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不可压饱和多孔弹性杆动力响应的多辛方法

刘雪梅 邓子辰 胡伟鹏

刘雪梅, 邓子辰, 胡伟鹏. 不可压饱和多孔弹性杆动力响应的多辛方法[J]. 应用数学和力学, 2015, 36(3): 242-251. doi: 10.3879/j.issn.1000-0887.2015.03.002
引用本文: 刘雪梅, 邓子辰, 胡伟鹏. 不可压饱和多孔弹性杆动力响应的多辛方法[J]. 应用数学和力学, 2015, 36(3): 242-251. doi: 10.3879/j.issn.1000-0887.2015.03.002
LIU Xue-mei, DENG Zi-chen, HU Wei-peng. A Multi-Symplectic Method for Dynamic Responses of Incompressible Saturated Poroelastic Rods[J]. Applied Mathematics and Mechanics, 2015, 36(3): 242-251. doi: 10.3879/j.issn.1000-0887.2015.03.002
Citation: LIU Xue-mei, DENG Zi-chen, HU Wei-peng. A Multi-Symplectic Method for Dynamic Responses of Incompressible Saturated Poroelastic Rods[J]. Applied Mathematics and Mechanics, 2015, 36(3): 242-251. doi: 10.3879/j.issn.1000-0887.2015.03.002

不可压饱和多孔弹性杆动力响应的多辛方法

doi: 10.3879/j.issn.1000-0887.2015.03.002
基金项目: 国家自然科学基金(11372252;11172239;11372253);中央高校基金(2014G1121096)
详细信息
    作者简介:

    刘雪梅(1980—),女,陕西榆林人,讲师,硕士(通讯作者. E-mail: liumei112@163.com).

  • 中图分类号: O343

A Multi-Symplectic Method for Dynamic Responses of Incompressible Saturated Poroelastic Rods

Funds: The National Natural Science Foundation of China(11372252;11172239;11372253)
  • 摘要: 研究了不可压饱和多孔弹性杆的一维动力响应问题.基于多孔介质理论,在流相和固相微观不可压、固相骨架小变形的假定下,建立了不可压流体饱和多孔弹性杆一维轴向动力响应的数学模型.利用Hamilton空间体系的多辛理论,构造了不可压饱和多孔弹性杆轴向振动方程的多辛形式及其多种局部守恒律.采用中点Box离散方法得到轴向振动方程的多辛离散格式和局部能量守恒律以及局部动量守恒律的离散格式;数值模拟了不可压饱和多孔弹性杆的轴向振动过程,记录了每一时间步的局部能量数值误差和局部动量数值误差.结果表明,已构造的多辛离散格式具有很高的精确性和较长时间的数值稳定性,这为解决饱和多孔介质的动力响应问题提供了新的途径.
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出版历程
  • 收稿日期:  2014-12-02
  • 修回日期:  2014-12-26
  • 刊出日期:  2015-03-15

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