留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

汽车车体振动系统的对称性与守恒量研究

翟晓洋 傅景礼

翟晓洋, 傅景礼. 汽车车体振动系统的对称性与守恒量研究[J]. 应用数学和力学, 2015, 36(12): 1285-1293. doi: 10.3879/j.issn.1000-0887.2015.12.007
引用本文: 翟晓洋, 傅景礼. 汽车车体振动系统的对称性与守恒量研究[J]. 应用数学和力学, 2015, 36(12): 1285-1293. doi: 10.3879/j.issn.1000-0887.2015.12.007
ZHAI Xiao-yang, FU Jing-li. Study on Symmetries and Conserved Quantities of Vehicle Body Vibration Systems[J]. Applied Mathematics and Mechanics, 2015, 36(12): 1285-1293. doi: 10.3879/j.issn.1000-0887.2015.12.007
Citation: ZHAI Xiao-yang, FU Jing-li. Study on Symmetries and Conserved Quantities of Vehicle Body Vibration Systems[J]. Applied Mathematics and Mechanics, 2015, 36(12): 1285-1293. doi: 10.3879/j.issn.1000-0887.2015.12.007

汽车车体振动系统的对称性与守恒量研究

doi: 10.3879/j.issn.1000-0887.2015.12.007
基金项目: 国家自然科学基金(11272287;11472247)
详细信息
    作者简介:

    翟晓洋(1991—),男,江苏东台人,硕士生(通讯作者. E-mail: jszxy@foxmail.com).

