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轴向变速运动黏弹性梁稳定性渐近分析和数值验证
  • ISSN号：0254-7805
  • 期刊名称：《固体力学学报》
  • 时间：0
  • 分类：O175.8[理学—数学;理学—基础数学] O175.26[理学—数学;理学—基础数学]
  • 作者机构：[1]上海大学上海市应用数学和力学研究所,上海200072, [2]上海大学力学系,上海200072
  • 相关基金：国家杰出青年科学基金（10725209）、国家自然科学基金（10672092）、上海市教育委员会科研项目（07ZZ07）和上海市重点学科建设项目（Y0103）资助.
作者： 王波[1], 陈立群[1,2]
关键词： 轴向变速运动梁, 黏弹性, 参数共振, 渐近摄动, 稳定性, 微分求积, axially accelerating beam, viscoelasticity, parametric resonance, asymptotic perturbation,stability, differential quadrature
中文摘要：

研究了轴向变速运动黏弹性梁参数振动的稳定性．对黏弹性本构关系采用物质时间导数，轴向速度用关于恒定平均速度的简单谐波变化来描述．发展渐近摄动法确定稳定性条件．应用微分求积法数值求解简支边界条件下的轴向变速运动黏弹性梁方程，并进而确定次谐波参数共振的稳定性边界．数值结果显示了梁的黏性阻尼和轴向平均速度的影响并验证了次谐波共振的解析结果．

英文摘要：

Stability of an axially accelerating viscoelastic beam is investigated. The material time derivative is used in the viscoelastic constitutive relation. The axial speed is characterized as a simple harmonic variation about the constant mean speed. The stability condition can be determined via the asymptotic per- turbation method. The differential quadrature scheme is developed to solve numerically the equation of axi- ally accelerating viscoelastic beams with simple supports. The stability boundaries are numerically located in the principal parametric resonance. Numerical examples show the effects of the beam viscoelasticity and the mean axial speed. The numerical calculations validate the analytical results in the principal parametric resonance.

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期刊信息
  • 《固体力学学报》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学技术协会
  • 主办单位:中国力学学会
  • 主编：方岱宁
  • 地址：武汉华中科技大学南一楼西北508室
  • 邮编：430074
  • 邮箱：amss@mail.hust.edu.cn
  • 电话：027-87543737
  • 国际标准刊号：ISSN：0254-7805
  • 国内统一刊号：ISSN：42-1250/O3
  • 邮发代号:38-44
  • 获奖情况:
  • 获得第二届全国优秀科技期刊三等奖,中国期刊方阵“双效”期刊
  • 国内外数据库收录:
  • 美国化学文摘（网络版）,荷兰文摘与引文数据库,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:6186