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基于高斯原理的非理想系统动力学建模

姚文莉 刘彦平 杨流松

姚文莉, 刘彦平, 杨流松. 基于高斯原理的非理想系统动力学建模[J]. 力学学报, 2020, 52(4): 945-953. doi: 10.6052/0459-1879-20-073
引用本文: 姚文莉, 刘彦平, 杨流松. 基于高斯原理的非理想系统动力学建模[J]. 力学学报, 2020, 52(4): 945-953. doi: 10.6052/0459-1879-20-073
Yao Wenli, Liu Yanping, Yang Liusong. DYNAMIC MODELING OF NONIDEAL SYSTEM BASED ON GAUSS'S PRINCIPLE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 945-953. doi: 10.6052/0459-1879-20-073
Citation: Yao Wenli, Liu Yanping, Yang Liusong. DYNAMIC MODELING OF NONIDEAL SYSTEM BASED ON GAUSS'S PRINCIPLE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 945-953. doi: 10.6052/0459-1879-20-073

基于高斯原理的非理想系统动力学建模

doi: 10.6052/0459-1879-20-073
基金项目: 1)国家自然科学基金(11272167)
详细信息
    通讯作者:

    姚文莉

  • 中图分类号: O316

DYNAMIC MODELING OF NONIDEAL SYSTEM BASED ON GAUSS'S PRINCIPLE

  • 摘要: 高斯原理给出了通过求函数极值、从可能运动中鉴别出真实运动的规则, 它可以使得多体系统动力学问题不需通过求解微分(代数)方程, 而是采用求解最小值的优化方法来解决, 从而提供了一种适用于优化算法的建模思路, 因此, 如何定义恰当的高斯拘束函数是动力学优化方法得以实现的前提. 对于理想系统而言, 约束对系统的作用可以通过约束方程来体现, 故高斯拘束可表达为系统质点加速度的函数, 系统的动力学问题因此可以描述为目标函数为高斯拘束函数、优化变量为质点加速度的约束最优化问题; 当系统中需要考虑干摩擦等非理想因素时, 部分相互作用不能被所定义的约束方程所涵盖而需要采用额外的物理规律来描述, 这种相互作用破坏了原有的针对理想系统的高斯拘束函数的极值特性. 基于变分类的高斯原理, 推导并证明了目标函数以理想约束力所表达的非理想系统的极值原理, 针对目前文献中用于非理想系统的高斯原理进行了讨论, 指出其实际为文中的极值原理在非理想约束力与理想约束力无明显关联时的一种特殊表达形式, 当非理想约束力与理想约束力有明显的函数关系(如库仑摩擦定律中滑动摩擦力与法向约束力间的线性关系)时, 该形式失效; 同时根据文中的极值原理, 得到了考虑库仑摩擦时非理想的多体系统动力学问题的优化模型. 例子中分析了优化模型及相应的线性互补性模型的关系, 分析发现在满足刚体滑动问题的唯一性条件下二者互为充分必要条件, 从而证明了文中优化模型的可靠性; 并采用优化计算方法进行了动力学模拟, 模拟结果显示了将高斯原理与优化算法相结合的可行性及有效性.

     

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出版历程
  • 收稿日期:  2019-03-05
  • 刊出日期:  2020-08-10

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