摘要
本文对谐波激励的悬索的非线性响应进行了研究,同时考虑了如下问题(1):面内第三阶对称模态的主共振:(2):面内第一阶、第三阶对称模态和面外第五阶模态之间的内共振。本方首先针对考虑大变形的悬索动力学方程,由线性理论求得各阶频率,考察可能出现的内共振。然后利用直接法对悬索的运动学方程和边界条件进行非线性求解。由多尺度法得到系统的平均方程和悬索响应的二阶近似解。随后利用Newton-Raphson方法和弧长法对特定张拉索进行数值仿真计算,得到面内第一阶对称模态、面内第三阶对称模态和面外第五阶模态的稳态解,并分析了解的稳定性。绘制幅频响应曲线,发现了关于悬索响应的多种分叉现象,并且对各种分叉现象周期解、混沌解进行了讨论。
Non-linear response of suspended cables under harmonic excition were investigated . Considering the following points.（1）the prinary resonances of the third in-plane symmetric mode. （2）internal resonances among the first in-plane symmetric mode, the third in-plane symmetric mode and the fifth out-of-plane mode. The method of multiple scales was applied to attack the equations of cables and boundary conditions, The frequency-response curves and the displacement of cables were received, Many bifurcations of the cable were found. The bifurcations and Chaos were also studied.
出处
《力学季刊》
CSCD
北大核心
2008年第1期15-23,共9页
Chinese Quarterly of Mechanics
基金
国家自然科学基金(10502020)
关键词
内共振
悬索
非线性振动
周期运动
混沌
internal resonances
suspended cables
non-linear vibration periodic motion
chaos
