共查询到20条相似文献,搜索用时 15 毫秒
1.
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
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.
研究基于Gauss 变分的超细长弹性杆动力学建模的分析力学方法.分别在弧坐标和时间的广义加速度空间定义虚位移,给出了非完整约束加在虚位移上的限制方程;建立了弹性杆动力学的Gauss原理,由此导出Kirchhoff方程、Lagrange方程、Nielsen方程以及Appell方程;对于受有非完整约束的弹性杆,导出了带乘子的Lagrange方程;建立了弹性杆截面动力学的Gauss最小拘束原理并说明其物理意义.
关键词:
超细长弹性杆动力学
分析力学
Gauss变分
最小拘束原理 相似文献
4.
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
5.
Noether symmetry and conserved quantities of the analytical dynamics of a Cosserat thin elastic rod 下载免费PDF全文
In this paper, we investigate the Noether symmetry and Noether conservation law of elastic rod dynamics with two independent variables: time t and arc coordinate s. Starting from the Lagrange equations of Cosserat rod dynamics, the criterion of Noether symmetry with Lagrange style for rod dynamics is given and the Noether conserved quantity is obtained. Not only are the conservations of generalized moment and generalized energy obtained, but also some other integrals. 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
8.
将圆截面Kirchhoff弹性压扭直杆的Greenhill公式推广到精确模型.基于平面截面假定,在弯扭的基础上增加了拉压和剪切变形,将弹性杆的位形表达为截面的弧坐标历程.由弹性杆精确模型的平衡微分方程,得到了两端受力螺旋作用时对应于直线平衡状态的特解,导出了线性化扰动方程及其通解,再根据两端为铰支时的边界条件以及积分常数存在非零解的条件导出弹性直杆精确模型的Greenhill公式.结果表明,由力螺旋表示的稳定域为一对称的封闭区域,拉压和剪切对稳定性的影响取决于拉压柔度与剪切柔度之差、抗弯刚度和杆长这三个因素. 相似文献
9.
刚性杆和滑块组成的单自由度非线性振动 总被引:1,自引:1,他引:0
用动力学方法,导出了刚性杆和滑块组成的单自由度非线性振动系统的运动微分方程;求出了杆的摆动角速度和角加速度、杆与滑块的相互作用力与杆的摆角间的关系式;给出了系统振动周期的计算公式;借助Matlab软件画出了杆与滑块的相互作用力随角坐标的变化曲线及周期随角振幅的变化曲线. 相似文献
10.
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
11.
将经典质量的变化和质量随速度变化这一相对论效应同时考虑,建立定轴转动变质量系统的相对论性基本动力学方程,达朗贝尔(d'Alembert)原理及Lagrange方程.
关键词: 相似文献
12.
采用Euler四元数表示的Kirchhoff方程来研究受力挤压作用下的弹性细杆的拓扑构形,进一 步研究弹性细杆的力学性质;将得到的微分方程与约束条件组成微分代数方程后再转化为微 分方程规范形式以便求解;为满足边界条件,应用数值打靶法求解边值条件,并将弹性细杆 在力作用下的拉压过程用Matlab仿真出来.同时对由于误差导致的违约现象进行处理,并针 对欧拉参数的特征,选取合适的修正系数以保持方程的稳定性.
关键词:
DNA
Euler四元数
Kirchhoff方程
弹性细杆
违约修正 相似文献
13.
14.
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
15.
Nondeterminacy of dynamics, i.e., the nonholonomic or the vakonomic, fundamental variational principles, e.g., the Lagrange-d'Alembert or Hamiltonian, and variational operators, etc., of nonholonomic mechanical systems can be attributed to the non-uniqueness of ways how to realize nonholonomic constraints. Making use of a variation identity of nonholonomic constraints embedded into the Hamilton's principle with the method of Lagrange undetermined multipliers, three kinds of dynamics for the nonholonomic systems including the vakonomic and nonholonomic ones and a new one are obtained if the variation is respectively reduced to three conditional variations: vakonomic variation, Hölder's variation and Suslov's variation, defined by the identity. Therefore, different dynamics of nonholonomic systems can be derived from an integral variational principle, utilizing one way of embedding constraints into the principle, with different variations. It is verified that the similar embedding of the identity into the Lagrange-d'Alembert principle gives rise to the nonholonomic dynamics but fails to give the vakonomic one unless the constraints are integrable. 相似文献
16.
17.
Zai-Dong Li 《Annals of Physics》2007,322(8):1961-1971
We study the magnetic soliton dynamics of spinor Bose-Einstein condensates in an optical lattice which results in an effective Hamiltonian of anisotropic pseudospin chain. An equation of nonlinear Schrödinger type is derived and exact magnetic soliton solutions are obtained analytically by means of Hirota method. Our results show that the critical external field is needed for creating the magnetic soliton in spinor Bose-Einstein condensates. The soliton size, velocity and shape frequency can be controlled in practical experiment by adjusting the magnetic field. Moreover, the elastic collision of two solitons is investigated in detail. 相似文献
18.
An approach for describing the dynamics of nuclear fission in the framework of generalized quantum mechanics is discussed.
The collective kinetic energy is assumed to be two dimensional, and the reduced mass is allowed to vary with the coordinates.
The generalized calculus of variation is employed for minimizing the action after being properly quantized as required by
Hamilton's principle, employing a curvilinear coordinate system. The corresponding Euler Lagrange equation is identified as
the required generalized equation of motion. The proposed generalized two-dimensional equation of motion is separated into
a vibrational eigenvalue equation and a set of coupled-channel one-dimensional equations which describe the translational
motion, by exploiting the completeness of the vibrational eigenfunctions. Such a system of coupled equations can be decoupled
by replacing the coupling matrix elements by a nonlocal interaction, which can be rendered local after employing the effective
mass approximation. As a consequence this differential equation is provided with an effective mass, an effective potential
barrier, and a differential boundary term which is responsible for restoring the self-adjointness of the kinetic energy differential
operator. 相似文献
19.
Cretu N 《Ultrasonics》2005,43(7):547-550
The present work represents both an experimental and theoretical investigation of the behavior of finite cylindrical rods with harmonic variation of the cross section. The matrix method was used to compute the transfer power spectra of elastic rods with uniform circular cross section and of rods with harmonic variation of the cross section with distance. Theoretical and experimental results show that for a rod with periodical variation of the cross section, a new set of supplementary frequencies appear for which the transfer power coefficient has significant values, which are in relation with the space period of the inhomogeneity. Also, due to the radial component of the displacement certain modes are enhanced which satisfy boundary conditions on the surface and are obtained from the zeroes of Bessel functions. 相似文献
20.
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