饱和地基上基础的摇摆振动特性研究
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摘要
半空间上地基与基础的相互作用问题不仅对于弹性动力学理论的发展有重要的学术价值,而且在地球物理学、地震工程及岩土力学等工程问题中均具有重要的现实意义,有着广泛的应用前景。
在前人工作的基础上,本文基于陈龙珠曾提出的一组饱和土弹性波动方程,用解析的方法较系统而深入地研究了饱和半空间地基与基础的摇摆振动问题。对于刚性圆板,作者首先采用Hankel变换对波动方程进行求解,得到了该控制方程在Hankel变换域内的通解,然后由混合边值条件建立了饱和地基上刚性基础摇摆振动的对偶积分方程,并将其化为第二类Fredholm积分方程,用数值方法计算了不同频率下基础的动力柔度系数,从而考察孔隙水的存在对基础摇摆振动特性的影响。
而对于饱和地基上弹性圆板和含刚核弹性圆板的振动,将对偶积分方程的右端项按混合边值条件做适当的修改,得到相应的Fredholm积分方程,通过数值算例分析了弹性板的柔度、或含刚核圆板刚域尺寸与弹性部分柔度的大小对动力响应的影响。
此外,作者考虑到地下水的存在,将地下水以下的部分视为饱和土,将地下水以上的部分视为弹性干土,按此模型研究了上覆单相弹性层的饱和地基上基础的摇摆振动问题,分析了弹性层的存在对基础振动的影响。
最后,本文还采用Laplace-Hankel联合变换技术初步分析了在一般摆矩作用下饱和地基上刚性圆板的摇摆振动问题,给出了摆矩、应力和位移的通解,并给出了特例情况下的数值解。
The study of dynamic interaction of foundations and grounds on half space is of great value to the development of the elastodynamics and is helpful on physical geography, seismography, and rock and soil mechanics, owning practical.This dissertation is based on the practical saturated governing equations of elastic waves in saturated soils established by Longzhu Chen,ect. On the basis of the existing work, the rocking vibrations of foundations resting on saturated grounds are studied analytically in details and systematically. For rigid footings, the governing equations are solved by Hankel transform and the general solutions in the Hankel transform field are formulated. Then, under the consideration of mixed boundary value condition, a pair of dual integral equations for the rocking vibrations of a disk on saturated grounds are obtained, which can be reduced to a Fredholm integral equation of the second kind and solved by numerical procedures. Consequently, the dynamic compliance coefficient is evaluated and numerical results are presented to portray the influence of poroelastic effects on the dynamic interaction problem.For the flexible circular plate or the one with a rigid core, through modifying the right term of the dual integral equations according to mixed boundary value condition, the corresponding dual integral equations are derived. The influence of the elasticity of the elastic plate, or the size of the core and the compliance of the elastic part of the elastic plate with core is analyzed by some numerical examples.Moreover, considering the existing of the ground water, the author treat the soil layer below the water lever as the saturated one and the soil layer above the water level as the single-phased elastic one. Using this model, the rocking vibrations of the rigid disk resting on the saturated ground with an elastic layer is studied and the effects of the elastic layer on the foundation's vibration are discussed.Finally, the rocking vibration of a rigid disk resting on the saturated grounds under the general moment for rocking is primary discussed by the
means of Laplace-Hankel transform. The general solutions of the moment, stress and displacement are given and the numerical solutions in special cases are also obtained.
在前人工作的基础上,本文基于陈龙珠曾提出的一组饱和土弹性波动方程,用解析的方法较系统而深入地研究了饱和半空间地基与基础的摇摆振动问题。对于刚性圆板,作者首先采用Hankel变换对波动方程进行求解,得到了该控制方程在Hankel变换域内的通解,然后由混合边值条件建立了饱和地基上刚性基础摇摆振动的对偶积分方程,并将其化为第二类Fredholm积分方程,用数值方法计算了不同频率下基础的动力柔度系数,从而考察孔隙水的存在对基础摇摆振动特性的影响。
而对于饱和地基上弹性圆板和含刚核弹性圆板的振动,将对偶积分方程的右端项按混合边值条件做适当的修改,得到相应的Fredholm积分方程,通过数值算例分析了弹性板的柔度、或含刚核圆板刚域尺寸与弹性部分柔度的大小对动力响应的影响。
此外,作者考虑到地下水的存在,将地下水以下的部分视为饱和土,将地下水以上的部分视为弹性干土,按此模型研究了上覆单相弹性层的饱和地基上基础的摇摆振动问题,分析了弹性层的存在对基础振动的影响。
最后,本文还采用Laplace-Hankel联合变换技术初步分析了在一般摆矩作用下饱和地基上刚性圆板的摇摆振动问题,给出了摆矩、应力和位移的通解,并给出了特例情况下的数值解。
The study of dynamic interaction of foundations and grounds on half space is of great value to the development of the elastodynamics and is helpful on physical geography, seismography, and rock and soil mechanics, owning practical.This dissertation is based on the practical saturated governing equations of elastic waves in saturated soils established by Longzhu Chen,ect. On the basis of the existing work, the rocking vibrations of foundations resting on saturated grounds are studied analytically in details and systematically. For rigid footings, the governing equations are solved by Hankel transform and the general solutions in the Hankel transform field are formulated. Then, under the consideration of mixed boundary value condition, a pair of dual integral equations for the rocking vibrations of a disk on saturated grounds are obtained, which can be reduced to a Fredholm integral equation of the second kind and solved by numerical procedures. Consequently, the dynamic compliance coefficient is evaluated and numerical results are presented to portray the influence of poroelastic effects on the dynamic interaction problem.For the flexible circular plate or the one with a rigid core, through modifying the right term of the dual integral equations according to mixed boundary value condition, the corresponding dual integral equations are derived. The influence of the elasticity of the elastic plate, or the size of the core and the compliance of the elastic part of the elastic plate with core is analyzed by some numerical examples.Moreover, considering the existing of the ground water, the author treat the soil layer below the water lever as the saturated one and the soil layer above the water level as the single-phased elastic one. Using this model, the rocking vibrations of the rigid disk resting on the saturated ground with an elastic layer is studied and the effects of the elastic layer on the foundation's vibration are discussed.Finally, the rocking vibration of a rigid disk resting on the saturated grounds under the general moment for rocking is primary discussed by the
means of Laplace-Hankel transform. The general solutions of the moment, stress and displacement are given and the numerical solutions in special cases are also obtained.
引文
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