粘性阻尼土中变截面桩的纵向振动特性与应用研究

考虑土体轴对称波动效应,对变截面桩在任意激振力作用下的纵向振动特性进行了研究。假定桩为竖直、弹性、变截面体,土为线性粘弹性体,其材料阻尼为粘性阻尼。利用拉普拉斯变换,将定解问题转化到拉普拉斯域内求解,通过引入势函数并结合阻抗函数的传递性,得到了拉普拉斯域内的桩顶阻抗函数解析解,进而可得到频域内的桩顶阻抗函数和速度导纳的解析解,利用卷积定理和傅里叶逆变换,求得了半正弦脉冲激振力作用下桩顶速度时域响应半解析解。基于所得解对桩的纵向振动特性进行了分析,重点讨论了桩身截面变化情况对速度导纳曲线和反射波曲线的影响,得到了许多重要结论。     

非饱和土中弹性支承桩的扭转振动响应分析

基于已建立的非饱和土中的波动方程,对均质非饱和滞回阻尼土层中的弹性支承桩扭转振动特性进行了分析.首先利用拉普拉斯变换,在拉氏交换域中求得了土体振动位移形式解,依据桩土接触面处的衔接条件将该解耦合进桩身动力平衡方程,求解桩的动力平衡方程,得到了桩顶速度导纳的频域响应解析解和半正弦脉冲激励作用下桩顶时域响应的半解析解,并分析了主要参数对振动特性的影响.结果表明,桩底支承刚度因子影响较大,土滞回材料阻尼有一定的影响,而土底支承剐度因子基本没有影响.     

变截面阻抗桩纵向振动问题积分变换解

利用拉普拉斯（Laplace)变换,将变截面阻抗桩振动的时域定解问题转换到频域的形式,求得了关于桩顶位移响应及速度响应的传递函数,然后利用求留数的方法求得了桩土系统的脉冲响应函数,利用脉冲响应函数求得了多种不同激振波形条件下（稳态正弦激励,瞬态半正弦激振及叠加有高频干扰波的瞬态半正弦激振等）的桩顶速度响应的表达式,并对桩土系统的频域特性作了深入的研究,得到了许多重要的结论。此外还将稳态正弦激振、态半正弦激振条件下的解与有关文献所采用分离变量法得到的解进行了对比,为两者的正确性提供了重要的证明。     

垂直受荷群桩在半空间饱和土中的稳态反应

研究了均质半空间饱和土中群桩在垂直稳态荷载作用下的动力反应问题。半空间饱和土采用Biot提出的三维波动原理。将桩看作是一维的弹性杆单元。利用圆形简谐载荷作用下的Biot固结方程的基本解和桩土之间的变形协调条件得到饱和土中群桩的第二类Fredholm积分方程,群桩的动力阻抗采用动力相互作用因子的方法。分析桩距等参数对群桩阻抗、轴力和孔压等的影响。本文的方法可以用于计算层状饱和土中群桩的动力反应问题。     

饱和土中端承桩纵向振动特性研究

基于饱和多孔介质理论研究了三维轴对称条件下端承桩在饱和土中的纵向耦合振动. 首先通 过引入势函数对Biot动力固结方程解耦，采用算子分解方法及分离变量法求得饱和土层振动 解，进而利用桩土完全耦合条件得到桩土系统定解. 然后对桩顶的频率和时域响应进行参数 研究，结果表明，桩的长径比和桩土模量比对桩顶动力响应有较大影响，而渗透力对其影响 较小. 最后将幅频及时域反射波理论拟合结果与桩基实测结果加以对比，结果表明理论曲线 与实测曲线规律一致.     

Wave propagation in a pre-strained compressible elastic sandwich plate

The extensional and flexural Lamb waves in a sandwich plate with finite initial strains made from compressible highly elastic materials is investigated. It is assumed that the initial strains are caused by the uniformly distributed normal compression forces acting on the face planes of the plate. The cases where the compression forces are “dead” (Case 1) and “follower” (Case 2) are considered. The investigations are carried out within the scope of the piecewise homogeneous body model with the use of the 3D linearized theory of elastic waves in initially stressed bodies. Numerical results for the dispersion of the extensional and flexural Lamb waves on the influence of the initial strains and on the influence of the character of the external compression forces are presented and discussed.     

Dynamic response of a pile embedded in elastic half space subjected to harmonic vertical loading

An analytical method is developed to investigate the dynamic response of a pile subjected to harmonic vertical loading.The pile is modeled as a one-dimensional(1D)elastic rod.The elastic soil is divided into a homogeneous half space underlying the base of pile and a series of infinitesimally thin layers along the vertical shaft of pile.The analytical solution for the soil-pile dynamic interaction problem is obtained by the method of Hankel transformation.The proposed solution is compared with the classical plane strain solution.Arithmetical examples are presented to demonstrate the sensitivity of the vertical impedance of the pile to relevant parameters.     

