Winkler弹性地基板梁的自由振动分析

中短型轨道板的几何构型介于梁、板之间,属于宽梁结构。从Mindlin板理论出发,退化得到适用于宽梁的Mindlin板梁控制方程;引入Winkler地基刚度系数,推导得到位移和转角的模态函数表达式。考虑两端简支的边界条件,得到弹性地基板梁的自由振动特征方程。通过无量纲数值算例求解出弹性地基板梁的自振频率,并与Timoshenko梁理论和Mindlin板理论进行对比。研究高跨比、泊松比和弹性地基刚度等参数对结构自振特性的影响,总结出弹性地基板梁方程的特点及适用范围,即宽度效应显著且泊松比较大的宽梁结构。     

地震作用对轻轨铁路车桥系统耦合振动的影响

本文分析地震作用对考虑土-结构相互作用的轻轨铁路车桥系统耦合振动的影响。文中建立了车桥系统考虑土-结构相互作用的三维空间模型，推导了考虑地震作用车桥系统的耦合振动方程，并编制了相应的计算程序。以时速100km的列车通过天津轻轨的一座四跨预应力混凝土连续刚构桥为例，对受天津波和El Centro波地震作用的车桥系统的耦合振动响应进行了仿真分析。结果表明：地震作用下车桥系统的耦合振动响应近似为桥梁地震响应与车桥系统耦合振动响应之和；地震作用对车桥系统横桥向耦合振动响应的影响最大，对竖向耦合振动响应的影响较小，而对顺桥向耦合振动响应的影响甚微；且不同地震波激励的影响程度有所不同。由此得出结论，地震作用与车桥系统的耦合振动存在很大程度的耦合，因此，在对高架桥梁上的轻轨铁路进行车桥耦合振动分析时必须考虑地震作用的影响，以保证列车运行的安全性和稳定性。     

结构-地基耦合振动下地震反应谱特性

随着结构震害统计资料的不断增加,许多结构在地震作用下的宏观破坏现象用现有的反应谱理论不能获得合理的解释。在地震中,结构-地基耦合振动十分明显。就此问题出发,利用集总参数法建立了结构-地基耦合振动模型,分析推导了该模型下的地震反应谱公式。通过实例计算得出了耦合体系在不同频率地震波作用下的反应谱曲线,得出了一些有意义的结论。研究结果表明,对于具有浅埋刚性基础的结构体系在考虑耦合后的地震响应值与现有反应谱理论计算值有明显差异,地震作用在较大结构周期跨度上得到折减,同时,耦合体系对特定频率的地震波有吸收作用,现有反应谱理论没有体现这一点有利作用。     

贮仓—地基相互作用系统的振动试验研究

通过贮仓－地基相互作用系统的振动试验，研究了贮仓的动力反应特点，研究表明，地基的特性对贮仓的振动有着明显的影响，因此在研究贮仓的动力反应时，应该考虑贮仓与地基的相互作用。     

机器基础动力相互作用的研究

本文分别对单台、双台、联合基础与地基土相互作用体系在扰力作用下的振动特性进行了研究。在计算中考虑了外围土体的影响。通过算例,得到了单台、双台、联合基础的一些振动规律。     

相邻结构-地基-土相互作用的分支模态实用研究

本文在提出模态综合二步分析法研究相邻结构－地基－土相互作用的基础上,采用振动特性和实际结构相同的模拟结构,求得上,下部之间的耦合项,将耪合项和地震动一起组成修正地震动,以此作为刚性基础的结构抗震的分析的地震输入,本文为利用专业程序进行相邻结构－地基－土相互作用抗震分析提供了新的途径。     

