Abstract
At present, the control of vibration problem of many engineering equipment can be simplified as a study on transverse vibration of axially traveling string system. In this paper, transverse vibration control and energy dissipation of axially traveling string system is investigated by using a boundary viscous damper. By analyzing the nature frequencies of the fixed length and the variable length of the string system, the resonance frequency of the external concentrated force is obtained. The amplitude and the energy reflection ratio of reflected wave to incident wave is investigated respectively by the force equilibrium principle and the energy equation at the boundary. According to amplitude and the energy reflection ratio, the range and the optimal value of damping coefficient are obtained. The effect of vibration dissipation with a viscous damper and an external concentrated force at the left boundary is investigated respectively by the numerical simulation.
Highlights
In the present paper, the transverse control study of axially traveling string system using the nature frequency, the boundary force equilibrium principle and the energy equation
In contrast to the previous work on the vibration control of axially traveling string system based on energy change and boundary feedback which requires many complex calculations, the present work focuses on using the characteristics of wave propagation to study the boundary damping control and to analyze the natural frequencies of the string system can effectively simplify the calculation process and the result is obvious
1) Based on Hamilton principle and Lagrangian function, a model of axially traveling string is built and the natural frequencies of a traveling string with constant and variable length is given analytically using the reflection of wave propagation at the boundary of a string
Summary
The transverse control study of axially traveling string system using the nature frequency, the boundary force equilibrium principle and the energy equation. This model can be used to study the transverse vibration problems of engineering equipment, such as conveyor belt, band-saws, tape, elevator, tethered satellite, etc. In contrast to the previous work on the vibration control of axially traveling string system based on energy change and boundary feedback which requires many complex calculations, the present work focuses on using the characteristics of wave propagation to study the boundary damping control and to analyze the natural frequencies of the string system can effectively simplify the calculation process and the result is obvious.
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