均质土中半埋入变截面桩的瞬态波动响应

基于回传射线矩阵法,求得单位脉冲作用下均质土中半埋入变截面桩的桩顶速度导纳,然后利用Fourier逆变换和卷积定理得到瞬态半正弦激振力作用下的桩顶时域速度响应。比较半埋入缩颈桩、半埋入扩颈桩与半埋入完整桩的速度导纳和反射波,分析缺陷类型和长度、缺陷埋深和程度对速度导纳和反射波的影响,并进行缩颈-扩颈桩与扩颈-缩颈桩的桩顶速度导纳和反射波曲线的对比。结果表明,桩侧介质变化对桩顶速度导纳和反射波的影响小于桩身缺陷。     

考虑桩土相互作用效应的桩顶纵向振动时域响应分析

在考虑桩土耦合作用以及土竖向波动效应条件下，对均质滞回材料阻尼土中弹性支承桩桩顶纵向振动时域响应进行了理论研究。首先建立了桩与滞回阻尼土在谐和振动情况下的定解问题，然后先对土层动力平衡方程进行求解并得到土体振动位移形式解，接着依据平衡条件将该形式解祸合进桩身动力平衡方程，并通过对桩动力平衡方程的求解，最终得到桩顶位移和速度频域响应解析解和半正弦脉冲激励作用下桩顶时域响应的半解析解。通过与其它相关理论解的对比验证了本文解的正确性和适用性，并基于所得解对桩顶时域响应特性进行了分析，最后将理论曲线与现场工程实测曲线进行了拟合对比，结果表明两者符合较好。     

Vibration and wave propagation analysis of twisted micro-beam using strain gradient theory

In this research, vibration and wave propagation analysis of a twisted microbeam on Pasternak foundation is investigated. The strain-displacement relations (kinematic equations) are calculated by the displacement fields of the twisted micro-beam. The strain gradient theory (SGT) is used to implement the size dependent effect at microscale. Finally, using an energy method and Hamilton’s principle, the governing equations of motion for the twisted micro-beam are derived. Natural frequencies and the wave propagation speed of the twisted micro-beam are calculated with an analytical method. Also, the natural frequency, the phase speed, the cut-off frequency, and the wave number of the twisted micro-beam are obtained by considering three material length scale parameters, the rate of twist angle, the thickness, the length of twisted micro-beam, and the elastic medium. The results of this work indicate that the phase speed in a twisted micro-beam increases with an increase in the rate of twist angle. Moreover, the wave number is inversely related with the thickness of micro-beam. Meanwhile, it is directly related to the wave propagation frequency. Increasing the rate of twist angle causes the increase in the natural frequency especially with higher thickness. The effect of the twist angle rate on the group velocity is observed at a lower wave propagation frequency.     

考虑土体三维波动效应时弹性支承桩的振动理论及其应用

从三维轴对称土体模型出发,同时考虑土体竖向和径向位移,对弹性支承桩在垂直谐和激振力作用下与土的耦合振动特性进行了分析。假定桩为竖直弹性等截面体,土为线性粘弹性体,其材料阻尼为滞回阻尼。首先通过引入势函数对土体位移进行分解,从而将土体动力平衡方程解耦,求解得到了土层的振动模态形式,然后利用桩土接触面上力平衡和位移连续条件来考虑桩土耦合作用,求解桩的动力平衡方程,得到了桩顶的频域响应解析解、复刚度和速度导纳,利用卷积定理和傅立叶逆变换,求得了半正弦脉冲激振力作用下桩顶速度时域响应半解析解。利用所得解对桩的振动特性进行了无量纲参数分析,得到了许多新的结论。     

标准线性固体土模型条件下桩的动力响应分析与应用

在桩侧土为标准线性固体模型条件下，建立了成层土中考虑桩端和桩侧土作用的有限长桩，桩顶受纵向激励情况下的定解问题，用拉氏变化(Laplace)求得桩顶阻抗函数和速度频率响应的函数，然后利用卷积定理和傅立叶(Fourier)逆交换求得任意激振力作用下桩顶速度响应的半解析解，并研究了模型中各个主要参数对桩顶响应及速度响应曲线的影响，并分析了缺陷桩和不同土参数对曲线的影响，得到了许多新的有意义的结论。     

横观各向同性层状场地中的单桩横向动力阻抗函数

本文采用横观各向同性层状弹性模型，模拟半空间上的层状场地，用阻尼器模拟透射边界代替半空间以吸收能量。利用薄层元素法和于结构法，并利用在这种边界下受水平简谐荷载作用下的格林函数，推导了这种场地中竖直单桩在水平—摇摆简谐荷载作用下的横向动力阻抗函数，并用实例计算了不同横观各向同性性质场地下的动力阻抗函数，并由此分析了场地的横观各向同性性质的强弱对单桩的横向动力阻抗函数所将产生的影响。计算表明：弱横观各向同性场地对阻抗函数的影响很小，以至可以忽略这种影响；而强横观各向同性场地对阻抗函数的影响较大，必须考虑其影响。另外，桩头约束的存在与否，对单桩的横向阻抗函数值也有较大的影响，桩头有约束的阻抗函数值要明显大于无约束的阻抗函数值。     

