A superposition method for vibration of travelling string with constant length based on moving waves reflected at fixed-dashpot boundaries

作者：Chen, En Wei; Zhang, Kai; Wang, Jun; Wei, Hao Zheng; Lu, Yi Min

来源：Journal of Vibration Engineering, 2018, 31(5): 870-874.

DOI：10.16385/j.cnki.issn.1004-4523.2018.05.017

• Axially moving strings
• Boundary reflection
• Central difference method
• Continuity conditions
• Engineering equipments
• Non-classical boundary
• Superposition method
• Transverse vibrations

The vibration problem in the various engineering equipment is widely concerned, such as the cable of the tethered satellite, aerial ropeway, material conveyer belt, which can be simplified as the axially moving string system. At present, the research on axially moving string system mostly concentrates on the classical boundary conditions while few on the non-classical boundary conditions. In this paper, a traveling wave boundary reflection superposition method is studied based on the classical theory of traveling wave reflection. Taking the axially moving string with non-classical boundary conditions for example, the expressions of the reflected waves are obtained through the reflection of the left and right traveling waves on both sides, with considering its initial conditions and the continuity conditions of both sides. Then the reflection processes are deduced in three phases and finally its determinate expressions of transverse vibration are obtained. Take the axially moving string with a fixed boundary as well as a dashpot boundary for example, the correctness and advantages of the method of boundary reflection superposition are verified by MATLAB simulation combined with central difference method.

• 出版日期2018
• 单位合肥工业大学