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非圆截面弹性细杆
相关语句
  “非圆截面弹性细杆”译为未确定词的双语例句
     Stability and Bifurcation of Equilibrium of a Thin Elastic Rod with Noncircular Cross-Section
     非圆截面弹性细杆的平衡稳定性与分岔
短句来源
     Helical Equilibrium and Stability of a Thin Elastic Rod with Noncircular Cross-Section
     非圆截面弹性细杆的螺旋线平衡及稳定性
短句来源
     The problem on equilibrium of a thin elastic rod with noncircular cross-section and with initial curvature or twisting is discussed in this paper.
     本文研究存在初始曲率或挠率的非圆截面弹性细杆的干衡及稳定性问题。
短句来源
     The helical equilibrium and its stability of a thin elastic rod with noncircular cross section and intrinsic curvature and twisting under application of force and torque were discussed.
     本文研究端部受力和力矩作用,且存在初曲率和初扭率的非圆截面弹性细杆的螺旋线平衡及其稳定性。
短句来源
     The problem on stability of helical equilibrium of a thin elastic rod with noncirular cross-section and intrinsic twisting was discussed in view of dynamics.
     本文从动力学观点讨论具有初扭率的非圆截面弹性细杆的螺旋线平衡稳定性。
短句来源
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The problem on equilibrium of a thin elastic rod with noncircular cross-section and with initial curvature or twisting is discussed in this paper. The differential equation of equilibrium of the rod subjected to torques on both ends can be transformed to an autonomous system of Eulerian angles. The stability and bifurcation of the equilibrium states of the rod are analysed by using the singularity theory of phase plane. A qualitative analysis for the influence of the asymmetry of the cross-section, as well as...

The problem on equilibrium of a thin elastic rod with noncircular cross-section and with initial curvature or twisting is discussed in this paper. The differential equation of equilibrium of the rod subjected to torques on both ends can be transformed to an autonomous system of Eulerian angles. The stability and bifurcation of the equilibrium states of the rod are analysed by using the singularity theory of phase plane. A qualitative analysis for the influence of the asymmetry of the cross-section, as well as the initial curvature and twisting is given, some stability criteria in analytical form are derived, and a phenomenon of static bifurcation is shown.

本文研究存在初始曲率或挠率的非圆截面弹性细杆的干衡及稳定性问题。在两端受力矩单独作用的条件下,杆的平衡微分方程可转换为用欧拉角表述的一阶自治系统,并有可能利用相平面的奇点理论分析弹性细杆平衡状态的稳定性。文中对杆截面的非对称性,以及杆的初始曲率和挠率对平衡状态稳定性的影响进行了定性分析,导出了解析形式的稳定性判据,揭示了杆平衡状态的静态分岔现象。

The helical equilibrium and its stability of a thin elastic rod with noncircular cross section and intrinsic curvature and twisting under application of force and torque were discussed. The Kirchhoff equations describing the equilibrium of elastic thin rod has a particular solution, corresponding to the helical e-quilibrium. The straight rod and the planar ring are two special cases of helix. The relationship between geometric behavior of the helix and the external force and torque was analyzed, and a stability...

The helical equilibrium and its stability of a thin elastic rod with noncircular cross section and intrinsic curvature and twisting under application of force and torque were discussed. The Kirchhoff equations describing the equilibrium of elastic thin rod has a particular solution, corresponding to the helical e-quilibrium. The straight rod and the planar ring are two special cases of helix. The relationship between geometric behavior of the helix and the external force and torque was analyzed, and a stability criterion of helical equilibrium in analytical form was derived in first approximation. It is shown that the relaxed state of a rod can be a helical state, and the helical equilibrium of a straight rod can be maintained only under axial pressure forces. The necessary stable condition of helical equilibrium of a rod without intrinsic curvature and twisting is that the bending rigidity of the rod about the binormal axis is larger than the bending rigidity about the normal axis. The same condition applies for a elastic ring with intrinsic twisting and more general cases too. The helical equilibrium of a rod with circular section but without intrinsic curvature and twisting is always stable.

本文研究端部受力和力矩作用,且存在初曲率和初扭率的非圆截面弹性细杆的螺旋线平衡及其稳定性。描述弹性细杆平衡状态的Kirchhoff方程存在与杆的螺旋线平衡状态相对应的特解。直杆和圆环杆为螺旋线状态的两种特例。文中分析了螺旋线的几何特性与作用力和力矩之间的相互关系,并导出螺旋线平衡的一次近似解析形式稳定性判据。分析表明,松弛状态下弹性杆可处于螺旋线状态,直杆只有在轴向压力的作用下才能保持螺旋线平衡。无初曲率和初扭率弹性杆的螺旋线平衡稳定性必要条件是杆截面绕副法线轴的抗弯刚度大于或等于绕法线轴的抗弯刚度。此条件也适用于带初扭率的圆环杆及更普遍情形。无初曲率和初扭率的圆截面杆的螺旋线平衡恒稳定。

The problem on stability of helical equilibrium of a thin elastic rod with noncirular cross-section and intrinsic twisting was discussed in view of dynamics. The dynamical stability analysis was based on the concepts of Lyapunov stability for a discrete dynamical system with arc-coordinate s and time t as dual arguments. In the case of the rod with fixed end constraints, and the conditions of static stability are satisfied, the eigenvalues corresponding to the arc-coordinate can be determined by the boundary...

The problem on stability of helical equilibrium of a thin elastic rod with noncirular cross-section and intrinsic twisting was discussed in view of dynamics. The dynamical stability analysis was based on the concepts of Lyapunov stability for a discrete dynamical system with arc-coordinate s and time t as dual arguments. In the case of the rod with fixed end constraints, and the conditions of static stability are satisfied, the eigenvalues corresponding to the arc-coordinate can be determined by the boundary conditions. Then the dynamic stability of the helical equilibrium depends on the eigenvalues in the time domain. Under the condition of slow perturbed motion, the dynamical process of the rod can be regarded as a perturbation of equilibrium state in statics. Introducing a scale-reduced time variable T=εt, the dynamical equations of the rod and its perturbed equations of helical equilibrium were established on the basis of Kirchhoffs theory. It is proved that in the sense of first approximation with precision of ε 2 when the conditions of stability of helical equilibrium of the rod are satisfied within the scope of statics, the stability conditions with consideration of dynamical factors are satisfied in the same time.

本文从动力学观点讨论具有初扭率的非圆截面弹性细杆的螺旋线平衡稳定性。弹性杆平衡的动态稳定性建立在以弧坐标s 和时间坐标t 为双自变量的离散系统的Lyapunov稳定性概念基础上。对于两端约束状况固定不变的弹性杆,若静态稳定性条件已满足,其与弧坐标对应的本征值可根据端部约束条件确定。则螺旋线平衡的动态稳定性由时间域的本征值判断。在缓慢受扰运动条件下,引入尺度缩小的时间变量T=εt ,可将动力学过程视为对平衡状态的摄动。证明在ε2 计算精度范围内,当螺旋线平衡的一次近似静态稳定性条件得到满足时,考虑动力学因素的稳定性条件必也同时满足。

 
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