Anelastic degradation of acoustic pulses in rock

Measurements on acoustic pulses propagating in massive rock lead to a simple empirical relationship between the pulse rise time, τ and the time of propagation of a pulse, t:

$\text{τ=τ}{}_0\text{+C}\text{∫}\text{)}\text{T}\text{Q}{}^{\mathrm{?1}}\text{d}\text{t}$

where τ₀ is the initial rise time (at t = 0), Q is the anelastic parameter which may be expressed in terms of the fractional loss of energy per cycle of a sinusoidal wave, Q = 2π(ΔE/E)^?1, and is assumed to be essentially independent of frequency, and C is a constant whose value we estimate experimentally to be 0.53 ± 0.04. Of the linear theories of seismic pulse attenuation, model 2 of Azimi et al. (1968) is favoured. Pulse shapes computed from equations of Futterman (1962) also give C = 0.5, but the pulse arrives earlier than in a non-attenuating medium with the same elasticity and density. Pulse shapes calculated using Strick's (1967, 1970, 1971) theory give values of C incompatible with our results. The observations suggest that a method of estimating the Q-structure of the earth from seismic pulse rise times may have a particular advantage over the spectral ratio method.     

Anelastic acoustic impedance and the correspondence principle

A general definition of seismic wave impedance is proposed as a matrix differential operator transforming the displacement boundary conditions into traction ones. This impedance is proportional to the standard acoustic impedance at all incidence angles and allows extensions to attenuative media and to the full elastic case. In all cases, reflection amplitudes at the contact of two media are uniquely described by the ratios of their impedances. Here, the anelastic acoustic impedance is studied in detail and attenuation contrasts are shown to produce phase‐shifted reflections. Notably, the correspondence principle (i.e., the approach based on complex‐valued elastic modules in the frequency domain) leads to incorrect phase shifts of the impedance due to attenuation and consequently to wrong waveforms reflected from attenuation contrasts. Boundary conditions and the Lagrange formulation of elastodynamics suggest that elastic constants should remain real in the presence of attenuation and the various types of energy dissipation should be described by their specific mechanisms. The correspondence principle and complex‐valued elastic moduli appear to be applicable only to homogeneous media and therefore they should be used with caution when applied to heterogeneous cases.     

The role of damping in seismic isolation

In the current code requirements for the design of base isolation systems for buildings located at near-fault sites, the design engineer is faced with very large design displacements for the isolators. To reduce these displacements, supplementary dampers are often prescribed. These dampers reduce displacements, but at the expense of significant increases in interstorey drifts and floor accelerations in the superstructure. An elementary analysis based on a simple model of an isolated structure is used to demonstrate this dilemma. The model is linear and is based on modal analysis, but includes the modal coupling terms caused by high levels of damping in the isolation system. The equations are solved by a method that avoids complex modal analysis. Estimates of the important response quantities are obtained by the response spectrum method. It is shown that as the damping in the isolation system increases, the contribution of the modal coupling terms due to isolator damping in response to the superstructure becomes the dominant term. The isolator displacement and structural base shear may be reduced, but the floor accelerations and interstorey drift are increased. The results show that the use of supplemental dampers in seismic isolation is a misplaced effort and alternative strategies to solve the problem are suggested. Copyright © 1999 John Wiley & Sons, Ltd.     

黏性阻尼与复阻尼对钢筋混凝土框架结构地震响应影响的分析

本文讨论了利用黏性阻尼和复阻尼模型求解结构动力响应的方法;按相同的阻尼比,分别采用复阻尼模型和黏性阻尼模型计算了两个框架结构在不同地震波作用下的响应,并将结果进行对比,分析了两种不同的阻尼模型对结构动力响应的影响。结果表明,采用不同类型的阻尼对结构响应影响很大。     

