Transient analysis of three-dimensional dynamic interaction between multilayered soil and rigid foundation

The study of dynamic soil-structure interaction is significant to civil engineering applications, such as machine foundation vibration, traffic-induced vibration, and seismic dynamic response. The scaled boundary finite element method (SBFEM) is a semi-analytical algorithm, which is used to solve the dynamic response of a three-dimensional infinite soil. It can automatically satisfy the radiation boundary condition at infinity. Based on the dynamic stiffness matrix equation obtained by the modified SBFEM, a continued fraction algorithm is proposed to solve the dynamic stiffness matrix of layered soil in the frequency-domain. Then, the SBFEM was coupled with the finite element method (FEM) at the interface to solve the dynamic stiffness matrices of the rigid surface/buried foundation. Finally, the mixed-variable algorithm was used to solve the three-dimensional transient dynamic response of the foundation in the time domain. Numerical examples were performed to verify the accuracy of the proposed algorithm in solving the dynamic stiffness matrix of the infinite domain in the frequency domain and the dynamic transient displacement response of the foundation in the time domain. Compared with the previous numerical integration technique, the dynamic stiffness matrix in the frequency domain calculated by using the proposed algorithm has higher accuracy and higher efficiency.     

任意层地基中粘弹性楔形桩纵向振动响应研究

考虑楔形桩的横向惯性效应,研究了任意层地基中粘弹性楔形桩的纵向振动问题。首先,根据楔形桩的变截面特性并考虑桩侧土的成层性,将桩土系统沿纵向划分为有限个单元。然后,采用平面应变模型模拟桩侧土,采用Rayleigh-Love杆模拟楔形桩,运用Laplace变换技术和阻抗函数传递方法,求解得到了任意层地基中桩顶速度频域响应的解析解及桩顶速度时域响应的半解析解。最后,采用参数分析方法,对楔形桩单元划分精度进行了讨论,并讨论了楔形桩设计参数及材料参数和桩侧土成层性对楔形桩纵向振动响应的影响。     

桥梁抖振时域和频域分析的一致性研究

为考查时域分析方法用于桥梁抖振分析的可行性和可靠性,基于相同的分析参数,分别采用时域和频域分析方法对一斜拉桥的抖振响应进行分析,并从结构振动型态、抖振响应均方根及抖振响应功率谱密度函数三个方面对时域和频域分析结果的一致性进行了较详细的比较。时域抖振响应分析中,采用谱解法模拟了斜拉桥的脉动风场,抖振力采用准定常表达形式,自激力采用Y.K. Lin 表达形式。由于自激力的存在,结构的运动方程为非线性,提出了一种迭代方法来考虑自激力引起的非线性。采用Newmark-β方法进行积分计算。频域抖振分析采用多模态耦合分析方法。时域及频域抖振响应分析结果的一致性较好,这表明了大跨度斜拉桥时域抖振响应分析的可行性和可靠性。     

埋置基础近似动力模型及其应用

采用一种适用于筏形和箱形类基础的地基离散模型，建立上部结构－基础－地基系统在时域内的运动方程。采用时程分析法对高层筒体结构进行地震反应分析。讨论了不同场地，不同地震输入以及基础埋深等因素对结构地震反应的影响。     

粘弹性分数阶导数模型的有限元法

本文给出了粘弹性分数阶导数模型的有限元格式,并用模态分析的方法进行了运动方程解耦。用Laplace变换及其反变换,解析地计算了解耦后单自由度系统的时域和频域响应。时域响应被分为极点部分和截断部分,它们分别代表短期内的衰减振动和长时间内的缓慢恢复效应。以一维杆件为例,对有限元算法和解析解做了对比,分析了响应精度与单元个数的关系。结果表明用有限元法计算的位移接近解析解,而要得到准确的高频加速度响应,则需要划分许多单元格。     

基于滞变阻尼模型的时域计算方法

复阻尼时域运动方程的自由振动解中包含发散项,导致时域数值计算结果不能稳定收敛。在复阻尼模型的频域运动方程基础上可得到滞变阻尼模型的时域运动方程。针对滞变阻尼模型的特点,依据复平面法和地震加速度的三角级数表达式,该文提出了滞变阻尼模型的时域理论计算方法;假定时间步长内结构的振动响应为简谐振动响应,同时借助于常平均加速度法,提出了滞变阻尼模型的时域数值计算方法。算例分析表明,与复阻尼模型的时域数值计算方法相比,滞变阻尼模型的时域理论计算方法和时域数值计算方法可有效避免时域发散现象;滞变阻尼模型的时域理论计算结果和时域数值计算结果与复阻尼模型的频域计算结果近似相等,进一步证明了该文方法的正确性。     

弹性动力学的多变量响应问题的解法

基于瞬时混合变分原理与乘积型二元三次B样条函数,以板壳为例,建立样条动力方程。引入样条参数及其对时间的导数作为状态变量,导出状态方程,对空间域采用混合样条元法,对时间域采用现代控制论中的状态空间法。文中还建立了一种状态变量的递推计算格式,可以直接计算出多变量动力响应值,数值计算结果表明,本文方法的计算精度与效率是令人满意的。本文方法对计算多输入与多输出,时不变与时变系统和线性与非线性系统等多变量动力响应问题,有广阔的应用与发展前景。     

