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。     

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.     

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.     

地震动作用下刚体扭转效应的振动台模拟试验

2008年汶川地震中江油市太白公园曲径桥上的石雕发生转动破坏现象,本文对这一转动现象进行了振动台模拟试验。模拟试验结果表明:① 在振动台三向加载1.5倍的汶川地震江油台记录的平动加速度后,模型的转动情况与实际观测的石雕转动情况比较一致;② 石雕的转动与石雕的非对称性、地震动输入角度和地震动的竖向作用有关;③ 加载竖向地震动作用后,石雕模型会发生摇摆现象,说明竖向地震动是造成模型扭转现象的重要原因,这也说明在分析相似震害现象时竖向地震动作用不可忽视。      

Semiactive control of rigid blocks under earthquake excitation

This paper investigates the usefulness of a semiactive control to reduce the overturning vulnerability of a rigid block on a rigid plane under earthquake excitation. The proposed feedback law is used to set the stiffness of restraints placed at the 2 lower corners of the block. The performance of the semiactive control is numerically validated by subjecting the block to 100 recorded accelerograms. Specific simulations are performed to study the effect of different anchorage design parameters on the utility of the control. Finally, the robustness of the proposed control is addressed with respect to typical issues of the real‐world implementation.     

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.     

First passage of a sliding rigid structure on a frictional foundation

The first passage problem for a sliding rigid block on a frictional foundation, subjected to Gaussian white noise through the foundation, is studied. A well-posed boundary value problem is formulated from Markov process theory and solved for the ordinary moments of time to first passage by the finite element method. A range of parameters is studied representing a simple seismic base isolation system. Results of Monte Carlo simulation are given for comparison.     

Steady state rocking response of rigid blocks part 1: Analysis

The result of a theoretical study on the rocking response of rigid blocks subjected to sinusoidal base motion is presented. The study indicates that, for a given excitation amplitude and frequency, a rigid block can respond in several different ways. Based on analysis, the regions of different classes of steady state symmetric response solutions are mapped on the excitation amplitude-frequency parameter space. The steady state response solutions (both harmonic and subharmonic) are classified into two classes, out-of-phase and in-phase with respect to the excitation. Only out-of-phase solutions are found to be stable. A parametric study shows that steady rocking response amplitude is highly sensitive to the size of the block and the excitation frequency in the low frequency range. It is relatively insensitive to the excitation amplitude and the system's coefficient of restitution of impact. For two blocks of the same aspect ratio and coefficient of restitution subjected to the same excitation, the larger block always responds in smaller amplitude than the smaller block. Computer simulation is carried out to study the stability of the symmetric steady state response solutions obtained from analysis. It is found that as the excitation frequency is decreased beyond the boundary of stable symmetric response, the response becomes unsymmetric where the mean amplitude of oscillation is non-zero. Further decrease in excitation frequency beyond the stable unsymmetric response boundary causes instability in the form of overturning.     

Steady state rocking response of rigid blocks part 2: Experiment

The results of an experimental investigation on the rocking response of rigid blocks subjected to sinusoidal base motion is presented. It is shown that two common types of steady state response are harmonic and 1/3 subharmonic response. The measured steady state response amplitudes correlate well with theoretical predictions for both harmonic and 1/3 subharmonic responses. Within each type of steady state response, theoretical studies show that the system may respond in either a symmetric or an unsymmetric mode. A symmetric mode denotes that the block oscillates about a mean zero position while an unsymmetric mode implies the mean position of oscillation is at an inclined position. One form of unsymmetric response was observed in the experiment. In addition, almost periodic responses were also observed in the experiment, although their existence has not been reported in theoretical studies.     

浅埋地下结构顶板在竖向地震作用下的动力响应

采用结构动力学的方法研究了浅埋地下箱形结构在竖向地震作用下的动力响应。鉴于土与结构动力相互作用分析的复杂性,为了简化分析,整个分析过程分为2步。第1步把结构看作是刚体,利用刚体与地基的相互作用分析求得刚体在竖向地震分量作用下的动力响应;第2步首先考虑到了侧墙对于顶板的抗弯约束作用,求得了顶板的固有频率及振型,并把第1步刚体的动力响应作为输入求解顶板梁的受迫振动,进而求得了顶板弯矩。