恒以及平衡时的应变能积分;守恒问题给出了例子. 积分形式的守恒量对于弹性杆动力学的理论分析和数值计算都具有实际意义.
关键词:
守恒量
Cosserat弹性杆
动力学普遍定理
双自变量 相似文献
10.
基于Kirchhoff理论讨论圆截面弹性螺旋杆的动力学问题.以杆中心线的Frenet坐标系为参考系,建立用欧拉角描述的弹性杆动力学方程.讨论其在端部轴向力和扭矩作用下保持的无扭转螺旋线平衡状态.在静力学和动力学领域内讨论其平衡稳定性问题.还讨论了弹性杆平衡的Lyapunov稳定性和欧拉稳定性两种不同稳定性概念之间的区别和联系.在一次近似意义下证明了螺旋杆在空间域内的欧拉稳定性条件是时域内Lyapunov稳定性的必要条件.导出了解析形式螺旋杆三维弯曲振动的固有频率,为螺旋线倾角和受扰挠性线波数的函数.
关键词:
弹性螺旋杆
Kirchhoff动力学比拟
Lyapunov稳定性
欧拉稳定性 相似文献
11.
The analysis of kinematics and dynamics of an elastic rod with
circular cross section is studied on the basis of exact Cosserat
model under consideration of the tension and shear deformation of
the rod. The dynamical equations of a rod with arbitrary initial
shape are established in general form. The dynamics of a straight
rod under axial tension and torsion is discussed as an example. In
discussion of static stability in the space domain the Greenhill
criteria of stability and the Euler load are corrected by the
influence of tension and shear strain. In analysis of dynamical
stability in the time domain it is shown that the Lyapunov and Euler
stability conditions of the rod in space domain are the necessary
conditions of Lyapunov's stability in the time domain. The longitudinal,
torsional and lateral vibrations of a straight rod based on exact
model are discussed, and an exact formula of free frequency of
lateral vibration is obtained. The free frequency formulas of
various simplified models, such as the Rayleigh beam, the Kirchhoff
rod, and the Timoshenko beam, can be seen as special cases of the
exact formula under different conditions of simplification. 相似文献
12.
Sébastien Neukirch Joël Frelat Alain Goriely Corrado Maurini 《Journal of sound and vibration》2012,331(3):704-720
The small-amplitude in-plane vibrations of an elastic rod clamped at both extremities are studied. The rod is modeled as an extensible, shearable, planar Kirchhoff elastic rod under large displacements and rotations, and the vibration frequencies are computed both analytically and numerically as a function of the loading. Of particular interest is the variation of mode frequencies as the load is increased through the buckling threshold. While for some modes there are no qualitative changes in the mode frequencies, other frequencies experience rapid variations after the buckling threshold, the thinner the rod, the more abrupt the variations. Eventually, a mismatch for half of the frequencies at buckling arises between the zero thickness limit of the extensible model and the inextensible model. 相似文献
13.
The extended Schro^edinger equation for the Kirchhoff elastic rod with noncircular cross section is derived using the concept of complex rigidity. As a mathematical model of supercoiled DNA, the SchrSdinger equation for the rod with circular cross section is a special case of the equation derived in this paper. In the twistless case of the rod when the principal axes of the cross section are coincident with the Frenet coordinates of the centreline, the Schro^edinger equation is transformed to the Dulling equation. The equilibrium and stability of the twistless rod are discussed, and a bifurcation phenomenon is presented. 相似文献
14.
以杆的横截面为研究对象,讨论了其自由度,给出了截面虚位移定义,并定义变分和偏微分运算对独立坐标服从交换关系. 给出了曲面约束的基本假设,讨论了约束对截面自由度的影响以及加在虚位移上的限制方程. 从D'Alembert原理出发结合虚功原理,建立了弹性杆动力学的D'Alembert-Lagrange原理,当杆的材料服从线性本构关系时,化作Euler-Lagrange形式、Nielsen形式和Appell形式. 由此导出了Kirchhoff方程以及Lagrange方程、Nielsen方程和Appell方程,得到
关键词:
超细长弹性杆
分析力学方法
Kirchhoff动力学比拟
变分原理 相似文献
15.
A super thin elastic rod is modeled with a background of DNA super coiling structure, and its dynamics is discussed based on the Jourdain variation. The cross section of the rod is taken as the object of this study and two velocity spaces about are coordinate and the time are obtained respectively. Virtual displacements of the section on the two velocity spaces are defined and can be expressed in terms of Jourdain variation. JourdMn principles of a super thin elastic rod dynamics on arc coordinate and the time velocity space are established, respectively, which show that there are two ways to realize the constraint conditions. If the constitutive relation of the rod is linear, the Jourdain principle takes the Euler-Lagrange form with generalized coordinates. The Kirchhoff equation, Lagrange equation and Appell equation can be derived from the present Jourdain principle. While the rod subjected to a surface constraint, Lagrange equation with undetermined multipliers may be derived. 相似文献
16.
We investigate the application of the Mei symmetry analysis in finding conserved quantities for the thin elastic rod statics. By using the Mei symmetry analysis, we have obtained the Jacobi integral and the cyclic integrals for a thin elastic rod with intrinsic twisting for both the cases of circular and non-circular cross sections. Our results can be easily reduced to the results without the intrinsic twisting that have been reported. Through calculation, we find that the Noether symmetry can be more directly and easily used than the Mei symmetry in finding the first integrals for the thin elastic rod. These first integrals will be helpful in the study of exact solutions and stability, as well as the numerical simulation of the elastic rod model for DNA. 相似文献