动力机器框架式基础的隔振研究

针对辽宁某热电厂大型汽轮机发电机组框架式基础的局部振动问题,通过在基础局部引入弹簧阻尼器隔振元件,导出了隔振基础的动力方程。并建立有限元模型,计算框架基础振动在频域内的响应,同时将隔振基础控制点的分析结果与非隔振基础的动力分析结果进行比较,结合算例分析表明:采用弹簧阻尼隔振元件对汽轮发电机组框架式基础进行隔振控制是正确和可行的。     

TBM液压管道频谱特性分析和结构优化

考虑到全断面硬岩推进机(TBM)掘进过程中轴向基础振动对流体流速和压力波动的影响,运用输流管道流固耦合轴向运动4-方程模型,分析基础振动的影响,建立轴向基础振动下的TBM液压管道轴向耦合振动方程组,并用直接解法在频域内对其进行求解,再运用MATLAB软件对管道出口处流速和压力的频域响应特性进行仿真计算,随之分析基础振动和不同结构参数对流体频域响应的影响规律。同时,为减弱基础振动对流体出口参数的影响,运用正交实验法对管道进行结构优化,优化后的管道系统流速的频域幅值整体上减小了48.61%,从而在一定程度上抑制了因基础振动带来的流体波动。     

随机参数梁在考虑热弹耦合下的动力响应分析

以随机参数梁为研究对象,分析其在温度载荷和力载荷共同作用并考虑热弹耦合关系时的动力响应。建立了热弹耦合动力学有限元模型,给出了在时间域内差分离散、相互交替迭代的耦合计算方法。利用随机因子法推导了结构温度场和动力响应的数字特征表达式,其中温度场的求解利用θ 时间积分法,动力响应则利用Newmark-β 积分法。在求出结构各时间步温度场和动力响应数字特征的基础上,应用耦合算法获得了整个时间域内的结构响应数字特征。通过悬臂梁算例分析了热弹耦合项对动力响应的影响,并考察了诸随机参数分散性对结构动力响应分散性的影响。     

基于时间序列模型自回归系数灵敏度分析的结构损伤识别方法

该文在分析了时间序列模型的自回归系数对结构单元刚度灵敏度的基础上,提出了一种采用随机载荷作用下结构的时域响应数据进行损伤识别的新方法。该方法首先根据随机载荷作用下的结构响应拟合适用的时序模型;然后建立基于自回归系数的损伤灵敏度矩阵,通过该矩阵可以建立由单元损伤导致的自回归系数的变化与损伤系数变化之间的关系;最后通过求解损伤系数向量来识别损伤位置和损伤程度。对一悬臂梁结构损伤识别的数值结果表明:在计入1%和2%测量噪声的情况下,该方法仅利用单个传感器的时域测量数据,就能够较好地识别单个单元和多个单元损伤;如果对基于多个传感器的识别结果进行综合,识别结果则更加准确、可靠。     

弹性-粘弹性复合结构随机响应的各阶谱矩的计算方法

提出了一种新的计算弹性-粘弹性复合结构随机响应的各阶谱矩的计算方法，它是一种时域复模态分析方法。利用此方法获得了弹性-粘弹性复合结构在白噪声、滤过白噪声等典型平稳随机激励下随机响应的各阶谱矩的解析表达式，分析了粘弹性对各阶谱矩的影响。此计算方法简便、易用，无论单自由度或多自由度系统均适用，为进一步研究弹性-粘弹性复合结构在随机激励下的可靠性打下良好基础。     

基于香农采样定理的结构风振时域计算改进

基于同步测点的风压时程数据的响应计算有两种方法:时域法和频域法,它们得到的结果存在一定的差异。针对如何改善时域算法的精度进行研究,提出基于香农采样定理对风压时程数据进行加密的方法。将此方法运用到一个有解析解的两自由度结构算例和一个实际工程算例中,对采样数据量和采样频率都一定的荷载时程数据进行香农插值加密;分别采用插值加密之后的数据与未插值加密的数据进行计算,得到频域和时域结果。通过计算结果的比较得到以下结论:荷载时程数据相同的情况下,对于风致振动响应,频域计算的结果一般比时域计算更精确,时域计算的误差主要由高频部分的误差引起;运用香农采样定理,对已采得的数据进行插值加密,频域计算精度基本不变,但时域计算精度能得到提高。     

基于模态应变能和小波变换的结构损伤识别研究

针对单一方法对结构同时发生多处不同程度损伤识别的不敏感性缺陷,本文结合小波变换在时域、频域内表征信号局部特性且能够聚焦到信号或函数的任意细节进行处理的能力,提出了一种基于单元模态应变能和小波变换的结构损伤识别方法。在单元模态应变能基础上,利用小波变换系数的变化和分布情况构建单元模态应变能小波变换结构损伤指标,通过对简支梁的数值模拟和斜拉桥模型试验研究的结果与单元模态应变能平均变化率作为损伤识别指标的计算结果进行对比,结果表明该方法能有效确定结构同时发生多处不同程度损伤的位置和估计损伤程度,为实际工程应用奠定了基础。     

