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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
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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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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
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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
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Optical forces acting on a micro-sphere were studied to corroborate the single-beam fiber optic trap. Transverse optical force acted to pull the micro-sphere back to the beam axis, but axial force always acted in the direction away from the optical fiber end because the laser beam from optical fiber could not be strongly focused. A stable two-dimensional optical trapping could be obtained by the weakly focused laser beam from the fiber end inserted at an angle. 相似文献
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Pierre-Michel Déjardin 《Journal of magnetism and magnetic materials》2010,322(20):3112-3116
The nonlinear ac stationary response of the magnetization of noninteracting uniaxial single-domain ferromagnetic particles acted on by superimposed dc and ac magnetic fields applied along the anisotropy axis is evaluated from the Fokker-Planck equation, expressed as an infinite hierarchy of recurrence equations for Fourier components of the relaxation functions governing longitudinal relaxation of the magnetization. The exact solution of this hierarchy comprises a matrix continued fraction, allowing one to evaluate the ac nonlinear response and reversal time of the magnetization. For weak ac fields, the results agree with perturbation theory. It is shown that the dc bias field changes substantially the magnetization dynamics leading to new nonlinear effects. In particular, it is demonstrated that for a nonzero bias field as the magnitude of the ac field increases the reversal time first increases and having attained its maximum at some critical value of the ac field, decreases exponentially. 相似文献
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The mass transfer process and the crystal growth rate have been proved to be very important in the study of crystal growth kinetics, which influence the crystal quality and morphological stability. In this paper, a new method based on temporal phase evaluation was presented to characterize the mass transfer process in situ and determine the crystal growth rate. The crystallization process of NaCl crystal growth by evaporation was monitored in situ by a Mach-Zehnder interferometer, and the absolute concentration evolution, the evaporation rate and the real-time supersaturation of solution were obtained using temporal phase analysis, which acted as a novel technique to extract phase variation along time axis recently. Based on the evaporation rate and the absolution concentration, a new method to calculate mass transfer flux during the crystal growth without the knowledge of the mass transfer coefficient was proposed, and then the crystal growth rate could also be retrieved under the hypothesis of cubic crystals. The results show that the crystal growth rate increases with the supersaturation linearly. It is in agreement with the diffusion theories, which presume that matter is deposited continuously on a crystal face at a rate proportional to the difference in concentration between the points of deposition and the bulk of solution. The method is applicable to the research of crystallization process based on evaporation or vapor diffusion of which the precise conditions of nucleation and supersaturation are usually unknown because of the complexity of the evaporation rate and crystal growth rate. 相似文献
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熊猫光纤背向衍射图样的图像互相关定轴方法 总被引:1,自引:0,他引:1
针对基于背向衍射图像的熊猫光纤定轴法需要建立标准图样库的难题,进行了熊猫光纤在不同方位角所产生的背向衍射图样相关性分析的实验研究.实验显示:快轴方向的背向衍射图样与慢轴方向的背向衍射图样之间具有差异性;在快轴或慢轴方向附近的背向衍射图样之间具有相似性;快轴或慢轴方向的背向衍射图样自身具有对称性.根据差异性、相似性和对称性这三个特性,建立了一种基于熊猫光纤背向衍射图样的图像互相关定轴方法,用于确定熊猫光纤快轴或慢轴这些特殊方位角.此方法不用建立标准图库就可以实现熊猫光纤特殊方位角的定轴. 相似文献
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设计了具有抛物面结构的卡塞格伦光学天线.通过对偏轴下的卡塞格伦光学天线系统的分析,得到了不同偏转角所对应的接收光斑面积表达式和功率衰减曲线.讨论了偏轴下的接收天线增益与波长及偏转角的关系,仿真出在偏轴与轴对准两种情形下的增益曲线.仿真结果表明,〖JP2〗最大偏轴比轴对准情形增益降低了6.564dB.最后分别针对轴对准与某种偏轴情形下的系统做了光斑测试实验与天线耦合效率测试实验.结果为:偏轴下天线耦合效率降低了26.966%.这些研究为星间光通信中控制系统实现光轴的精确对准提供了理论依据,具有重要的实用价值
关键词:
偏轴
卡塞格伦光学天线
偏转角
增益 相似文献