含液饱和多孔波阻板的地基振动控制研究

基于含液饱和多孔介质中的流-固耦合作用,提出了以含液饱和多孔材料作为隔振屏障的一类新型的地基振动控制体系。考虑在弹性地基内部设置饱和多孔波阻板,基于线弹性理论和Biot多孔介质模型,采用Fourier级数展开的方法,分别建立了地基表面和内部受到条形简谐荷载作用下地基动力响应的计算列式。通过数值算例,与传统的单相固体波阻板的隔振效果进行了比较,并且分析了多孔材料波阻板中固相材料性质、孔隙率、孔隙流体性质等物理力学参数对地基隔振性能的影响规律。结果表明,相对于单相固体波阻板隔振体系,基于含液饱和多孔波阻板的地基隔振体系更加具有优越性,并且更具有可设计性。     

集中载荷作用下饱和多孔Timoshenko简支梁的动力响应

基于饱和多孔弹性Timoshenko梁的动力数学模型,研究了梁中点承受突加载荷作用两端可渗透饱和多孔弹性Timoshenko简支梁的动力响应,得到了问题的解析解,给出了梁中点无量纲挠度、固相骨架弯矩和孔隙流体压力等效力偶等随无量纲时间的响应。考察了剪切和横截面转动惯性效应等对动力响应的影响,比较了饱和多孔Timoshenko、Shear、Rayleigh和Euler-Bernoulli梁的动力响应,结果表明:剪切效应使饱和多孔Timoshenko梁动力响应的幅值和周期增大,而横截面转动惯性仅增加梁动力响应的周期;固相骨架与孔隙流体的相互作用具有粘性效应,随着相互作用系数的增加,饱和多孔梁挠度和弯矩幅值减小,流体压力等效力偶幅值增大,且振幅衰减加快。同时,随着长细比的增加,饱和多孔Timoshenko梁的挠度幅值和周期逐渐减小,并最终趋于饱和多孔Euler-Bernoulli梁的挠度幅值和周期。     

环形含液容器动力分析

环形含液容器在以华龙一号、AP1000和CAP1400为代表的第三代核电站中得到普遍应用,其本身的动力特性与动力反应是有待解决的重要安全问题。该文以环形含液系统动力学方程的建立和求解为主要研究目的,基于势流体理论和第二类边界条件的Bessel函数展开,推导环形容器液体小幅振动的振动频率和动液压力响应的理论解。通过极限分析、与试验结果以及与有限元方法对比,验证理论公式的正确性。对环形水箱动力反应问题开展计算,初步分析了环形水箱内外环动水压力反应规律和特点,并与同几何尺寸的圆柱形水箱对比,分析其振动频率与动液压力响应规律的异同。结果表明:由于环形水箱与圆柱形水箱液体振动频率的差异,两者动水压力反应在可引发其中某一模型液体共振的荷载作用下将出现较大差异。该文研究可为环形含液容器的工程应用提供理论支持。     

含液饱和多孔弹性梁随机振动

据不可压多孔弹性介质理论及随机振动理论,建立孔隙流体沿轴向扩散情形下含液饱和多孔弹性梁在集中荷载作用下横向弯曲随机振动方程。分析梁位移响应及截面固相弯矩响应,获得输入集中荷载为平稳随机过程时简支梁位移、弯矩响应的功率谱密度函数及方差等数字特征。作为数值算例,考虑理想白噪声平稳随机集中荷载作用下的简支饱和多孔梁,分析其位移响应及界面固相弯矩功率谱密度函数,讨论流-固耦合项对梁位移及弯矩的减振效果。结果表明,通过控制孔隙中流体的渗透系数可达到控制梁的随机振动目的。     

基于非局部Biot理论的循环荷载下饱和土地基动力特性研究

为探究循环动荷载下,孔隙尺寸对饱和土地基动力特性的影响,利用虚位移原理及Newmark积分法对非局部Biot模型进行了空间及时间离散,并采用有限单元法编制了循环荷载下饱和土地基动力响应的计算程序。将该程序计算得到的饱和土一维固结结果和二维单相弹性地基的动力响应结果与已有文献对比,验证了该程序的正确性。研究了循环荷载下孔隙尺寸效应对一维饱和地基,二维饱和地基及饱和路基动力特性的影响。结果表明：荷载频率较高时,随着非局部参数的增加,饱和土地基的动力响应明显滞后,孔隙尺寸效应对饱和土地基动力响应的影响明显,即荷载频率较高时,孔隙尺寸效应不可忽略。     