结构减震隔震设计最优化问题研究

针对结构抗震减震隔震设计结构动力学基本方程,进行了基本结构刚度、阻尼和质量三方面减震隔震设计问题特征分析,专门指出刚度和阻尼的减震隔震设计研究已经有规范规定,但对减轻结构质量的减震隔震设计仍是需要深入研究的创新问题。目前采用新材料进行设施农业结构减震隔震设计,特别是采用玄筋混凝土现代无金属结构进行结构抗震减震隔震设计,结构最优化设计的实现便有了新契机,且容易实现抗力均匀分布,将较为彻底地解决地震工程的最优结构抗震问题。     

A review of adverse effects of damping in seismic isolation

In this paper the question of possible adverse effects of damping in seismic isolation because of higher mode response is investigated by means of simple models with a few degrees of freedom (DOF). In particular the second mode response of a 2 DOF system is examined in detail for both viscous and hysteretic (e.g. friction or elastoplastic) damping devices. Qualitative and approximate quantitative estimates are obtained by neglecting the influence of the modal coupling terms, due to viscous damping or friction forces, on the first mode response. It is shown that additional viscous damping has a diminishing effect on base displacement, storey shear force and floor spectra values in the vicinity of the first mode resonance. However, a significant amplification of the floor spectra values near the higher mode frequencies may occur. In accordance with the results of previous works, compared with the viscous damping case, hysteretic damping amplifies moderately the first storey shear force and significantly the upper storeys shear force. It also results, in a much more pronounced amplification of the floor spectral values than viscous damping, in the vicinity of the higher eigenfrequencies. However, the higher modes' response is milder if a realistic velocity dependence of the friction coefficient is taken into account. Copyright © 2007 John Wiley & Sons, Ltd.     

复阻尼地震反应谱计算的再研究

本文订正了前文[1]公式中的符号差错，重新计算了犁阻尼加速度反应谱，另外又计算了速度谱和位移谱，并与相应的粘性阻尼谱作了比较，取得了一定的认识。现有计算结果显示，复阻尼速度谱和位移谱有一定特点，在中长周期和长周期部分可比相应的粘性阻尼谱高出10％左右。     

Suboptimal Rayleigh damping coefficients in seismic analysis of viscously-damped structures

An optimization method for the consistent evaluation of two Rayleigh damping coefficients is proposed. By minimizing an objective function such as an error term of the peak displacement of a structure, the two coefficients can be determined with response spectral analysis. The optimization method degenerates into the conventional method used in current practices when only two modes of vibration are included in the objective function. Therefore, the proposed method with all significant modes included for simplicity in practical applications results in suboptimal damping coefficients. The effects of both spatial distribution and frequency content of excitations as well as structural dynamic characteristics on the evaluation of Rayleigh damping coefficients were investigated with a five-story building structure. Two application examples with a 62-story high-rise building and a 840 m long cable-stayed bridge under ten earthquake excitations demonstrated the accuracy and effectiveness of the proposed method to account for all of the above effects.     

半主动磁流变阻尼控制结构的地震反应分析

本文对磁流变阻尼器的性能及恢复力模型进行了介绍,并对其参数进行了设计,提出了基于现代最优控制理论的半主动控制方法．计算实例分析结果表明,采用磁流变阻尼器对结构进行半主动控制能够有效地减小结构的地震反应．     

Influence of seismic input mechanisms and radiation damping on arch dam response

In this study, two different earthquake input models are introduced, i.e. massless foundation model and viscous-spring boundary input model considering radiation damping. Linear elastic and nonlinear contraction joint opening analyses of the 210 m high Dagangshan arch dam under construction in China are performed using the two different earthquake input models. First, the responses of the three-dimensional (3-D) canyon without the dam are analyzed, respectively, with massless-truncated foundation and with viscous-spring boundary; second, linear and nonlinear analyses of the dam–foundation system are performed and compared by using the two input models. Hydrodynamic effects are considered using finite element discretization for incompressible reservoir fluid. It is concluded that stresses and displacements and contraction joint opening in the dam are significantly reduced both in linear and nonlinear analyses when using viscous-spring boundary model. Interestingly, in the case of linear analysis of the Dagangshan, the massless foundation input model with a relatively higher damping ratio of 10% leads to a comparable response of the dam to that using viscous-spring boundary model. In addition, the maximum tensile stresses from nonlinear analysis are 10–25% larger than that of the corresponding linear cases due to a partial release of the arch action.     

