| 引用本文： |
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刘瑞春,刘林超.分数导数粘弹性地基上无限长弹性梁的稳态响应分析[J].广西科学,2010,17(2):126-128. [点击复制]
- LIU Rui-chun,LIU Lin-chao.Steady State Response of Elastic Beam with Infinite Length on Viscoelastic Ground Described by Fractional Derivative Model[J].Guangxi Sciences,2010,17(2):126-128. [点击复制]
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| 摘要: |
| 将土体视为粘弹性材料,用分数导数Kelvin粘弹性模型描述土体的应力-应变关系,建立分数导数模型描述粘弹性地基上无限长弹性梁的运动控制方程,并通过数值算例分析分数微分算子的阶数对无限长弹性梁稳态响应的影响.结果表明,分数导数微分算子的阶数对梁的稳态响应有较大的影响,在低频和高频时的影响相反,在低频时,分数导数微分算子的阶数越大,位移和弯矩越大,分数导数粘弹性模型比经典粘弹性模型应用范围还要广. |
| 关键词: 分数导数 粘弹性地基 稳态响应 |
| DOI： |
| 投稿时间：2009-06-19修订日期：2009-09-14 |
| 基金项目:上海市自然科学基金项目(06ZR14037),信阳师范学院2009年度青年基金项目(200942)资助。 |
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| Steady State Response of Elastic Beam with Infinite Length on Viscoelastic Ground Described by Fractional Derivative Model |
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LIU Rui-chun1, LIU Lin-chao2
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| (1.Henan Water Conservancy Construction Engineering Co., LTD, Zhengzhou, Henan, 450008, China;2.School of Civil Engineering, Xinyang Normal University, Xinyang, Henan, 464000, China) |
| Abstract: |
| The soil is regarded as viscoelastic material, and the stress-strain relationship of soil is described by fractional derivative Kelvin viscoelastic model.The fractional derivative model is established, the motion control equations of the elastic beam with infinite length on foundation described.The influence of the order of fractional differential operator on the steady-state response elastic beam with infinite length is analyzed by numerical example. The result indicated that the order of fractional differential operator had great effect on the steady response to the beam, and the influence is opposite and higher frequency.At lower frequency the larger the order of fractional derivative the larger the disaplacement and bending moment.The fractional derivativer viscoelastic model has larger application scope than classic viscoelastic model. |
| Key words: fractional derivative viscoelasticity foundation steady response |