移动荷载下有限深度Winkler地基上梁的动力响应研究EI北大核心CSCD

基于考虑有限深度土体运动的Winkler地基梁理论,建立移动荷载作用下弹性地基上有限长梁的横向运动方程。利用模态叠加法求得移动荷载作用下有限长梁动力响应的解析解,进而以移动荷载离开时梁的响应为初值,采用分离变量法求得有限长梁自由振动的一阶近似解;通过数值计算和参数分析,揭示了移动荷载作用下有限深度Winkler地基上简支边界梁的动力学特性,分析地基深度、地基黏滞阻尼系数和荷载移动速度等对有限长梁受迫振动阶段和自由振动阶段动力响应的影响,全面揭示有限深度土体运动对临界速度的作用效应。结果表明:地基深度显著降低了临界速度,且弹性地基黏滞阻尼明显延长了自由振动衰减时间;荷载移动速度加剧了有限深度弹性地基与其支承梁的相互作用效应,系统振动的幅值和响应周期均发生显著变化。     

饱和土中球形空腔稳态振动及其在基桩中的应用

利用Ｂｉｏｔ饱和土波动理论求解了饱和土中球形空腔内部受周期性动荷载作用下的动力响应，并分析了球形空腔表面排水条件和振动频率对位移和孔隙水压力的影响。利用上述结果分析了桩在稳态振动下桩端的刚度和阻尼。     

埋置移动荷载作用下饱和成层地基-梁耦合系统动力响应分析

针对地铁列车运行中引起的地表振动问题,研究了埋置移动荷载作用下饱和成层地基-梁耦合系统的动力响应。将地基土体采用Biot饱和多孔介质理论来模拟,将地下轨道结构简化为埋置无限长Euler-Bernoulli梁,埋置移动荷载作用在梁上。并采用传递透射矩阵法(TRM法)考虑地基的成层性。利用Fourier变换及逆变换,结合梁与土体间的力与位移连续条件,得到了地基在时间空间域内的动力响应解答。当饱和成层地基退化为均质黏弹性地基时,所得解与已有解能很好地吻合。最后,通过数值算例分析了梁的刚度﹑埋置深度及荷载移动速度、频率等因素对地表振动的影响。     

饱和黏弹性土中圆柱形隧洞的振动特性

基于流体不可压缩饱和多孔介质理论,将衬砌视为具有分数导数本构关系的多孔黏弹性体,在频率域内研究了在内水压力作用下饱和黏弹性土和衬砌系统的振动特性。通过引入与孔隙流体体积分数有关的应力系数,合理地确定了隧洞边界衬砌和孔隙水共同承担的内水压力值。利用衬砌内边界上的边界条件以及衬砌和土体界面处应力和位移的连续性条件,给出了隧洞边界部分透水条件下饱和黏弹性土和分数导数型黏弹性衬砌系统简谐耦合振动时系统动力响应的解析解。结果表明:饱和黏弹土和衬砌结构的动力响应与衬砌材料的黏性有关;应力系数合理地确定了衬砌和孔隙水共同承担的内水压力值。     

基于动力非线性有限元法的索-梁相关振动研究

根据考虑结构几何非线性的有限元动力时程积分算法,开发了有限元程序SD_FEM。使用该程序建立了精细的索-梁组合结构有限元模型,计算了结构的自振特性与结构在外部动力荷载作用下的振动响应。分别讨论了当整体结构自振频率与拉索局部自振频率有1:1、2:1和不成倍数关系时,索-梁相关振动导致拉索振动的状况。分析了数值计算结果,总结了索-梁相关振动的本质规律。     

