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轴向流作用下均布非线性弹簧支承二维壁板的复杂响应
Complicated responses of a two-dimensional plate under action of an axial liquid flow with cubic stiffness
投稿时间:2022-10-14  修订日期:2022-12-24
DOI:
中文关键词:  二维壁板  周期倍化分岔  模态缩减
英文关键词:two-dimensional plate  doubling-period bifurcations  model order reduction method
基金项目:国家自然科学基金(11872043,11772273)资助项目.
作者单位邮编
董宇 湖南工业大学 土木工程学院 412007
郑 辉 湖南工业大学 土木工程学院 412007
杨翊仁 西南交通大学 力学与工程学院 
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中文摘要:
      考虑刚性导流段和尾流段对流场的影响,建立轴向流作用下二维板的非线性流固耦合运动控制方程,用有限差分法对控制方程进行离散。为了克服差分网格较多时带来的计算规模较大的问题,对控制方程用主模态缩减法缩减自由度,然后对离散方程进行数值积分,得到系统的复杂响应,分析其分岔和混沌特性。计算结果表明,以来流流速幅值和阻尼参数为可变参数时,系统具有极其复杂的动态响应,通过分岔图、相图和庞加莱截面图等方法判断了系统的多种形式的周期、拟周期和混沌运动,在以来流流速幅值为可变参数时,系统一开始经由周期倍化分岔的方式进入混沌;在以阻尼系数为可变参数时,经由倒周期倍化分岔的方式从混沌运动退回到周期振动。
英文摘要:
      The complicated responses of a two-dimension simply supported plate in axial liquid flow with cubic stiffness are studied, the effect of the leading rigid edge and the trailing rigid edge of plate on flow is considered. The finite difference method is used to discrete the governing equation . In order to reduce the computation scale caused by a large number of the grids, the main model order reduction method is adopted. The complex responses of system are calculated by the numerical integration method. Calculations of bifurcation diagrams,phase-plane portraits and Poincaré maps for the plate"s responses confirmed definitively the existence of chaos and other complicated responses in terms of fluid velocity and damping coefficient.The vibration responses of the plate led to chaos from period-doubling bifurcations or quasi-periodic motion, the route from chaos to periodic motion is inverted period-doubling bifurcations.
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