共查询到11条相似文献,搜索用时 46 毫秒
1.
基于Kirchhoff理论讨论圆截面弹性细杆的平面振动.以杆中心线的Frenet坐标系为参考系建立动力学方程.杆作平面运动时,其扭转振动与弯曲振动解耦.讨论任意形状杆的扭转振动和轴向受压直杆在无扭转条件下的弯曲振动,证明直杆平衡的静态Lyapunov稳定性与欧拉稳定性条件为动态稳定性的必要条件.考虑轴向力和截面转动惯性效应的影响,导出弯曲振动的固有频率. 相似文献
2.
用奇异函数建立非单一材质的n级阶梯形闭口薄壁杆约束扭转自由振动和强迫振动的微分方程并求得其通解,用W算子给出主振型函数的表达式及常见支承条件下杆的频率方程。 相似文献
3.
基于Kirchhoff理论讨论端部受轴向压力作用的圆截面弹性螺旋杆的动态稳定性问题。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。杆的螺旋线平衡状态由方程的特解确定。基于静力学分析的结论,在动力学范畴内继续讨论轴向受压螺旋杆平衡状态的稳定性。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为时域内的Lyapunov稳定性条件。从而进一步认识Lyapunov和欧拉两种不同稳定性概念之间的相互关系。导出轴向受压螺旋杆弯扭耦合振动固有频率的近似解析表达式。 相似文献
4.
The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed.
The differential equations of dynamics of the constrained rod are established with Euler’s angles as variables describing
the attitude of the cross section. The existence conditions of helical equilibrium under constraint are discussed as a special
configuration of the rod. The stability of the helical equilibrium is discussed in the realms of statics and dynamics, respectively.
Necessary conditions for the stability of helical rod are derived in space domain and time domain, and the difference and
relationship between Lyapunov’s and Euler’s stability concepts are discussed. The free frequency of flexural vibration of
the helical rod with cylinder constraint is obtained in analytical form.
The project supported by the National Natural Science Foundation of China (10472067). The English text was polished by Yunming
Chen. 相似文献
5.
T.G. Chondros 《Theoretical and Applied Fracture Mechanics》2005,44(1):95-104
A variational formulation is developed for the torsional vibration of a cylindrical shaft with a circumferential crack. The work is compared with existing methods. The Hu–Washizu–Barr variational formulation was used to develop the differential equation and the boundary conditions of the cracked rod. The general variational principle and the independent assumptions about the displacement, the momentum, the strain and the stress fields of the cracked rod, and the equations of motion for a uniform rod in torsional vibration, are derived. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack, found with fracture mechanics methods. Rayleigh quotient was used to approximate the natural frequencies of the cracked rod. Independent evaluations of crack identification methods in rotating shafts are reported and compared with methods using the continuous crack flexibility theory. 相似文献
6.
The strain solitary waves in a nonlinear elastic rod 总被引:7,自引:0,他引:7
Solitary strain waves in a nonlinear elastic rod are analysed in this paper; influence of the physical and geometrical parameters
of the rod on the waves are discussed; some main properties of the solitary waves are pointed out. 相似文献
7.
8.
The experimental phenomenon and theoretical analysis are given for the torsional buckling of elastic cylindrical shells. From the experiment, it is found that the postbuckling deformation doesn't occupy the whole length when the shell is longer. In the theoretical calculation, only the normal displacement boundary condition is taken into account. By comparing the present calculation results with the accurate result of Yamakis theory and the results of the present experiment, it is shown that the influence of the axial and circumference boundary condition is less important. 相似文献
9.
10.
Whenwestudytorsionalvibration,thegearsaregenerallytreatedasrigiddisks,shaftsegmentastorsionalspringwithoutmass.Eveniftherotationalinertiaofshaftssegmentcannotbeneglected,theyareoftenallocatedtotheneighbordisksorreplacedwithsomerigiddisksconcatenatedb… 相似文献
11.
谷宇 《应用数学和力学(英文版)》2008,29(3):389-398
Sandwich composite material possesses advantages of both light weight and high strength. Although the mechanical behaviors of sandwich composite material with the influence of single external environment have been intensively studied, little work has been done in the study of mechanical property, in view of the nonlinear behavior of sandwich composites in the complicated external environments. In this paper, the problem about the bending of the three-layer elastic-plastic rod located on the elastic base, with a compressibly physical nonlinear core, has been studied. The mechanical response of the designed three-layer elements consisting of two bearing layers and a core has been examined. The complicated problem about curving of the three-layer rod located on the elastic base has been solved. The convergence of the proposed method of elastic solutions is examined to convince that the solution is acceptable. The calculated results indicate that the plasticity and physical nonlinearity of materials have a great influence on the deformation of the sandwich rod on the elastic basis. 相似文献