Identification of the dynamical properties of structures using free vibration data and distributed genetic algorithms

The dynamical properties of structures, such as natural frequencies, damping ratios and mode shapes, can be obtained by several identification methods. Some are based on the direct signal processing in a time domain; others transform response data to the frequency domain. The development of these techniques is useful in the production of more accurate structural models; they can be also used to test the level of damage in structures (or verify their strength to support new load actions) by using experimental data. There are situations where frequency domain algorithms and conventional system identification techniques fail, do not allow adequate solution of the identification problems or become trapped in a local optimum. It is in these cases where evolutionary optimization techniques are important tools for evaluating the dynamical properties of structural systems in practical applications. This article presents a methodology to determine the dynamic properties of structures knowing their response in terms of displacement, velocities or accelerations in the time domain when they are subjected to a free vibration excitation. In order to do that, a specialized evolutionary algorithm capable of adapting its parameters to the different types of registers obtained from the dynamic time response of a structure is implemented in a robust way, making this approach useful in practical situations. A distributed real genetic algorithm (DRGA) based on an island model of different subpopulations is used to adjust a simulated response signal of a building to the real response signal. Initially, computer-generated synthetic response signals are used but, in future, the approach will be validated with signals obtained from free vibration experimental tests and will be extended to other types of dynamical excitation signals. Finally, the method will be tested with data obtained from earthquake events.     

饱和层状地基条形基础动刚度的精细积分算法

采用基于积分变换、对偶方程和精细积分的算法求解饱和多层地基条形基础的动刚度问题。利用Fourier积分变换得到Biot多孔饱和介质波动方程在频域-波数域内的常微分方程,引入广义对偶变量,对二阶常微分波动方程进行降阶处理;针对地表自由排水和封闭排水边界条件,给出了适于精细积分算法的矩阵表达;对控制方程采用精细积分解答,得到波数域内的格林函数,对结果进行逆Fourier积分变换,得到空间域的力和位移关系;施加边界条件,最终得到刚性条形基础的动刚度的解答。通过与文献已有结果进行对比,验证了精细积分算法的准确性。最后计算两组算例,分别分析了表面薄层的孔隙率、渗透力阻尼系数对条形基础动刚度的影响。     

Time‐domain soil–structure interaction analysis in two‐dimensional medium based on analytical frequency‐dependent infinite elements

A direct method for soil–structure interaction analysis in two‐dimensional medium is presented in time domain, which is based on the transformation of the analytical frequency‐dependent dynamic stiffness matrix. The present dynamic stiffness matrix for the far‐field region is constructed by assembling stiffness matrices of the analytical frequency‐dependent dynamic infinite elements, so that the equation of motion can be analytically transformed into the time‐domain equation. An efficient procedure is devised to evaluate the dynamic responses in time domain. Verification of the present formulation is carried out by comparing the compliances for a strip foundation on a homogeneous and layered half‐spaces with those obtained by other methods. Numerical analyses are also carried out for the transient responses of an elastic block and tunnel in a homogeneous and a layered half‐space. The comparisons with those by other approaches indicate that the proposed time‐domain method for soil–structure interaction analysis gives good solutions. Copyright © 2000 John Wiley & Sons, Ltd.     

用GDQ空-时半解析法分析圆弧拱强迫振动

从圆弧拱的强迫振动控制方程出发,在空间域采用广义微分求积法,将广义微分求积法中的节点参数在时域内取为响应的时间级数,通过时域配点求解该六阶偏微分方程得到全域内的响应位移场,分析了圆弧拱的平面内强迫振动问题。运用Matlab语言编制圆弧拱强迫振动时程分析的计算程序,并进行了相应的算例分析,数值计算结果表明该方法对于求圆弧拱的强迫振动问题具有较高的精度和效率。     

Earthquake response analysis in the time domain for 2D soil–structure systems using analytical frequency‐dependent infinite elements

This paper presents a time domain method for soil–structure interaction analysis under seismic excitations. It is based on the finite element formulation incorporating analytical frequency‐dependent infinite elements for the far‐field soil region. Equivalent earthquake input forces are calculated based on the free‐field responses along the interface between the near‐ and far‐field soil regions using the fixed exterior boundary method in the frequency domain. Then, the input forces are transformed into the time domain by using inverse Fourier transform. The dynamic stiffness matrices of the far‐field soil region formulated using the analytical frequency‐dependent infinite elements in the frequency domain can be easily transformed into the corresponding matrices in the time domain. Hence, the response can be analytically computed in the time domain. A recursive procedure is proposed to compute the interaction forces along the interface and the responses of the soil–structure system in the time domain. Earthquake response analyses have been carried out on a multi‐layered half‐space and a tunnel embedded in a layered half‐space, and results are compared with those obtained by the conventional method in the frequency domain. Copyright © 2003 John Wiley & Sons, Ltd.