Using an analytic approach, the critical velocity of chaos for an axially moving viscoelastic string under a noisy axial tension was studied in this paper. A Wiener process non-Gaussian bonded noise was selected to model the noisy fluctuations of axial force, and the Melnikov-based criterion was chosen to obtain the boundaries of chaotic behavior and consequently the critical velocity. The latter was obtained in terms of the amplitude, frequency and bandwidth of the noise. The effect of variation of the elastic and the viscous properties of the string on the qualitative and quantitative behaviors was also investigated. It was observed that the unstable area and the critical velocity depend completely on the bandwidth of the noise. Also, to ensure the correctness of the method, some of the results were validated using the corresponding Poincaré maps.

本文使用解析方法研究了轴向运动粘弹性弦在噪声轴向张力下的临界混沌速度。选择维纳过程非高斯键合噪声来模拟轴向力的噪声波动，并选择基于 Melnikov 的准则来获得混沌行为的边界，从而获得临界速度。后者是根据噪声的幅度、频率和带宽获得的。还研究了弦的弹性和粘性变化对定性和定量行为的影响。观察到不稳定区域和临界速度完全取决于噪声的带宽。另外，为了确保方法的正确性，