Periodic response of a sliding oscillator system to harmonic excitation

This paper deals with the periodic response of an oscillating system which is supported on a frictional interface. The base excitation is assumed harmonic and the frictional force is assumed to be of the Coulomb type. Though each segment of the motion of such a system is described by linear equations, its complete response is highly non-linear and varied. The most fundamental periodic solutions are derived analytically and numerically. The results indicate that such a system has several subharmonic resonant frequencies and that while the friction reduces the peak response of the system when it is excited at its ‘fixed-base’ natural frequency, ω_n, the sliding can induce considerably higher levels of response, when compared with those of a non-sliding, fixed-base system, for frequencies less than ω_n. The results obtained herein may find application in the area of vibration isolation.     

位移谐波激励下拱顶锚固储罐的动力响应分析

地震中拱顶锚固储罐的破坏将造成严重的后果,研究其地震作用下的动力响应特性具有一定工程意义。以位移简谐波为水平激励,运用AD INA有限元软件对一座3 000m3的拱顶锚固储罐模型进行动力数值模拟,系统分析了储罐内液面晃动波高、动水压力极值、罐壁应力、拱顶应力、拱顶位移等动力响应结果,将以位移谐波激励和以加速度谐波激励的储罐动力响应结果进行比较。分析表明,位移谐波激励下拱顶锚固储罐的液面晃动波高受场地影响较大;储罐应力分布具有一定规律性;采用位移谐波激励时其应力、位移和动水压力等较采用加速度谐波激励时大,液体晃动波高较小。     

Sliding-uplifting response of rigid blocks to base excitation

In the present paper a two-degree-of-freedom system is considered which allows the simulation of rigid blocks uplifting and sliding on frictional foundations; the monolateral constraint between block and base is schematized by means of a joint model, which allows the contact problem to be discretized. The joint model is governed by normal and shear constitutive laws, which have been derived by the phenomenological behaviour of stone blocks and rock joints, as given by rock mechanics. Furthermore, a numerical procedure has been developed in order to solve the non-linear equations governing the motion of the block-base system, and to analyse the dynamic response of this system under seismic excitation; particular attention has been paid to the influence of the vertical displacement on the slip response.     

位移谐波激励下拱顶锚固储罐的动力屈曲研究

地震下储罐罐壁发生屈曲是其主要的震害形式,研究储罐的动力屈曲特性尤为重要.以位移简谐波为水平激励,运用ADINA有限元软件对高径比分别为0.82、1.24和1.85的3种拱顶锚固储罐进行动力屈曲分析.根据Budiansky-Roth动力屈曲准则,通过谐波位移幅值对应的加速度峰值PGA和储罐位移响应,绘制特征节点的"伪平衡路径"轨迹,以确定临界加速度峰值,判断储罐动力屈曲.3种储罐模型在位移谐波激励下均为弹性屈曲.通过动力屈曲分析得出结论:储罐屈服的位置随高径比的不同有所不同,屈服多发生在径向变形最大处,罐壁内外面的塑性总应变值和屈服应力值大小不同等.最后以储罐模型B为例,将以"伪平衡路径"轨迹确定的临界应力与规范公式的计算结果进行了比较.     

The many steady state responses of a rigid block under harmonic forcing

Recent mathematical advances in the study of the response of a rigid block to horizontal simple harmonic forcing conclude that (i) all types of subharmonic response are possible, (ii) several types can occur at one point in parameter space, (iii) exact expressions are available for stability boundaries in parameter space, (iv) asymmetric solutions exist just outside the upper boundaries of symmetric solutions, (v) period- and impact-doubling cascades occur as parameter values are varied even further outside the boundaries, (vi) aperiodic (or chaotic) responses are possible, (vii) periodic responses can occur which appear to violate West's formula and (viii) steady state responses of the forced system can be so large as to produce toppling of the block if the system were unforced. These results are used to explain and extend recent computational work. Also we find quantitative agreement between our theoretical work and some recent experimental work of Tso and Wong.     

