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1.
圆截面弹性螺旋杆的稳定性与振动   总被引:2,自引:0,他引:2       下载免费PDF全文
刘延柱  盛立伟 《物理学报》2007,56(4):2305-2310
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   

2.
王鹏  薛纭  楼智美 《物理学报》2017,66(9):94501-094501
基于坐标基矢摄动的方法研究了黏性流体中超细长弹性杆动力学稳定性判据与失稳后的模态选择,推导出了黏性介质中超细长弹性杆Kirchoff动力学方程的一阶摄动表示,即线性的二阶偏微分方程组.以平面扭转DNA环为例,说明了以上结果的应用,得到了平面扭转DNA环的稳定性判据及其稳定的临界区域,讨论了其失稳后的模态选择及黏性阻力对其的影响.  相似文献   

3.
Kirchhoff弹性直杆在力螺旋作用下的稳定性   总被引:1,自引:0,他引:1       下载免费PDF全文
薛纭  刘延柱 《物理学报》2009,58(10):6737-6742
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   

4.
刘延柱  薛纭 《物理学报》2009,58(9):5936-5941
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   

5.
Kirchhoff方程的相对常值特解及其Lyapunov稳定性   总被引:5,自引:0,他引:5       下载免费PDF全文
薛纭  陈立群  刘延柱 《物理学报》2004,53(12):4029-4036
对于超细长弹性杆静力学的Kirchhoff方程,用动力学的概念和方法研究其常值特解 和稳定性问题.计算了Kirchhoff方程相对固定坐标系、截面主轴坐标系以及中心线Frenet 坐标系的常值特解,进行了Kirchhoff动力学比拟,用一次近似理论分别讨论了它们的Lyapu nov稳定性,导出了若干稳定性判据,并在参数平面上绘出了稳定域. 关键词: 超细长弹性杆 Kirchhoff方程 常值特解 Lyapunov稳定性  相似文献   

6.
扭转超声振动系统中局部共振的研究   总被引:2,自引:0,他引:2       下载免费PDF全文
刘世清  林书玉 《应用声学》2004,23(2):11-14,44
本文从扭转振动波动方程出发,推导出了具有类圆锥过渡段的复合阶梯型扭转变幅杆的频率方程解析表达式。从实验和理论上对该复合变幅杆的谐振频率随杆细端长度和直径的变化进行了测量和计算。通过对比,证明了复合振动系统中局部扭转共振现象的存在,并得到了其产生条件。  相似文献   

7.
受曲面约束弹性细杆的平衡问题   总被引:5,自引:0,他引:5       下载免费PDF全文
薛纭  陈立群  刘延柱 《物理学报》2004,53(7):2040-2045
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.
弹性细杆平衡的动态稳定性   总被引:11,自引:0,他引:11       下载免费PDF全文
刘延柱  薛纭  陈立群 《物理学报》2004,53(8):2424-2428
从动力学观点讨论弹性细杆的平衡稳定性问题.建立了弹性杆的动力学方程,导出了杆的弯扭度与截面角速度之间的运动学关系式.对具有弧坐标s和时间t双重自变量的离散动力系统扩充了Lyapunov 稳定性定义.以具有初扭率的非圆截面直杆的平衡稳定性为例,应用一次近似方法证明了当静力学意义下的稳定性条件得到满足时,动力学意义下的稳定性条件必同时满足. 关键词: 弹性杆动力学方程 Kirchhoff理论 Lyapunov稳定性  相似文献   

9.
黄磊  包光伟  刘延柱 《物理学报》2005,54(6):2457-2462
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   

10.
自由阻尼复合板的模态密度研究   总被引:2,自引:0,他引:2       下载免费PDF全文
模态密度是统计能量分析(SEA)的一个重要参数,尽管有关阻尼复合板振动特性的文献很多,便至今为止,研究其模态密度及变化规律的论文尚未见到,为此本文利用弹性最小势能原理和变分法,并考虑振动阻尼的影响,导出了自由阻尼复合板的弯曲振动模态密度计算公式,系统地分析了模态密度随阻尼层厚度、温度和频率而变化的规律。  相似文献   

11.
刘延柱  盛立伟 《中国物理》2007,16(4):891-896
The stability and vibration of a thin elastic helical rod with circular cross section in a viscous medium are discussed. The dynamical equations of the rod in the viscous medium are established in the Frenet coordinates of the centreline with the Euler angles describing the attitudes of the cross section as variables. We have proved that the Lyapunov and Euler conditions of stability of a helical rod in the space domain are the necessary conditions for the asymptotic stability of the rod in the time domain. The free frequencies and damping coefficients of torsional and flexural vibrations of the helical rod in the viscous medium are calculated.  相似文献   