用动力测量值确定基础—地基系统的频变参数

提出了基础－地基系统具有频变参数的质－弹－阻模型，在这个模型中，系统的刚度Ｋ＝Ｋ０－Ｋ１ω＾２和阻尼系数Ｃ＝Ｃ０＋Ｃ１ω随系统振动频率而变化。文章以竖向振动为例，给出了用稳态激振下的动力反应测量值确定系统参数Ｋ０，Ｋ１，Ｃ０，Ｃ１的方法；讨论了基础频变刚度系统与附加质量系统的等效范围和差别。     

端承桩在层状地基波动与辐射阻尼影响下的横向地震反应分析

通过对层状地层中端承桩的分析,建立了合理的几何,数学及力学模型。考虑层状地基ＳＨ与ＳＶ波波动及非线性辐射阻尼影响,应用Ｄｉｒａｃ广义函数及Ｗｉｎｋｌｅｒ地基理论计入各种动力,抗力,地震力及内力等,建立地基波动方程,桩振动方程,地基与桩耦合振动方程。给出了柯西型函数的自由振动解。利用非经典理论正交条件和卷积定理给出了强迫振动地震反应解析解,算例结果充分表明了动力特性及振动规律非常正确,充分体现了本文     

双向水平—扭转耦合振动基底隔震系统参数的反应控制确定

本文讨论利用设计反应谱确定双向水平－扭转耦合振动基础底隔震系统的参数，即水平ｘ，ｙ两个方向和扭转方向的刚度ｋｘ，ｋｙ，ｋｏ与阻尼常数ｃｘ，ｃｙ，ｃｏ，使基础在ｘ向特定地面运动作用下产生的双向水平和扭转绝对加速度反庆分别满足预先限定的数值。为此，文中提出了一个确定限定速度反应的双向水平－扭转耦合振动基础底隔震系统参数的迭代修正方法。计算表明，只要参数的迭代初值选择适当，迭代过程可以将参数确定到任意的     

动力基础系统非线性力学模型

采用定参理想集总参数计算体系，以动力基础非线性动力学模型和非线性广义刚度函数的概念为基础，将动力基础模型从竖向非线性振动推广至水平非线性振动、扭转非线性振动以及水平-回转二自由度耦合非线性振动和竖向-水平-回转三自由度非线性耦合振动，建立了动力基础非线性动力学模型的一般表达式，为动力基础非线性设计提供了理论。     

Energy-based dynamic parameter identification for Pasternak foundation model

Parameter identification of Pasternak foundation models(PFM) is never satisfactory, which discourages the application and popularization of PFM. In the present study, an energy-based model to predict the dynamic foundation coefficients was proposed using the vibration kinetic energy and potential energy of a Pasternak foundation-rigid plate system. On the basis of the Pasternak foundation, the relationship among the natural frequency, dynamic foundation coefficients, rigid plate configuration, and vibrating soil equivalent mass per unit area was considered. To obtain the natural frequencies of the Pasternak foundation-rigid plate system, dynamic tests were performed. Using two or more dynamic test results of various rigid plates on a foundation, a set of equations of dynamic foundation coefficients was set up to directly identify the foundation coefficients and equivalent mass per unit area of vibrating soil. The feasibility of the proposed method was verified by comparing it with the outdoor and indoor test results and finite element analysis results. When the proposed method is used to obtain the dynamic parameters, PFM can be generalized and applied more widely in engineering practice.     

Winkler model for dynamic response of composite caisson–piles foundations: Seismic response

A simplified method with a dynamic Winkler model to study the seismic response of composite caisson–piles foundations (CCPF¹) is developed. Firstly, with the dynamic Winkler model, the kinematic response of the CCPF subjected to vertically propagating seismic S-wave is analyzed by coupling the responses of caisson part and pile part. Secondly, a simplified model for the foundation–structure system is created with the structure simplified as a lumped mass connected to the foundation with an elastic column, and through the Fast Fourier Transformation (FFT) this model is enabled to solve transient seismic problems. Thirdly, the proposed method for the seismic response of CCPF-structure systems is verified by comparison against 3D dynamic finite element simulation, in which the Domain Reduction Method (DRM²) is utilized. Lastly, the mechanism and significance of adding piles in improving the earthquake resistance of the foundation and structure is analyzed through an example with different soil conditions. Discovered in this study is that adding piles under the caisson is an efficient way to increase seismic resistant capability of the soil–foundation–structure system, and the main mechanism of that is the elimination of the pseudo-resonance.     