Steady-state harmonic response of a rigid plate bearing on a liquid-saturated poroelastic halfspace

Soil–structure interaction problems are typically modelled by assuming subgrade behaviour to be either elastic or viscoelastic. Herein, compliance functions that may be used to solve soil–structure interaction problems are evaluated by treating the subgrade as a liquid-saturated poroelastic material whose behaviour is governed by Biot's theory. The compliances are evaluated for the harmonic rocking and vertical motions of rigid permeable and impermeable plates bearing on a poroelastic halfspace. Comparisons are made with elastic solutions which assume the subgrade to be either completely drained or undrained. Also, solid and fluid contact stresses are reported for the poroelastic case and compared to the solid contact stresses for the elastic cases.     

Experimental assessment of contact forces on a rigid base following footing uplift

A number of investigations in the recent decades have shown that footing uplift can reduce the seismic loading on a structure. Guidelines to design a structure with seismic uplift capability have been proposed. However, these studies mainly focus on the structural response and neglect the impact forces on the footing from re‐contact between the footing and the supporting medium. A small number of computational studies of the induced forces on the footing have been performed. This paper presents the results of free vibrations and shake table tests on a single degree‐of‐freedom model of a bridge pier with footing uplift on a rigid base. Two support conditions are considered, that is, footing fixed to the base and footing free to uplift on a rigid base. Load cells were placed at the interface of the footing and rigid base to measure the contact forces during structural vibration. The footing responses of both flexible and rigid structures due to free vibration are compared. The results show that the flexibility of the structure has significant effects on footing uplift duration and amplitude and reduces the contact force, in some cases very significantly. The flexible structure was also subjected to harmonic base excitations. It is found that varying the characteristics of the excitation changes the uplift amplitude but does not affect the contact force significantly. Copyright © 2017 John Wiley & Sons, Ltd.     

多点输入随机地震动拱坝-地基体系反应分析

采用等效地基集总参数方法,推导了拱坝－地基体系的简化多点随机输入分析模型,对拱坝－地基动力相互作用体系在多点随机输入地震波作用下的随机响应到进行了分析,并对地基柔度及地震动空间相干性损失对拱坝随机响应的影响进行了讨论。     

墩底可抬升刚构桥模型振动台试验研究

桥墩基础抬升可以切断地震动向上部结构传播,基础与地基碰撞还可以耗散地震能量,然而已有研究大多集中在数值模拟或理论分析,缺乏大型振动台试验验证.文中设计制作了一座基础固接和基础可抬升的连续刚构桥模型并进行振动台试验.对2种模型的动力特性、加速度响应和位移响应等进行对比分析.结果表明:基础可抬升桥梁较基础固接桥梁固有频率小...     

On rigid foundations subjected to seismic waves

In the analysis of structural foundations for seismic loads, it is customary to distinguish two types of soil-structure interaction effect: kinematic interaction (or wave passage), and inertial interaction. The former refers to the phenomenon of wave scattering, which occurs because the foundation is much stiffer than the surrounding soil and cannot accommodate to its distortions. Inertial interaction, on the other hand, is caused by feedback of kinetic energy of the structure into the soil. This paper is concerned only with the first phenomenon. The rigorous analysis of rigid, embedded foundations subjected to seismic disturbances requires, in general, substantial computational effort. Indeed, a typical analysis would normally require models with finite elements and/or boundary elements. Although such methods may be used to find an accurate solution to the problem of kinematic interaction, their use is not always warranted, given the many uncertainties involved and the multitude of assumptions that must be considered. Hence, approximate solutions are attractive for this problem. One such approximate method is the remarkably simple algorithm proposed by Iguchi.³ This paper presents first an appraisal of this method by way of a comparison with accurate numerical solutions for cylindrical foundations; next the algorithm is applied to rectangular (prismatic) foundations. It is found that Iguchi's method gives results that are adequate for engineering purposes, even if not entirely accurate.     

