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弹性边界条件下带有任意分布弹簧质量系统的梁自由振动的解析解 被引量：5

AN ANALYTIC SOLUTION FOR A BEAM WITH ARBITRARILY DISTRIBUTED SPRING-MASS SYSTEMS UNDER ELASTIC BOUNDARY CONDITION
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摘要 基于正弦展开方法,对弹性边界条件下带有任意分布弹簧质量系统的梁的振动微分方程进行了求解,获得了一种近似解析解。运用该方法分析了带有均匀分布弹簧质量系统的梁的自由振动,模态频率的计算结果与参考文献中的数值结果一致,验证了该文算法的正确性。以此为基础,进一步研究了弹簧质量系统五种不同的分布形式对梁归一化模态频率的影响,结合不带弹簧质量系统的梁的振型图可得:弹簧质量系统分布形式在梁某阶模态振型幅值最大处的分布范围越广、分布密度越大,对该阶模态频率影响越大。 An analytic solution for a beam with arbitrarily distributed spring-mass systems under elastic boundary condition is obtained by using sine expansion method. It is applied to solving free vibration of a beam carrying uniformly distributed sprung masses, and results compared with those in reference show good agreement, which validates the methodology. Additional, effects of five different distributions of spring-mass system on dimensionless natural frequencies of beam are studied. Considering modes of beam without spring-mass, it is concluded that the higher the density and the wider the distribution of spring-mass system locating at the largest magnitude of a mode, the greater influences the spring-mass system has on the dimensionless natural frequencies of that mode.
作者 肖和业 盛美萍 赵芝梅
机构地区 西北工业大学航海学院
出处 《工程力学》 EI CSCD 北大核心 2012年第9期318-323,共6页 Engineering Mechanics
关键词 振动与波 解析解 自由振动 弹簧质量系统 任意分布 vibration and wave analytic solution free vibration spring-mass system arbitrary distribution
分类号 TH113.1 [机械工程—机械设计及理论] O328 [理学—一般力学与力学基础]
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参考文献11

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同被引文献58

  • 1肖世富,陈滨.挠性根部梁的动力学建模[J].力学与实践,2005,27(5):21-24. 被引量：5
  • 2JT391-1999公路桥梁盆式橡胶支座[S].北京:人民交通出版社,1999.
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  • 4徐腾飞,向天宇,赵人达.变截面Euler-Bernoulli梁在轴力作用下固有振动的级数解[J].振动与冲击,2007,26(11):99-101. 被引量：16
  • 5Chen D W,Wu J S.The exact solution for the natural frequencies and mode shapes of non-uniform beams with multiple spring-mass systems[J].Journal of Sound and Vibration,2002,255(2):299―322.
  • 6Barun Pratiher.Vibration control of a transversely excited cantilever beam with tip mass[J].Archive of Applied Mechanics,2012,82(1):31―42.
  • 7Nikkhah Bahrami M,Khoshbayani Arani M,Rasekh Salehb N.Modified wave approach for calculation of natural frequencies and mode shapes in arbitrary non-uniform beams[J].Scientia Iranica,2011,18(5):1088―1094.
  • 8Firouz-Abadi R D,Haddadpour H,Novinzadeh A B.An asymptotic solution to transverse free vibrations of variable-section beams[J].Journal of Sound and Vibration,2007,304(1/2):530―540.
  • 9Korak Sarkar,Ranjan Ganguli.Closed-form solutions for non-uniform Euler-Bernoulli free-free beams[J].Journal of Sound and Vibration,2013,332(3):6078―6092.
  • 10Qibo Mao.Free vibration analysis of multiple-stepped beams by using Adomian decomposition method[J].Mathematical and Computer Modelling,2011,54(1):756―764.

引证文献5

二级引证文献5

工程力学
2012年 第9期

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