  • 中图分类号: O316

Study on Symmetries and Conserved Quantities of Vehicle Body Vibration Systems

Funds: The National Natural Science Foundation of China(11272287;11472247)
  • 摘要: 用Lie群方法研究汽车车体振动系统的对称性,寻找其存在的守恒量.以汽车车体做上下垂直振动和绕其质心的前后俯仰振动,采用Lagrange函数的方法,构建汽车车体振动系统.以此系统为对象,引入Lie群方法,给出该振动系统的Noether对称性理论与Lie对称性理论;由此推导该汽车系统存在的Noether对称性与Lie对称性,并得到系统相应的的守恒量.该方法对车体振动问题提出了新的对称性解法,同时扩大了Lie群方法的应用范围.
  • [1] 梅凤翔. 李群和李代数对约束力学系统的应用[M]. 北京: 科学出版社, 1999.(MEI Feng-xiang. Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems [M]. Beijing: Science Press, 1999.(in Chinese))
    [2] 薛纭, 曲佳乐, 陈立群. Cosserat生长弹性杆动力学的Gauss最小拘束原理[J]. 应用数学和力学,2015,36(7): 700-709.(XUE Yun, QU Jia-le, CHEN Li-qun. Gauss principle of least constraint for Cosserat growing elastic rod dynamics[J]. Applied Mathematics and Mechanics,2015,36(7): 700-709.(in Chinese))
    [3] 顾书龙, 张宏彬. Kepler方程的Noether对称性与Hojman守恒量[J]. 物理学报, 2010,59(2): 716-718.(GU Shu-long, ZHANG Hong-bin. Noether symmetry and the Hojman conserved quantity of Kepler equation[J].Acta Physica Sinica,2010,59(2): 716-718.(in Chinese))
    [4] 张毅. Lagrange系统的共形不变性与Noether对称性和Lie对称性[J]. 苏州科技学院学报(自然科学版), 2009,26(1): 1-5.(ZHANG Yi. Conformal invariance, Noether symmetry and Lie symmetry of Lagrangian systems[J].Journal of Suzhou University of Science and Technology(Natural Science),2009,26(1): 1-5.(in Chinese))
    [5] 葛伟宽, 张毅, 薛纭. Rosenberg问题的对称性与守恒量[J]. 物理学报, 2010,59(7): 4434-4436.(GE Wei-kuan, ZHANG Yi, XUE Yun. Symmetries and conserved quantities of the Rosenberg problem[J].Acta Physica Sinica,2010,59(7): 4434-4436.(in Chinese))
    [6] FU Jing-li, CHEN Li-qun. On Noether sysmmetries and form invariance of mechanico-electrical systems[J]. Physics Letters A,2004,331(3/4): 138-152.
    [7] FANG Jian-hui. A new type of conserved quantity of Lie symmetry for the Lagrange system[J].Chinese Physics B,2010,19(4): 21-24.
    [8] 楼智美. 两自由度弱非线性耦合系统的一阶近似Lie 对称性与近似守恒量[J]. 物理学报, 2013,62(27): 220202.(LOU Zhi-mei. The first order approximate Lie symmetries and approximate conserved quantities of the weak nonlinear coupled two-dimensional system[J].Acta Physica Sinica,2013,62(27): 220202.(in Chinese))
    [9] 刘畅, 刘世兴, 梅凤翔, 郭永新. 广义Hamilton系统的共形不变性与Hojman 守恒量[J]. 物理学报, 2008,57(11): 6709-6713.(LIU Chang, LIU Shi-xing, MEI Feng-xiang, GUO Yong-xin. Conformal invariance and Hojman conserved quantities of generalized Hamilton systems[J].Acta Physica Sinica,2008,57(11): 6709-6713.(in Chinese))
    [10] 梅凤翔. 具有可积微分约束的系统的Lie对称性[J]. 力学学报, 2000,32(4): 466-472.(MEI Feng-xiang. Lie symmetries of mechanical system with integral differential constraints[J].Acta Mechanica Sinica,2000,32(4): 466-472.(in Chinese))
    [11] 黄卫立, 蔡建乐. 变质量Chetaev型非完整系统的共形不变性[J]. 应用数学和力学, 2012,33(11): 1294-1303.(HUANG Wei-li, CAI Jian-le. Conformal invariance for the nonholonomic system of Chetaev’s type with variable mass[J]. Applied Mathematics and Mechanics,2012,33(11): 1294-1303.(in Chinese))
    [12] 邹丽, 王振, 宗智, 王喜军, 张朔. 指数同伦法对Cauchy条件下变系数Burgers方程的解析与数值分析[J]. 应用数学和力学, 2014,35(7): 777-789.(ZOU Li, WANG Zhen, ZONG Zhi, WANG Xi-jun, ZHANG Shuo. Analytical and numerical investigation of the variable coefficient Burgers equation under Cauchy condition with the exponential homotopy method[J].Applied Mathematics and Mechanics,2014,35(7): 777-789.(in Chinese))
    [13] 梅凤翔. Lagrange系统的形式不变性[J]. 北京理工大学学报, 2000,9(2): 120-124.(MEI Feng-xiang. Form invariance of Lagrange system[J].Journal of Beijing Institute of Technology,2000,9(2): 120-124.(in Chinese))
    [14] ZHANG Yi. Symmetries and conserved quantities of generalized Birkhoffian systems[J].Journal of Southeast University(English Edition),2010,26(1): 146-150.
    [15] 方建会, 丁宁, 王鹏. Hamilton系统Mei对称性的一种新守恒量[J]. 物理学报, 2007,56(6): 3039-3042.(FANG Jian-hui, DING Ning, WANG Peng. A new type of conserved quantity of Mei symmetry for Hamilton system[J].Acta Physica Sinica,2007,56(6): 3039-3042.(in Chinese))
    [16] 郑世旺, 解加芳, 陈向炜, 杜雪莲. 完整系统Tzénoff方程的Mei对称性直接导致的另一种守恒量[J]. 物理学报, 2010,59(8): 5209-5212.(ZHENG Shi-wang, XIE Jia-fang, CHEN Xiang-wei, DU Xue-lian. Another kind of conserved quantity induced directly from Mei symmetry of Tzénoff equations for holonomic systems[J].Acta Physica Sinica,2010,59(8): 5209-5212.(in Chinese))
    [17] 张策. 机械动力学[M]. 第二版. 北京: 高等教育出版社, 2008: 142-143.(ZHANG Ce. Machinery Dynamics [M]. 2nd ed. Beijing: Higher Education Press, 2008: 142-143.(in Chinese))
  • 加载中
计量
  • 文章访问数:  1094
  • HTML全文浏览量:  82
  • PDF下载量:  543
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-05-07
  • 修回日期:  2015-08-22
  • 刊出日期:  2015-12-15

目录

    /

    返回文章
    返回