12.
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   

13.
Biological growth is a common phenomenon in nature, and some organisms such as DNA molecules and bacterial filaments grow in viscous media. The growth induced instability of morphoelastic rod in a viscous medium is studied in this paper. Based on the Kirchhoff kinetic analogy method, the mechanical model for growing elastic thin rod in the viscous medium is established. A perturbation analysis is used to analyze the stability of the growing elastic rod in the viscous medium. We apply the results into planar growing ring and get its criterion of instability. Take the criterion into DNA ring to discuss the influence of viscous resistance on its instability.  相似文献   

14.
A double shell-Stokes flow model is developed to study the axisymmetric vibration of single-walled carbon nanotubes (SWCNTs) immerged in water. In contrast to macroscopic solid-liquid system, a submerged SWCNT is coupled with surrounding water via the van der Waals interaction. It is shown that this unique feature substantially reduces viscous damping of the axisymmetric radial, longitudinal and torsional vibrations and significantly up-shifts the frequency of the radial vibration of an SWCNT. The study offers a theoretical explanation for the experimental observation and molecular dynamics simulations available in particular cases, and provides an efficient modelling tool and useful guidance for the study of the general dynamic behaviour of SWCNTs in a fluid.  相似文献   

15.
The complex modal analysis of rods equipped with an arbitrary number of viscous damping devices is addressed. The following types of damping devices are considered: external (grounded) spring-damper, attached mass-spring-damper and internal spring-damper. Within a standard 1D formulation of the vibration problem, the theory of generalized functions is used to model axial stress and displacement discontinuities at the locations of the damping devices. By using the separate variable approach, a simple solution procedure of the motion equation leads to exact closed-form expressions of the characteristic equation and eigenfunctions, which inherently fulfill the required matching conditions at the locations of the damping devices. Based on the characteristic equation, a closed-form sensitivity analysis of the eigensolution is implemented. The displacement eigenfunctions exhibit orthogonality conditions. They can be used with the complex mode superposition principle to tackle forced vibration problems and, in conjunction with the stress eigenfunctions, to build the exact dynamic stiffness matrix of the rod for complex modal analysis of truss structures. Numerical results are discussed for a variety of parameters.  相似文献   

16.
为探究地铁车辆阻尼环扩张状态对阻尼环车轮声振特性影响,在半消声室内进行阻尼环车轮自由状态下的声振特性实验研究,结合有限元仿真对实验结果进行分析。研究表明,环-轮组合振动固有频率与原车轮相比变化不大,但阻尼环使车轮的模态阻尼比显著增加,有效抑制了车轮各模态的振动幅值。改变阻尼环扩张状态,阻尼环降噪效果发生非线性变化,幅值在5.6 dB(A)之内。阻尼环扩张状态可通过调节非闭合阻尼环两端扩张装置来改变。阻尼环处于非最大扩张状态W_3时,可获得最佳降噪效果。  相似文献   

17.
第三代同步辐射光源储存环支撑组件振动控制研究   总被引:1,自引:0,他引:1  
第三代同步辐射光源对束流轨道稳定性要求很高, 上海光源是一台在建的第三代光源, 束流位置稳定度要求达到微米乃至亚微米级. 地基振动会使储存环磁聚焦结构中的各种元件发生机械振动引起随时间变化的束流闭合轨道畸变, 影响束流轨道稳定性. 上海光源场地振动幅值大, 需要研究措施控制机械组件的振动. 阻尼减振是一种有效的振动控制方法, 针对上海光源储存环机械组件, 作者设计了一种阻尼减振方案. 试验结果表明, 该方案能有效地控制机械组件的振动. 这对于保证上海光源的束流稳定性要求有积极意义.  相似文献   

18.
Based on the theory of coupling vibration and flexural vibration of thin rod of rectangular cross section, the fiexural vibration of rectangular thin plate was studied. The frequency equation was derived under the condition of freeboundaries. The normal modes and the relation between the normal modes and the resonant frequency were obtained. Experiments showed that the calculated resonant frequencies agree well with the measured results, and the rectangular thin plate in flexural vibration has abundant resonant frequencies. The radiator of flexural vibration used in ultrasonic cleaning and other techniques has the advantages of large acoustic radiating area, uniform acoustic field and easy adjustment of resonant frequencies, proving that it is a promising ultrasonic source.  相似文献   

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