Principal axes of M-DOF structures Part II: Dynamic loading

This paper is the second in a two-part series that discusses the principal axes of M-DOF structures subjected to static and dynamic loads. The primary purpose of this series is to understand the magnitude of the dynamic response of structures to enable better design of structures and response modification devices/systems. Under idealized design conditions, the structural responses are obtained by using single direction input ground motions in the direction of the intended response modification devices/systems, and by assuming that the responses of the structure is decoupleable in three mutually perpendicular directions. This standard practice has been applied to both new and retrofitted structures using various seismic protective systems. Very limited information is available on the effects of neglecting the impact of directional couplings (cross effects of which torsion is a component) of the dynamic response of structures. In order to quantify such effects, it is necessary to examine the principal axes of structures under both static and dynamic loading. In this two-part series, the first paper is concerned with static loading, which provides definitions and fundamental formulations, with the conclusion that cross effects of a statically loaded M-DOF structure resulting from the lack of principal axes are of insignificant magnitude. However, under dynamic or earthquake loading, a relatively small amount of energy transferred across perpendicular directions is accumulated, which may result in significant enlargement of the structural response. This paper deals with a formulation to define the principal axes of M-DOF structures under dynamic loading and develops quantitative measures to identify cross effects resulting from the non-existence of principal axes.     

Scattering of waves by subterranean structures via the boundary element method

The boundary element method (BEM) is used to study the two-dimensional wave field generated when buried structures of arbitrary shape (i.e. inclusions) in an elastic medium are illuminated (or insonified) by dynamic line sources. Both steady-state responses and time-domain transients are presented. The problem is formulated in the frequency domain by means of appropriate Green's functions. The evaluation of the singular integrals is achieved (and to the best of the writers' knowledge, for the first time in the technical literature) in analytical form, which results in improvements in computational efficiency and accuracy. Closed-form solutions for regular geometries are then used to validate the method. The interaction of two cavities, the formation of shadow zones by inclusions and the complexity of the scattered field from bodies with irregular shapes are used as examples to demonstrate the versatility of the method. The responses computed in the time domain were invariably found to be causal, even for non-convex domains, which belies a recent assertion by some researchers that the application of boundary element methods to concave domains is associated with non-causal effects.     

广东永梅坳陷南段成矿区构造特征及找矿方向

永梅坳陷南段是粤东地区重要的成矿区，银铜多金属矿床的产出严格受地洼阶段形成的断裂构造控制；通过对该区构造层与成矿关系研究，阐述了成矿的构造基本特征和地洼阶段构造活动控矿的规律，指出了找矿方向。     

地图异构变换的数学模型及其在地图发展演进中的意义

给出了地图图象异构变换的数学模型，如制图选取，制图综合等。这些模型已屡地图编制中的经验事实所验证并作为实例给出。图象异构变换推动着地图的发展与进步。     

地震作用下剪切型结构的可靠性分析

本文利用Ｍｏｎｔｅ－Ｃａｒｌｏ数字模拟原理，以同一集系的多条地震加速度时程为输入，利用作者提出的考虑结构低周疲劳特性，首超破坏与累积损伤破坏合一的地震破坏准则，通过时程反应分析，直接统计反应量的随机特征来寻求结构的抗震可靠度，避免了建立地面运动简化模型和求解强非线性随机振动问题带来的近似与误差，在可靠度分析中采用了一次二阶矩的验算点法，将结构抗震可靠性统一到可靠指标β上来分析，便于在工程中实际运用     

天山造山带地壳结构与构造──乌鲁木齐─库尔勒地震转换波测深剖面

沿乌鲁木齐－库尔勒３５０余公里长的测线上完成了穿越天山的地震转换波野外观测，得出天山造山带的深部构造剖面图和壳内Ｐ，Ｓ波速度结构模型．天山的结晶地壳可分为４层，各层的速度分别是：Ｖｐ值为５．９，６．３，６．６，６．９ｋｍ／ｓ；Ｖｓ值为３．２，３．５，３．７，３．９ｋｍ／ｓ。上地幔顶部的波速：Ｖｐ值为８．１０ｋｍ／ｓ。Ｖｓ值为４．６ｋｍ／ｓ。天山地区的地壳厚度为４２－５６ｋｍ，中天山最厚，达到５０－５６ｋｍ。地壳中部存在低速透镜体。探测结果表明，天山大地构造可分为北天山、中天山和南天山３个区，其地壳深部构造特征各不相同。用颤动构造理论来解释天山造山带的形成机制和演化较板块构造理论更为合理。     

结构抗震设计中的强度折减系数研究

借助于单自由度弹塑性动力时程分析程序，对延性结构的强度折减系数进行了研究，在统计平均和回归分析的基础上，建立了平均强度折系数的函数形式，本文所建立的平强度折减系数函数，从理论上明确了结构具有延性对弹性地震力的折减关系，研究成果可供结构抗震设计规范采纳应用。     

Simplified transverse seismic analysis of buried structures

This paper presents a simplified method for the analysis of square cross-section buried structures (tunnel) subjected to seismic motion. Finite element analyses are performed to assess the fundamental modes of vibration of the soil layer with and without the tunnel. The influence of the tunnel on the modes of vibrations is taken into account by comparing the modal deformations in the free-field to those in the presence of the tunnel. From this comparison the zone of influence of the modal displacements due to the presence of the structure is determined. The resulting model is subjected to horizontal and vertical excitation of statistically independent accelerograms compatible with the response spectra of the Regulatory Guide 1.6 of the Nuclear Energy Commission. The free-field displacement is introduced at the boundaries of the zone of influence. The proposed simplified static analysis yields a state of stresses similar to that obtained from a full dynamic analysis of the complete soil–tunnel system. Several examples are solved to corroborate the validity of the method.     

A preliminary prediction of seismic damage‐based degradation in RC structures

Estimation of structural damage from a known increase in the fundamental period of a structure after an earthquake or prediction of degradation of stiffness and strength for a known damage requires reliable correlations between these response functionals. This study proposes a modified Clough–Johnston single‐degree‐of‐freedom oscillator to establish these correlations in the case of a simple elasto‐plastic oscillator. It is assumed that the proposed oscillator closely models the response of a given multi‐degree‐of‐freedom system in its fundamental mode throughout the duration of the excitation. The proposed model considers the yield displacement level and ductility supply ratio‐related parameter as two input parameters which must be estimated over a narrow range of ductility supply ratio from a frequency degradation curve. This curve is to be identified from a set of recorded excitation and response time‐histories. Useful correlations of strength and stiffness degradation with damage have been obtained wherein a simple damage index based on maximum and yield displacements and ductility supply ratio has been considered. As an application, the proposed model has been used to demonstrate that ignoring the effects of aftershocks in the case of impulsive ground motions may lead to unsafe designs. Copyright © 2001 John Wiley & Sons, Ltd.