Site response of heterogeneous natural deposits to harmonic excitation applied to more than 100 case histories

Variation of shear-wave propagation velocity (SWV) with depth was studied by analyzing more than one hundred actual SWV profiles. Linear, power, and hyperbolic variation schemes were investigated to find the most representative form for naturally occurred alluvial deposits. It was found that hyperbolic (asymptotic) variation dominates the majority of cases and it can be reliably implemented in analytical or analytical-numerical procedures. Site response analyses for a one-layer heterogeneous stratum were conducted to find an equivalent homogeneous alternative which simplifies the analysis procedure but does not compromise the accuracy of the resonance and amplification responses. Harmonic average, arithmetic average and mid-value equivalents are chosen from the literature for investigation. Furthermore, full and partial depth averaging schemes were evaluated and compared in order to verify the validity of current practices which rely upon averaging shallow depths, viz., the first 30 m of the strata. Engineering bedrock concept was discussed and the results were compared.     

Response of rigid body assemblies to dynamic excitation

Shaking table tests were conducted to investigate the response of rectangular wooden blocks and block assemblies of various sizes and slenderness to harmonic and earthquake base excitation. The shaking tests were followed by an analytical and a numerical study of response of single blocks and block assemblies. The analytical study was aimed at establishing criteria for the initiation of rocking and of overturning in response to harmonic base motion and consisted of solving numerically the differential equations of motion of a rigid block on a rigid foundation. The numerical study, in the course of which the response of both single blocks and block assemblies was examined, was implemented by means of the Distinct Element Method (DEM). Prior to the DE simulation of actual shaking tests, preliminary analyses were conducted to confirm numerical stability and to evaluate material and damping parameters. Comparing the recorded time histories with those given by the analytical study and the DE simulation, good agreement was found. The distinct element model in use appeared to follow the highly non-linear motion of rigid body assemblies faithfully to reality. On the basis of the results, provided that the necessary parameters are carefully estimated, the employed DE model can be regarded as an appropriate tool to simulate response of rigid body assemblies to dynamic base excitation.     

TMD结构基于双过滤白噪声随机地震激励的系列响应的简明解

针对既有方法在分析TMD结构基于双过滤白噪声激励下结构响应的解表达式复杂而导致计算效率低的问题,提出了一种简明封闭解法。首先,利用双过滤白噪声谱的滤波方程与TMD结构的地震动方程联立,可将TMD结构基于复杂的双过滤白噪声激励准确的表示为易于求解的运动方程;其次,基于复模态法获得TMD耗能结构位移、层间位移的系列响应的复特征值及复模态参与系数;然后基于随机振动理论获得了TMD结构随机地震动系列响应（相对于地面绝对位移和结构层间位移）的功率谱统一形式的二次正交解,进而获得了TMD结构系列随机响应的0-2阶谱矩和方差的简明封闭解。最后研究了基于首超破坏准、Markov过程假设及串联失效模式的TMD结构的体系动力可靠度。通过一算例分析,表明了本文方法的正确性和高效性。因此,本文方法可用于各类线性结构基于复杂的随机地震动响应的分析及其动力可靠度计算。     

Hanger replacement influence on seismic response of suspension bridges: Implementation to the Bosphorus Bridge subjected to multi-support excitation

The effects of hanger replacement from inclined to vertical configuration on seismic response of long-span suspension bridges are investigated considering multi-support earthquake excitation. The Bosphorus Bridge is investigated due to its recent comprehensive rehabilitation, mainly involving hanger replacement. The finite-fault stochastic simulation method (FINSIM) is utilized for multi-point earthquake time-history generation. The developed finite element (FE) model both for the inclined and vertical hanger arrangement are verified through the structural health monitoring (SHM) data. Based on the comparative analysis, the tension force of vertical hangers is found to be lower than that of inclined hangers, whereas the tension force of the main and back-stay cables remains the same. The compressive axial force of the deck decreases relatively in the case of the vertical hanger arrangement, whereas the cross-sectional forces at the tower base section increase. The approach viaducts are not affected by the vertical hanger arrangement. According to the demand/capacity ratios for damage estimation under the max. earthquake (2475 years return period), structural damage on the tower base section may be expected for both hanger arrangements, while these sections perform well under design scenario earthquake. The expansion joint of the bridge with inclined hangers is also estimated to be damaged; however, this displacement is lower in the case of the vertical hanger arrangement due to the viscous dampers. The findings also reveal that a change in hanger form of a suspension bridge can necessitate other structural retrofit, such as using viscous dampers to limit longitudinal displacements of the deck and retrofitting the bridge towers.     

