Abstract

Bifurcation characteristics of a fractional non-smooth oscillator containing clearance constraints under sinusoidal excitation are investigated. First, the bifurcation response equation of the fractional non-smooth system is obtained via the K–B method. Second, the stability of the bifurcation response equation is analyzed, and parametric conditions for stability are acquired. The bifurcation characteristics of the fractional non-smooth system are then studied using singularity theory, and the transition set and bifurcation diagram under six different constrained parameters are acquired. Finally, the analysis of the influence of fractional terms on the dynamic characteristics of the system is emphasized through numerical simulation. Local bifurcation diagrams of the system under different fractional coefficients and orders verify that the system will present various motions, such as periodic motion, multiple periodic motion, and chaos, with the change in fractional coefficient and order. This manifestation indicates that fractional parameters have a direct effect on the motion form of this non-smooth system. Thus, these results provide a theoretical reference for investigating and repressing oscillation problems of similar systems.

摘要

研究了在正弦激励下具有间隙约束的分数非光滑振荡器的分叉特性。首先，通过K–B方法获得分数阶非光滑系统的分叉响应方程。其次，分析了分叉响应方程的稳定性，并获得了稳定性的参数条件。然后利用奇异性理论研究了分数阶非光滑系统的分岔特性，获得了六种不同约束条件下的转移集和分岔图。最后，通过数值模拟强调了分数项对系统动态特性的影响分析。系统在不同分数系数和阶数下的局部分歧图证明，随着分数系数和阶数的变化，系统将呈现各种运动，例如周期性运动，多个周期性运动和混沌。这种表现表明分数参数直接影响该非光滑系统的运动形式。因此，这些结果为研究和抑制相似系统的振荡问题提供了理论参考。