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求解周期性分段线性系统动态响应的高效数值方法

何冬东 高强 钟万勰

何冬东, 高强, 钟万勰. 求解周期性分段线性系统动态响应的高效数值方法[J]. 应用数学和力学, 2018, 39(7): 737-749. doi: 10.21656/1000-0887.390055
引用本文: 何冬东, 高强, 钟万勰. 求解周期性分段线性系统动态响应的高效数值方法[J]. 应用数学和力学, 2018, 39(7): 737-749. doi: 10.21656/1000-0887.390055
HE Dongdong, GAO Qiang, ZHONG Wanxie. An Efficient Numerical Method for Computing Dynamic Responses of Periodic Piecewise Linear Systems[J]. Applied Mathematics and Mechanics, 2018, 39(7): 737-749. doi: 10.21656/1000-0887.390055
Citation: HE Dongdong, GAO Qiang, ZHONG Wanxie. An Efficient Numerical Method for Computing Dynamic Responses of Periodic Piecewise Linear Systems[J]. Applied Mathematics and Mechanics, 2018, 39(7): 737-749. doi: 10.21656/1000-0887.390055

求解周期性分段线性系统动态响应的高效数值方法

doi: 10.21656/1000-0887.390055
基金项目: 国家自然科学基金(11572076;914748203);国家重点基础研究发展计划(973计划)(2014CB049000)
详细信息
    作者简介:

    何冬东(1988—),男,博士生(E-mail: d.dong.he@mail.dlut.edu.cn);高强(1978—),教授,博士,博士生导师(通讯作者. E-mail: qgao@dlut.edu.cn).

  • 中图分类号: TB122; O322

An Efficient Numerical Method for Computing Dynamic Responses of Periodic Piecewise Linear Systems

Funds: The National Natural Science Foundation of China(11572076;914748203);The National Basic Research Program of China(973 Program)(2014CB049000)
  • 摘要: 基于参变量变分原理,提出了一种求解具有大量间隙弹簧的周期性分段线性系统动态响应的高效率数值方法.通过参变量变分原理来描述间隙弹簧,将复杂的非线性动力问题转化为线性互补问题求解,避免了求解过程中的迭代和刚度阵更新,该算法能准确判断间隙弹簧的压缩和松弛状态.基于结构的周期性和能量传播速度的有限性,提出了一种求解系统动态响应的高效率精细积分方法.该算法指出周期结构的矩阵指数中存在大量的相同元素和零元素,从而不需要重复计算和存储这部分元素,节省了计算量并降低了计算机存储要求.分析了一个五自由度分段线性系统在简谐荷载作用下的动力学行为,包括稳定的周期运动、准周期运动和混沌运动.通过与RungeKutta方法的比较,该文方法的正确性和高效率得到了验证.
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出版历程
  • 收稿日期:  2018-02-04
  • 刊出日期:  2018-07-15

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