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    分数导数Kelvin粘弹性土中管桩的扭转振动
    刘林超, 闫启方, 牛洁楠
    信阳师范学院 建筑与土木工程学院, 河南 信阳 464000
    摘要:
    将管桩桩周土和桩芯土均看作粘弹性介质,同时运用分数导数Kelvin粘弹性本构模型描述桩周土和桩芯土的应力应变关系。仅考虑桩周土和桩芯土的环向位移,通过Fourier变换和分离变量法求解了桩周和桩芯分数导数Kelvin粘弹性土的扭转振动。考虑桩周土和桩芯土对管桩的作用力,建立了分数导数Kelvin粘弹性土中管桩的扭转振动方程,通过求解管桩的扭转振动得到了频率域内管桩桩顶的扭转复刚度。结果表明:桩周土本构模型参数α1Tb1对管桩的扭转振动有一定的影响,而桩芯土的本构模型参数α2Tb2对管桩扭转振动的影响与频率有关;桩芯土与桩周土剪切模量比μ小于1且μ较大时,扭转复刚度实部和虚部随频率变化曲线波动较大,而μ大于1时其对管桩扭转振动的影响很小;管桩壁厚、长径比和管桩与土体的剪切模量比Gp对管桩的扭转影响较大。
    关键词:  粘弹性  分数导数  Fourier变换  扭转振动  复刚度
    DOI:10.11835/j.issn.1674-4764.2018.06.007
    分类号:TU473.16
    基金项目:国家自然科学基金(U1504505);河南省科技发展计划(142102210063);河南省高等学校重点科研项目(19B560008);信阳师范学院南湖学者奖励计划青年项目(201506)
    Torsional vibration of a pipe pile in soil described by fractional derivative Kelvin viscoelastic model
    Liu Linchao, Yan Qifang, Niu Jienan
    School of Architecture and Civil Engineering, Xinyang Normal University, Xinyang 464000, Henan, P. R. China
    Abstract:
    The soil around the pipe pile and pile core soil are regarded as viscoelastic medium, and the stress-strain relationship for them are described by fractional derivative Kelvin viscoelastic constitutive model. The torsional vibrations are solved by Fourier transformation and separation variable method by considering the circumferential displacement of the soil only. Considering the forces acting on the pipe piles, the torsional vibration in the fractional derivative Kelvin viscoelastic soil is established. The torsional complex stiffness at pipe pile head is obtained by solving the torsional vibration of the pipe pile. The results show that the model soil parameters α1 and Tb1 have certain influence on the torsional vibration while the influence of the pile core soil model parameters α2 and Tb2 is related to frequency. The curves of real and imaginary parts of torsional complex stiffness with frequency fluctuate more greatly when the shear modulus ratio μ is larger and μ<1, and the influence of shear modulus ratio μ on the torsional vibration of pipe pile is very small when μ>1. Wall thickness, length diameter ratio of pipe pile, as well as the shear modulus of pipe pile and soil have great influence on the torsional vibration of pipe pile.
    Key words:  viscoelastic  fractional derivative  Fourier transform  torsional vibration  complex stiffness
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