Real-time dynamic hybrid testing for soil–structure interaction analysis

Simulating dynamic soil–structure interaction (SSI) problems is a challenge when using a shaking table because of the semi-infinity of soil foundations. This paper develops real-time dynamic hybrid testing (RTDHT) for SSI problems in order to consider the radiation damping effect of the semi-infinite soil foundation using a shaking table. Based on the substructure concept, the superstructure is physically tested and the semi-infinite foundation is numerically simulated. Thus, the response of the entire system considering the dynamic SSI is obtained by coupling the numerical calculation of the soil and the physical test of the superstructure. A two-story shear frame on a rigid foundation was first tested to verify the developed RTDHT system, in which the top story was modeled as the physical substructure and the bottom story was the numerical substructure. The RTDHT for a two-story structure mounted on soil foundation was then carried out on a shaking table while the foundation was numerically simulated using a lumped parameter model. The dynamic responses, including acceleration and shear force, were obtained under soft and hard soil conditions. The results show that the soil–structure interaction should be reasonably taken into account in the shaking table testing for structures.     

Real-time dynamic hybrid testing for soil–structure interaction analysis

Simulating dynamic soil–structure interaction (SSI) problems is a challenge when using a shaking table because of the semi-infinity of soil foundations. This paper develops real-time dynamic hybrid testing (RTDHT) for SSI problems in order to consider the radiation damping effect of the semi-infinite soil foundation using a shaking table. Based on the substructure concept, the superstructure is physically tested and the semi-infinite foundation is numerically simulated. Thus, the response of the entire system considering the dynamic SSI is obtained by coupling the numerical calculation of the soil and the physical test of the superstructure. A two-story shear frame on a rigid foundation was first tested to verify the developed RTDHT system, in which the top story was modeled as the physical substructure and the bottom story was the numerical substructure. The RTDHT for a two-story structure mounted on soil foundation was then carried out on a shaking table while the foundation was numerically simulated using a lumped parameter model. The dynamic responses, including acceleration and shear force, were obtained under soft and hard soil conditions. The results show that the soil–structure interaction should be reasonably taken into account in the shaking table testing for structures.     

Discrete modelling of vertical track–soil coupling for vehicle–track dynamics

This paper presents a coupled lumped mass model (CLM model) for the vertical dynamic coupling of railway track through the soil. The well-known Winkler model and its extensions are analysed and fitted on the result obtained numerically with a finite–infinite element model in order to validate the approach in a preliminary step. A mass–spring–damper system with frequency independent parameters is then proposed for the interaction between the foundations, representing the contact area of the track with the soil. The frequency range of track–soil coupling is typically under 100 Hz. Analytical expressions are derived for calibrating the system model with homogeneous and layered half-spaces. Numerical examples are derived, with emphasis on soil stiffness and layering. The dynamic analysis of a track on various foundation models is compared with a complete track–soil model, showing that the proposed CLM model captures the dynamic interaction of the track with the soil and is reliable to predict the vertical track deflection and the reaction forces acting on the soil surface.     

