轴向绳移系统横向自由振动计算及边界特性研究

发布时间：2018-05-25 21:34

本文选题：横向自由振动 + 轴向绳移系统　；参考：《合肥工业大学》2017年硕士论文

【摘要】：在工程设备中广泛应用的轴向绳移系统以其振动问题,尤其是横向振动,而备受关注。不同的边界条件,系统的横向振动形式也不相同,本文针对四种不同的典型边界条件研究了轴向绳移系统的横向自由振动。本文以轴向绳移系统为研究对象,首先建立了两端固定、固定-自由、阻尼-固定和固定-移动四种边界条件下的物理模型,分别用两种不同的方法建立了轴向绳移系统的数学模型,第一种是基于拉格朗日方程和形函数建立的有限元动力学方程;第二种是基于哈密顿变分原理建立的偏微分运动方程。其次,针对传统有限元法对于高速移动绳横向振动计算误差大、易发散的问题,基于行波在不同边界的反射叠加技术,提出一种有限长度轴向移动绳横向振动计算方法。接着结合其初始条件以及四种边界条件分别获得反射波的表达式,从而将移动绳的横向自由振动等效为不同速度的行波及其反射波的叠加,推导出其理论表达式,并根据行波的运动规律分别获得了定绳长和变绳长系统的运动周期。最后以能量反射系数为切入点分析了能量变化的周期性,并分析了不同边界条件下系统的能量变化规律以及绳在通过边界处的能量转换机制。
[Abstract]:The axial rope moving system, which is widely used in engineering equipment, has attracted much attention for its vibration problem, especially transverse vibration. For different boundary conditions, the transverse vibration forms of the system are also different. In this paper, the transverse free vibration of the axial rope moving system is studied for four different typical boundary conditions. In this paper, the axial rope moving system is taken as the research object. Firstly, the physical models under four boundary conditions of fixed, fixed free, damping fixed and fixed moving are established. The mathematical models of the axial rope moving system are established by two different methods, the first is the finite element dynamic equation based on Lagrange equation and the form function, and the second is the partial differential motion equation based on Hamiltonian variational principle. Secondly, aiming at the problem that the traditional finite element method has a large error in calculating the lateral vibration of high speed mobile rope, based on the reflection superposition technique of traveling wave at different boundaries, a finite length axial moving rope lateral vibration calculation method is proposed. Then combined with the initial conditions and the four boundary conditions, the expressions of the reflected waves are obtained respectively, so that the lateral free vibration of the moving rope is equivalent to the stacking of the traveling waves and the reflected waves with different velocities, and the theoretical expressions are derived. According to the moving law of traveling wave, the motion periods of fixed rope length and variable rope length system are obtained respectively. Finally, the periodicity of energy change is analyzed with the energy reflection coefficient as the starting point, and the energy variation law of the system under different boundary conditions and the energy conversion mechanism of the rope passing through the boundary are analyzed.
【学位授予单位】：合肥工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH113.1

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