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一类随机边界刚性约束悬臂梁系统周期运动的稳定性分析
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Abstract:
本文研究了一类二阶可微随机约束下的碰撞悬臂梁系统周期解的稳定性。通过推导含参数的随机零时间不连续映射给出相应的跳跃矩阵，结合跳跃矩阵和光滑流映射的基解矩阵得到了随机线性化矩阵。基于随机线性化矩阵探讨了随机约束对系统稳定性的影响，进一步调查了周期解失稳之后的倍化分岔现象，数值仿真验证了理论的有效性。
This paper studies the stability of periodic solution for a class of second-order differentiable cantilever beam system with rigid and random constraints. The saltatory matrix is presented by deducing the random zero-time discontinuous mapping with parameters. The random linearization matrix is obtained by combining the saltatory matrix and the fundamental solution matrix of smooth flow mapping. Based on the random linearization matrix, the influence of stochastic constraints on the system stability is discussed, and the doubling bifurcation phenomenon after the instability of the periodic solution is further investigated. The validity of the theory is verified by numerical simulations.
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