基于Comsol的饱和多孔介质动力方程的数值模拟及应用

两相饱和多孔介质的动力响应问题在地震工程领域具有重要的研究意义,由于涉及到固相和液相的动力耦合,使得该问题的求解尤为复杂。本文利用Comsol在求解多场耦合问题上的优点,针对Biot饱和多孔介质u-U耦合形式下的波动方程特征,经过一系列微分算子运算和矩阵变换得到导数形式下的波动方程,基于Comsol Multiphysics提供的广义偏微分方程模式对变形后的波动方程进行求解,并把改进后的无限元边界应用到无限域动力问题的模拟中。通过与饱和多孔介质动力响应的解析解进行对比,验证模型求解技术的可行性和正确性,并在此基础上讨论饱和土地基中空沟隔振效果与饱和土体参数孔隙率、泊松比的关系。通过研究分析,可以为饱和土地基中空沟隔振设计提供一些有价值的参考。     

Discrete modelling of vertical track–soil coupling for vehicle–track dynamics

This paper presents a coupled lumped mass model (CLM model) for the vertical dynamic coupling of railway track through the soil. The well-known Winkler model and its extensions are analysed and fitted on the result obtained numerically with a finite–infinite element model in order to validate the approach in a preliminary step. A mass–spring–damper system with frequency independent parameters is then proposed for the interaction between the foundations, representing the contact area of the track with the soil. The frequency range of track–soil coupling is typically under 100 Hz. Analytical expressions are derived for calibrating the system model with homogeneous and layered half-spaces. Numerical examples are derived, with emphasis on soil stiffness and layering. The dynamic analysis of a track on various foundation models is compared with a complete track–soil model, showing that the proposed CLM model captures the dynamic interaction of the track with the soil and is reliable to predict the vertical track deflection and the reaction forces acting on the soil surface.     

Response of circular flexible foundations subjected to horizontal and rocking motions

A methodology using modal analysis is developed to evaluate dynamic vertical displacements of a circular flexible foundation resting on soil media subjected to horizontal and rocking motions. The influence of the soil reaction forces on the foundation is considered by introducing modal impedance functions, which can be determined by an efficient procedure with ring elements. The displacements of the foundation can then be easily solved by modal superposition. Parametric studies for modal responses of the flexible foundation indicate that the coupled response of the foundation is significantly influenced by relative stiffness among the foundation and the soil medium, vibration frequency range, foundation mass, and boundary contact conditions. The welded boundary condition should be considered to predict the coupling response while the relaxed boundary condition may be used to predict approximately the vertical displacements. As a foundation with a relative stiffness ratio more than three, it is found that the foundation can be considered as rigid to calculate coupling displacements. For a slightly flexible foundation, considerations of three modes are sufficient enough to obtain accurate foundation responses. Moreover, at low frequencies, the coupling effect due to higher mode can be neglected.     

结构-地基体系水平与扭转位移耦合效应研究

采用动力理论对地基-结构非线性相互作用体系的振动方程进行了定性分析.基于多线性随动强化模型,采用非线性有限元法求解了基础和地基土之间的水平刚度与摇摆刚度,建立了结构-地基非线性相互作用体系的力学模型.利用拉格朗日能量法推导了结构水平位移和扭转相耦合的振动方程.采用多尺度法研究了结构-地基相互作用体系的主共振.通过分析不...     

Dynamic behaviour of turbine-generator-foundation systems

In this paper a comprehensive investigation on the dynamic characteristics of turbine–generator–foundation systems is performed. All the major components of the system, including turbine–generator casing, shaft, rotors, journal bearings, deck, piers, foundation mat, piles, and soil medium, have been included. Full interaction between the turbine–generator set, the foundation superstructure, and the soil medium, is considered. A hybrid method is used to establish the mathematical model for the turbine–generator-foundation system. The analysis is conducted in the frequency domain through complex frequency response analysis. The response in the time domain is obtained by Fourier transform. The seismic excitation is represented as the control motion on the ground surface, which is generated as an artificial earthquake. A 300 MW turbine-generator-foundation system is analysed under excitations from rotor unbalances and earthquakes. The influence of turbine-generator casing and soil anisotropy on the response of the system is explored. It is found that the presence of casing and soil anisotropy strongly influences the displacements and internal forces of the system under rotor unbalance excitation. Under seismic excitation, however, although the presence of casing and soil anisotropy does affect the displacements of the system, their effect on the internal forces of the system is minimal.