简谐荷载下单层球面网壳动力失效机理研究

以具有实际工程意义的40m跨度K8型单层球面网壳为研究对象,采用ANSYS程序的Pipe20单元,考察不同矢跨比网壳在不同频率的简谐荷载作用下,随着荷载幅值的逐渐增大,其宏观和微观响应的变化,详细阐述了2类破坏行为的规律,并通过一定规模的参数分析,给出单层球面网壳动力强度破坏判别准则.     

Model for multiblock columns subjected to base excitation

A new model is presented for multiblock columns subjected to earthquakes, which contains an impact and an opening model. Both in the impact and in the opening model, all the possible opening configurations are investigated because it was found that in many practical cases, unexpected patterns may occur. The model is purely mechanical: assuming rigid blocks and classical (inelastic) impact. The effect of energy dissipation during impact was investigated. Using our model in accordance with the literature, it was found that monolithic blocks are more vulnerable to overturning than multiblock systems.     

正弦行波激励下单层偏心框架结构扭转响应的解析解

文中针对单层偏心框架结构,利用正弦行波激励研究了质量偏心率和激励频率对偏心框架结构行波扭转响应的影响规律.建立了行波激励下单层偏心框架结构的振动方程,采用相对运动法求解给出了正弦行波激励下单层偏心框架结构楼板的质心平动位移和转角位移以及楼板扭矩和柱剪力的解析解.计算了一个钢筋混凝凝土单层偏心框架结构的峰值楼板扭矩和峰值...     

Non‐linear response analyses of rectangular rigid bodies subjected to horizontal and vertical ground motion

This investigation deals with non‐linear seismic responses of free‐standing rectangular rigid bodies on horizontally and vertically accelerating rigid foundations. The responses are classified into two initial responses and four subsequent responses, accordingly the equations of motion governing the liftoff, slip and liftoff–slip interaction motions and boundary conditions corresponding to commencement and termination of the motions are defined. The time histories of responses presented herein show that the body is sensitive to small changes in the friction coefficient and slenderness, and to the wave properties and intensity of ground motions. Systematic trends are observed: the bodies on the low‐grip foundation avoid overturning while they are allowed to slip regardless of details of ground motions; the long period earthquakes tend to make the body overturn and slip largely. In contrast, the timing when liftoff and slip commences and terminates and their directions do not directly correspond with intensity of ground motions. Moreover, the vertical ground motion adds irregularities on the responses, since it excites or damps the responses. It is concluded that governing equations of motion and boundary conditions in view of discontinuous non‐linear systems are necessary to analyse actual motions of the rectangular rigid bodies subjected to horizontal and vertical ground motion. Copyright © 2002 John Wiley & Sons, Ltd.     

Response of a randomly inhomogeneous layer overlying a homogeneous half-space to surface harmonic excitation

The paper is concerned with the study of the effect of the randomness of material parameters on mean wave propagation in a semi-infinite viscoelastic medium. The medium considered in this paper is a configuration of a randomly non-homogeneous layer overlying a homogeneous half-space and is loaded harmonically on the top surface. The method used is that of Karal and Keller and is based on the idea of fundamental matrix and Bourret approximation. The integro-differential equation obtained in this paper is solved by the Laplace transform method. By using boundary and continuity conditions the mean wave solution is obtained. Numerical results show that the correlation functions, which introduce long-range interactions, can be the source of the wave amplification.