期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

分数阶导数阻尼下非线性随机振动结构响应的功率谱密度估计 被引量：6

Response power spectral density estimate of a fractionally damped nonlinear oscillator
下载PDF
导出
摘要 对于受到由分数阶导数模拟的粘弹性阻尼的非线性随机振动结构,本文给出了一种计算响应的功率谱密度方法。借助标准的随机平均法,首先得到了振动结构随机响应振幅的稳态概率密度。对于原振动结构的非线性项,运用改进的统计线性化方法得到了均方意义下的等价线性振动结构,并求得了其响应的依赖于振幅的条件功率谱密度。综合以上的结果,针对随机振动响应的功率谱密度的估计,通过与数值模拟结果进行验证,从而证明了所提方法的有效性和准确性。 A procedure for the response power spectral density estimate of a fractionally damped stochastic nonlinear vibration structure is proposed.The stationary probability density function of the response is firstly obtained with the application of stochastic averaging technique;and then improved statistical linearization is adopted to transform the original system into its linear equivalent,for which the conditional power spectral density can be derived immediately.Finally,an analytical formula of the response power spectral density of the fractionally damped vibration structure is calculated by integrating the obtained results.Numerical simulation verifies the validity of the proposed procedure.
作者 孙春艳 徐伟
机构地区 西北工业大学
出处 《应用力学学报》 CAS CSCD 北大核心 2013年第3期401-405,477,共5页 Chinese Journal of Applied Mechanics
基金 国家自然科学基金(11172233 11202160)
关键词 分数阶导数 粘弹性结构阻尼 随机平均法 统计线性化 功率谱密度 fractional derivative viscoelastic structural damping stochastic averaging statistical linearization power spectral density.
分类号 O327 [理学—一般力学与力学基础]
  • 相关文献

参考文献17

  • 1Bagley R L, Torvik P J. Fractional calculus a different approach to the analysis of viscoelastically damped structures[J]. AIAA Journal, 1983, 21(5): 741-748.
  • 2Bagley R L, Torvik P J. Fractional calculus in the transient analysis ofviscoelastically damped structures[J]. AIAA Journal, 1985, 23(6): 918-925.
  • 3Koeller R C. Application of fractional calculus to the theory of viscoelasticity[J]. ASME Journal of Applied Mechanics, 1984, 51 (2): 299-307.
  • 4Gaul L, Klein P, Kemple S. Impulse response function of an oscillator with fractional derivative in damping description[J]. Mechanics Research Communications, 1989, 16(5): 297-305.
  • 5Wahi P, Chatterjee A. Averaging for oscillations with light fractional order damping[C]//Proceedings of ASME 2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Chicago." ASME, 2003: 721-727.
  • 6Huang Z L, Jin X L. Response and stability of a SDOF strongly nonlinear stochastic system with light damping modeled by a fractional derivative[J]. Journal of Sound and Vibration, 2009, 319(3/5): 1121-1135.
  • 7Podlubny I. Fractional differential equations[M]. London: Academic Press, 1999.
  • 8Diethelm K, Ford N J, Freed A D, et al. Algorithms for the fractional calculus: A selection of numerical methods[J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194(6/8): 743-773.
  • 9Diethelm K, Ford N J, Freed A D. Apredictor-corrector approach for the numerieaU solution of fractional differential equations[J].Nonlinear Dynamics, 2002, 29(1/4): 3-22.
  • 10Yuan L, 'Agrawal O P. A numerical scheme for dynamic systemcontaining fractional derivatives[J]. Journal of Vibration and Acoustics, 2002, 124(2): 321-324.

同被引文献58

  • 1孙广俊,李鸿晶.平稳随机地震地面运动过程模型及其统计特征[J].地震工程与工程振动,2004,24(6):21-26. 被引量：11
  • 2Oldham K B, Spanier J. The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order[ M]. New York: Academic Press, 1974.
  • 3Miller K S, Ross B. An Introduction to the Fractional Calculus and Fractional Differential E- quatious[ M]. New York: 3ohn Wiley & Sons Inc, 1993.
  • 4Podlubny I. Fractional Differential Equations [ M ]. New York: Academic Press, 1999.
  • 5Samko S G, Kilbas A A, Marichev O I. Fractional Integrals and Derivatives [ M J. New York: Gordon and Breach Science Publishers, 1993.
  • 6Mandelbrot B B. The Fracta/Geometry of Nature[M]. New York: W H Freeman, 1982.
  • 7Bagley R L, Torvik P J. A theoretical basis for the application of fractional calculus to vis- coelasticity[J]. Journal of Rheology, 1983, 27(3) : 201-210.
  • 8Bagley R L, Torvik P J. Fractional calculus--a different approach to the analysis of viscoelas- tically damped structures[J]. A/AA Journal, 1983, 21(5) : 741-748.
  • 9Bagley R L, Torvik P J. Fractional calculus in the transient analysis of viscoelastically damped structures[J]. A/AA Journal, 1985, 23(6): 918-925.
  • 10Koeller R C. Applications of fractional calculus to the theory of viscoelasticity[ J]. Journal of Applied Mechanics-Transactions of the ASME, 1984, 51(2) : 299-307.

引证文献6

二级引证文献10

应用力学学报
2013年 第3期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部