饱和两相介质近场波动问题的一种时域全显式数值计算方法

基于 u -p形式的饱和两相介质弹性波动方程,开展了饱和两相介质近场波动问题时域显式数值计算方法的研究。通过对波动方程中的质量矩阵和孔隙流体压缩矩阵进行对角化处理,消除了方程中的动力耦联,实现了波动方程的解耦。分别应用中心差分法和Newmark常平均加速度法求解固相位移和速度,基于向后差分法求解孔隙流体压力,推导得到了饱和两相介质动力响应的时域显式逐步积分的计算列式,建立了饱和两相介质近场波动问题的一种新的时域全显式数值计算方法。进行了该文方法中矩阵对角化合理性的验证。将该方法的数值解与相应的解析解进行对比,二者符合良好,验证了该方法的正确性。将该文建立的时域数值计算方法与透射人工边界方法相结合,应用于饱和两相介质的近场波动问题,进行了饱和土场地地震响应的计算研究,计算结果符合弹性波动理论的基本规律,表明该方法对于饱和两相介质近场波动问题时域计算求解的适用性。基于该方法中时域递推计算格式的传递矩阵,进行了该方法稳定性特性的研究。该文建立的数值计算方法具有时域全显式算法的基本特征。方法中对动力响应的全部分量均采用递推和迭代的模式进行求解,避免了求解耦联的动力方程组。该方法具有较高的计算效率,是进行饱和两相介质近场波动问题时域计算求解的一种有效的算法。     

Energy focusing and the shapes of wave fronts in anisotropic fluid-saturated porous media

Summary The purpose of this paper is to investigate the energy focusing pattern evolution in the parameter space while the wave fronts propagate in the anisotropic fluid-saturated porous media. Firstly, the bifurcation conditions for a general anisotropic fluid-saturated porous material are deduced. Then, by choosing the material parameters as control variables, the influence of the anisotropy of the solid skeleton and pore fluid parameters on the development characteristics of energy focusing patterns is discussed, and the three-dimensional configurations for the focusing structures are explored. The results indicate that the energy focusing also exists on the wave fronts of the slow waves, which is a particular propagation characteristic for the slow waves in anisotropic fluid-saturated porous media. The distinct trends for the slow wave energy focusing are revealed. This has significant meaning in further understanding the roles of the fluid phase in the dynamic response of the fluid-saturated porous media.     

Hygrothermomechanical evaluation of porous media under finite deformation. Part I - finite element formulations

The coupled thermomechanical responses of fluid-saturated porous continua subjected to finite deformation are investigated. Field equations governing the transient response of the media are derived from a continuum thermodynamics mixture theory based on mass balance, momentum balance and energy balance laws as well as the Clausius-Duhem inequality. Finite element procedures for the two-dimensional response, employing updated Lagrangian formulations for the solid skeleton deformation and the weak formulations for fluid and thermal transport equations, are implemented in a fully implicit form. Temperature-dependent mechanical properties for the non-linear solid matrix, characterized by Perzyna's viscoplastic model, are assumed. An iterative scheme based on the full Newton-Raphson method is presented for simultaneously solving the coupled non-linear equations.     

Transient dynamic analysis of a fluid-saturated porous gradient elastic column

The dynamic response of a fluid-saturated porous gradient elastic column to a transient disturbance is determined analytically and numerically. The basic dynamic theory of a fluid-saturated poroelastic medium due to Biot is modified by replacing the classical linear elastic model of the solid skeleton by the simple gradient elastic model of Mindlin with just one elastic constant (internal length scale) in addition to the classical ones. Thus, the new theory, which is presently restricted to the one-dimensional case, can take into account the microstructural effects of the solid skeleton. After the establishment of appropriate boundary and initial conditions, the one-dimensional dynamic column problem is solved analytically with the aid of the Laplace transform with respect to time. The time domain response is finally obtained by a numerical inversion of the transformed solution. The effect of the solid microstructure on the response is assessed and discussed.     

Continuum effective-stress approach for high-rate plastic deformation of fluid-saturated geomaterials with application to shaped-charge jet penetration

A practical engineering approach for modeling the constitutive response of fluid-saturated porous geomaterials is developed and applied to shaped-charge jet penetration in wellbore completion. An analytical model of a saturated thick spherical shell provides valuable insight into the qualitative character of the elastic–plastic response with an evolving pore fluid pressure. However, intrinsic limitations of such a simplistic theory are discussed to motivate the more realistic semi-empirical model used in this work. The constitutive model is implemented into a material point method code that can accommodate extremely large deformations. Consistent with experimental observations, the simulations of wellbore perforation exhibit appropriate dependencies of depth of penetration on pore pressure and confining stress.     

