为了考虑截面剪切变形和转动惯量对弹性地基梁横向振动的影响,研究并完善了基于Pasternak弹性地基模型上变截面Timoshenko梁的有限元分析方法,建立了任意截面的Timoshenko梁的模态分析方法。具体来讲,基于Timoshenko梁理论和牛顿第二定律建立了地基梁结构的运动微分方程,并对变截面的分析运用分段等效的思想,将梁离散成一个个均匀的梁段,每个有限单元都有4个自由度,使得每个有限元的单元和梁段一一对应。以完全支撑在弹性地基上的简支梁为例,分析了结构的自由振动的特性。通过与可信赖的半解析方法的结果进行比较,结果表明了该方法的准确性和有效性,并为变截面地基梁模型的分析拓展了一种思路。
Abstract
To study the influence of cross sectional shear deformation and moment of inertia on transverse vibration of elastic foundation beam, the finite element analysis method for variable cross-sectional Timoshenko beam on Pasternak elastic foundation model was developed and improved, and the modal analysis method for arbitrary cross-section of Timoshenko beam was established. In specific, the motion differential equations of foundation beam were derived based on Timoshenko beam theory and Newton’s second law; in the light of piecewise equivalent idea, the variable cross-sections were discretized into many simple uniform beam sections, which corresponded respectively with each finite element with four degrees of freedom. Furthermore, with beam of simply supported boundary which is fully supported on elastic foundation as an example, the characteristics of free vibration were analyzed and compared with those obtained from reliable semi-analytical approach. The results showed that the present method is effective and accuracy and therefore a new insight is provided to the analysis of variable cross-sectional foundation-beam.
关键词
Pasternak地基模型 /
Timoshenko梁 /
有限元分析 /
变截面 /
模态分析
Key words
Pasternak elastic foundation model /
Timoshenko beam /
finite element analysis /
variable cross-section /
modal analysis
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参考文献
[1] SELVADURAI A P S. Elastic Analysis of Soil-Foundation Interaction [M]. Amsterdam: Elsevier, 1979.
[2] 卢 健,温中华,周 娟.弹性地基梁法计算地下钢筋混凝土岔管结构应力[J].raybet体育在线
院报,2008,25(1):80-81.
[3] EISENBERGER M, YANKELEVSKY D Z, ADIN M A. Vibrations of Beams Fully or Partially Supported on Elastic Foundations[J].Earthquake Engineering and Structural Dynamics,1985,13(5):651-660
[4] THAMBIRATNAM D,ZHUGE Y.Free Vibration Analysis of Beams on Elastic Foundation[J].Computers and Structures,1996, 60(6):971-980.
[5] 徐牧明,陈定安.一种新型的基准基床系数室内通用测试方法[J].raybet体育在线
院报,2017,34(1):109-113.
[6]VALSANGKAR A J, PRADHANANG R. Vibrations of Beam-columns on Two-parameter Elastic Foundations[J].Earthquake Engineering and Structural Dynamics, 1988, 16(2):217-225.
[7] DE ROSA M A, MAURIZI M J. The Influence of Concentrated Masses and Pasternak Soil on the Free Vibrations of Euler Beams—Exact Solution[J]. Journal of Sound and Vibration, 1998, 212(4):573-581.
[8] 刘学山,冯紫良,胥 兵.粘弹性地基上弹性梁的自由振动分析[J].上海力学,1999,20(4):470-476.
[9] 楼梦麟,沈 霞.弹性地基梁振动特性的近似分析方法[J].应用力学学报,2004,21(3):149-152.
[10]崔 灿,蒋 晗,李映辉.变截面梁横向振动特性半解析法[J].振动与冲击,2012,31(14):85-88.
[11]TIMOSHENKO S P. Vibration Problems in Engineering[M]. 2nd Edition. New York: Wolfenden Press, 2008.
[12]GUPTA A K. Vibration of Tapered Beams[J]. Journal of Structural Engineering, 1985, 111(1):19-36.
[13]YOKOYAMA T. Vibrations of Timoshenko Beam-columns on Two-parameter Elastic Foundations[J]. Earthquake Engineering and Structural Dynamics, 1991, 20(4):355-370.
[14]KARAMANLIDIS D, PRAKASH V. Exact Transfer and Stiffness Matrices for a Beam/column Resting on a Two-parameter Foundation[J]. Computer Methods in Applied Mechanics and Engineering, 1989, 72(1):77-89.
[15]CAO Chang-yong, ZHONG Yang. Dynamic Response of a Beam on a Pasternak Foundation and under a Moving Load[J].Journal of Chongqing University (English Edition),2008,7(4):311-316.
基金
国家自然科学基金重点项目(51621006)
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