基于积分型分数导数本构方程的黏弹性土层中单桩的竖向复刚度与导纳研究  

Study on vertical complex stiffness and admittance of single pile in soil based on constitutive equation with integral fractional derivatives

作　　者：刘林超[1] 姚庆钊[1] 闫启方[1] 余萍[1] 

机构地区：[1]信阳师范学院土木工程学院,河南信阳464000

出　　处：《水利学报》2012年第7期796-802,共7页Journal of Hydraulic Engineering

基　　金：河南省科技发展计划项目(112300410105);河南省教育厅自然科学研究计划项目(2011A1301001);信阳师范学院青年骨干教师资助计划(2011007)

摘　　要：建立了基于三维积分型本构方程的单桩在黏弹性土体的竖向振动微分方程。利用三维分数导数Kelvin黏弹性本构关系描述土体的应力应变关系,考虑分数导数和卷积的Fourier变换性质,利用势函数和分离变量法在频域内求解了分数导数黏弹性土层的竖向振动,并在此基础上求解了黏弹性土层中单桩的竖直振动。研究了土体本构模型参量对桩顶复刚度和桩顶导纳的影响。研究表明,分数导数的阶数对桩顶复刚度和桩顶导纳有较大的影响,土体黏性系数对桩顶复刚度的实部和桩顶导纳影响较大,而对桩顶复刚度虚部影响相对较小。Differential equations for the vertical vibration of single piles in viscoelastic soil were established based on the three dimensional and integral constitutive equations. The stress-strain relationship of soil was described by the three dimensional fractional derivatives for Kelvin viscoelastic constitutive relationship. The vertical vibration of fractional derivative viscoelastic soil was solved by potential functions and method of separation variables in frequency range by considering the properties of Fourier transform of fractional deriva- tive and convolution integral. The influence of constitutive model parameters on complex stiffness and admit- tance at pile head was investigated, the research indicated that the order of fractional derivative has great effect on the complex stiffness and admittance at pile head, and the influence of viscosity coefficient of soil on the real part of complex stiffness and admittance at pile head was greater, but the effect of viscosi- ty coefficient of soil on the image part of complex stiffness was relatively minor.

关 键 词：本构方程 黏弹性 竖直振动 FOURIER变换 复刚度 

分 类 号：TU573.12[建筑科学—建筑技术科学]