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柔性约束下压杆的一些稳定和不稳定的临界状态

赵艳萍 李琳 金明

赵艳萍, 李琳, 金明. 柔性约束下压杆的一些稳定和不稳定的临界状态[J]. 应用数学和力学, 2017, 38(8): 877-887. doi: 10.21656/1000-0887.370299
引用本文: 赵艳萍, 李琳, 金明. 柔性约束下压杆的一些稳定和不稳定的临界状态[J]. 应用数学和力学, 2017, 38(8): 877-887. doi: 10.21656/1000-0887.370299
ZHAO Yan-ping, LI Lin, JIN Ming. Some Stable and Unstable Critical States of a Compression Rod With a Flexible Support[J]. Applied Mathematics and Mechanics, 2017, 38(8): 877-887. doi: 10.21656/1000-0887.370299
Citation: ZHAO Yan-ping, LI Lin, JIN Ming. Some Stable and Unstable Critical States of a Compression Rod With a Flexible Support[J]. Applied Mathematics and Mechanics, 2017, 38(8): 877-887. doi: 10.21656/1000-0887.370299

柔性约束下压杆的一些稳定和不稳定的临界状态

doi: 10.21656/1000-0887.370299
基金项目: 高等学校博士学科点专项科研基金(20120009110019)
详细信息
    作者简介:

    赵艳萍(1982—),女,博士生(通讯作者. E-mail: zhaoyanping1103@126.com).

  • 中图分类号: O342; TB12

Some Stable and Unstable Critical States of a Compression Rod With a Flexible Support

  • 摘要: 研究了一端固定、一端弹簧约束滑动固定的压杆在Euler临界载荷作用下的稳定性.将系统的势能表示为转角的泛函,将扰动量展开成Fourier级数,将势能的二阶变分表示成一个二次型,得到在临界状态下势能的二阶变分半正定,并求得临界载荷与屈曲模态.进一步研究临界状态下高阶变分的正定性,包括四阶和六阶变分的正定性.结果表明,与刚性约束不同的是,柔性约束压杆临界状态的稳定性与约束的刚度有关,有稳定与不稳定之分,并给出了临界状态是稳定和不稳定的情况下柔性约束相对刚度的范围.
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出版历程
  • 收稿日期:  2016-09-29
  • 修回日期:  2016-12-01
  • 刊出日期:  2017-08-15

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