Finite element modelling of saturated porous media at finite strains under dynamic conditions with compressible constituents

Two finite element formulations are proposed to analyse the dynamic conditions of saturated porous media at large strains with compressible solid and fluid constituents. Unlike similar works published in the literature, the proposed formulations are based on a recently proposed hyperelastic framework in which the compressibility of the solid and fluid constituents is fully taken into account when geometrical non‐linear effects are relevant on both micro‐ and macroscales. The first formulation leads to a three‐field finite element method (FEM), which is suitable for analysing high‐frequency dynamic problems, whereas the second is a simplification of the first, leading to a two‐field FEM, in which some inertial effects of the pore fluid are disregarded, hence the second formulation is suitable for studying low‐frequency problems. A fully Lagrangian approach is considered, hence all terms are expressed with reference to the material setting; the balance equations for the pore fluid are also expressed in terms of the chemical potential and the mass flux of the pore fluid in order to take the compressibility of the fluid into account. To improve the numerical response in the case of wave propagation, a discontinuous Galerkin FEM in the time domain is applied to the three‐field formulation. The results are compared with analytical and semi‐analytical solutions, highlighting the different effects of the discontinuous Galerkin method on the longitudinal waves of the first and second kind. Copyright © 2010 John Wiley & Sons, Ltd.     

A phase field model for the freezing saturated porous medium

In terms of the mixture theory and phase field theory, a phase field model is developed for the saturated porous medium undergoing phase transition. In the proposed model, it is postulated that during the phase transition of the porous medium, both the solid skeleton and pore fluid will undergo phase transition. The phase states of the solid skeleton and pore fluid are characterized by respective order parameters. To simplify the proposed phase field model, the temperatures and order parameters of the solid skeleton and pore fluid are assumed to be equal. The balance laws of the porous medium are given by the conventional mixture theory. The order parameter and the porosity of the porous medium are considered as internal variables and their evolution equations are determined by the entropy inequality of the porous medium. The constitutive representations for the stresses, entropies, heat fluxes, drag force and the evolution equations for the order parameter and porosity are derived by exploitation of the entropy inequality. To illustrate the proposed model, a concrete phase field model for the freezing porous medium is established in the paper. In the model, the memory effect associated with phase transition of the porous medium is taken into account by assuming Stieltjes integral for the strain energy of the porous medium. The constitutive representations for the above variables are then derived according to the proposed free energy expression for the porous medium. Finally, the boundary condition associated with the proposed model and the determination of some parameters involved in our model are discussed in the paper briefly.     

Thermodynamics of fluid-saturated porous media with a phase change

Summary In the present paper some aspects of the thermodynamics of a fluid-saturated porous solid, taking into account the phase change of liquid into gas, are discussed. Based on the principles of the thermodynamics of irreversible processes, restrictions for the constitutive equations of the constituents are developed, in particular for the phase transition. The porous body is assumed to be incompressible and elastically deformed, and the pore space is filled with an immiscible liquid-gas mixture (moisture). The theory presented here provides some background that can be found suitable, e.g., for drying aspects.Dedicated to Professor Franz Kollmann on the occasion of his 60th birthday     

悬臂梁-流体-悬臂梁耦联系统的湿模态相互作用

应用流体的势流理论及悬臂梁振动方程，本文分析了悬臂梁-流体-悬臂梁耦联系统的自由振动问题。分析表明，悬臂梁除与流体发生相互作用外．两悬臂梁湿模态通过流体的耦合也发生相互作用．后者的作用使流固耦联系统的湿模态呈现新的振动特性．同一阶两个子结构(梁1，2)各自的干模态分别对应耦联系统同一阶的两个湿模态．一个以较低的湿频率出现，两梁呈反相位振型，另一个以较高的湿频率出现，两梁呈同相位振型。