沉桩问题的光弹性模拟研究

实现了桩身直接贯入的沉桩光弹性模拟方法。应用这一方法研究了沉桩过程中桩周土体中的弹性应力场及其影响区域，指出Ｖｅｓｉｃ土体扩孔理论的适用范围     

广义Voigt土模型条件下桩的纵向振动响应与应用

研究了桩侧土广义Voigt模型条件下，任意层桩土系统的振动特性，并求得了桩顶在瞬态半正弦脉冲荷载作用下，桩顶的时域纵向响应的半解析解，同时结合基桩完整性检测的机械阻抗法和反射波法研究了各主要模型参数以及土层界面、桩身缺陷等对桩顶时、频响应曲线的影响，得到了许多结论。结果表明，得到的理论成果相比于已有理论更加完善并能更好地反映客观实际，将为基桩完整性定量化检测创造条件。     

广义Maxwell体土模型条件下粘弹性桩纵向振动的半解析解及应用

研究考虑桩身材料阻尼，桩侧土采用广义Maxwell模型条件下，均质土中不均匀桩(截面面积或材料性质在桩长方向上突变)的纵向振动特性，求得了瞬态半正弦脉冲荷栽作用下，桩顶频域响应的解析解及时域响应的半解析解，分析了桩身材料阻尼及土质变化对桩顶时域、频域响应曲线的影响，得到了有关新的结论。通过本文理论结果与实际工程桩的实测曲线的拟合对比，表明本文所得结果能更好地反映客观实际。     

Axisymmetrical analytical solution for vertical vibration of end-bearing pile in saturated viscoelastic soil layer

Based on elasticity and the theory of saturated porous media, and regarding the pile and the soil as a single phase elastic and a saturated viscoelastic media, respectively, the dynamical behavior of vertical vibration of an end-bearing pile in a saturated viscoelastic soil layer is investigated in the frequency domain using the Helmholtz decomposition and variable separation method. The axisymmetrical analytical solutions for vertical vibrations of the pile in a saturated viscoelastic soil layer are obtained, and the analytical expression of the dynamical complex stiffness of the pile top is presented. Responses of dynamic stiffness factor and equivalent damping of pile top with respect to the frequency are shown in figures using a numerical method. Effects of the saturated soil parameters, modulus ratio of the pile to soil, slenderness ratio of pile and pile＇s Poisson ratio, etc. on the stiffness factor and damping are examined. It is shown that, due to the effect of the transversal deformation of the pile and the radial force of the saturated viscoelastic soil acting on the pile, the dynamic stiffness factor and the damping derived from the axisymmetrical solution are greatly different from those derived from the classical Euler-Bernoulli rod model, especially at some specific excitation frequencies. Therefore, there are limitations on applicability of the Euler-Bernoulli rod model in analyzing verticai vibration of the pile. More accurate analysis should be based on a three-dimensional model.     

侧向点爆炸作用下地下拱结构的动力响应

首先,利用几何关系与介质中超压、位移衰减公式得出结构表面自由场荷载和位移的分布形式,并对衰减因数、爆距等参数进行讨论;其次,利用MSSI（modified soil-structure interaction）相互作用模型对拱的振动方程进行正交求解,得到任意角度荷载作用下的结构弹性动力响应解析解。基于动力响应解析解,得到了土体的声阻抗对结构位移、速度、加速度时程响应曲线的影响。研究结果表明:侧向爆炸荷载作用下,岩土介质声阻抗越大,埋设其中的地下结构的位移、速度和加速度变化越大。为此,建议地下防护结构应修建在声阻抗小的岩土介质中。     

On longitudinal impact III

Summary The graphodynamical method which was introduced and applied to elastic longitudinal impact in the first two articles of this series is here used to study the transmission of a rectangular compressive pulse along a system consisting of a bar which is joined by friction to a stiff anvil or to a co-axial elastic tube. Some of these cases will in the next article be used as models of pile driving. The influence of the frictional force, of the dimensions of the pulse (the dimensions and impact velocity of the hammer) and of the area and length of the tube on the sign and magnitude of the slide at a concentrated friction joint and on the associated energy loss is determined, and the results are illustrated by diagrams. The results of a few simple experiments agree reasonably well with the theory. The theory is extended to a model of a pile with constant friction per length unit, and it is found that a light hammer with great impact velocity gives better penetration than a heavy hammer with the same energy and thus smaller velocity.     

桩-土接触效应及对桥梁结构地震反应的影响

目前有关涉及桥梁桩基础地震反应的研究大多是基于桩与桩侧土体之间无相对滑动、位移保持协调的假定。本文针对地震作用下桥梁桩基础的接触面效应及其对结构地震反应的影响问题,以某桥梁工程为背景,通过在桩-土交界面处设置接触单元来模拟桩-土间的接触非线性,建立了土-桩-桥梁结构相互作用体系的三维分析模型。利用这一模型,分析了地震作用下桩-土交界面处的动力反应形态,探讨了桩-土间的接触非线性及其对桥梁结构地震反应的影响。初步分析结果表明：在强震作用下,桩-土间会产生较强的接触非线性,在本文模型中,这种非线性主要表现为桩-土交界面处的滑移;考虑桩-土间的接触面效应将使结构的位移反应结果较基于桩-土间位移协调的情形有所增大。