Morison方程中动水阻力项对桥梁桩柱地震反应的影响

深水桥梁地震反应计算时,当采用Morison公式考虑水的作用时,增加了一个附加惯性项和一个附加阻尼项,其中附加阻尼项是非线性的。由于非线性附加阻尼项的存在,给采用反应谱方法求解桥梁的地震反应带来不便。讨论了非线性阻尼项对一般桥梁桩、墩结构地震反应的贡献,得到的结论是阻尼项的贡献很小,可以忽略。从而水中桥梁地震反应的计算就得到了很大的简化。     

基于位移的抗震设计方法中的等效阻尼模型的研究

对基于位移的抗震设计方法单自由度体系弹塑性位移计算的等效线性化方法中的等效阻尼模型进行研究.在统计分析的基础上,提出了考虑场地类别和设计地震分组的等效阻尼比公式,并与不同阻尼比公式进行了比较.对不同等效线性化方法的计算误差进行了统计分析,结果表明,本文建议的公式在预测单自由度体系位移反应方面与动力弹塑性分析结果在统计意义上吻合得最好.     

Effects of supplemental viscous damping on seismic response of asymmetric-plan systems

Coupling between lateral and torsional motions may lead to much larger edge deformations in asymmetric-plan systems compared to systems with a symmetric plan. Supplemental viscous damping has been found to be effective in reducing deformations in the symmetric-plan system. This investigation examined how supplemental damping affects the edge deformations in asymmetric-plan systems. First, the parameters that characterize supplemental viscous damping and its plan-wise distribution were identified, and then the effects of these parameters on edge deformations were investigated. It was found that supplemental damping reduces edge deformations and that reductions by a factor of up three are feasible with proper selection of system parameters. Furthermore, viscous damping may be used to reduce edge deformations in asymmetric-plan systems to levels equal to or smaller than those in the corresponding symmetric-plan system. © 1998 John Wiley & Sons, Ltd.     

A study of seismic response characteristics of structures with friction damping

The effectiveness of introducing Coulomb damping in structures to reduce seismic response is evaluated. Response characteristics of simple one-degree-of-freedom structures with sliding interfaces between the top slab and supporting frame and between the base and foundation are studied and compared. It is shown that, analytically, the top slab sliding system is a special case of the base sliding system. The slab sliding system is seen to offer certain advantages over the base sliding system inasmuch as it provides a more effective reduction in the lateral forces in the supporting frame as well as a better isolation of supported secondary systems, as depicted by a significantly reduced level of floor spectrum response. The analytical ease of predicting the response of the slab sliding system is also demonstrated. The required unobstructed sliding displacements seem to be reasonable except, may be, for flexible systems. The similarities and differences between the hysteretic and slab sliding systems are also highlighted by comparison of their response results.     

Passive seismic response controlled high-rise building with high damping device

This paper describes a feasibility study on a high-damping device (HiDAM) installed in a building structure by way of a bracing mechanism. A seismic response analysis with respect to a high-rise building approximately 100 m high is reported. Proper adjustment of the damping coefficient of the HiDAM (oil damper) provided an over all damping factor of about 10–20 per cent to the building structure, and reductions in the response, deformation and shear forces were verified analytically. This paper reports also the performance confirmation tests conducted on a model device of the HiDAM which satisfied the specifications determined from the analytical results. The test results demonstrate the feasibility of the HiDAM and the possibility of utilizing it in high-rise buildings.     

Thermal signature of in situ soil damping under severe seismic actions

This paper gives a synthesis on a series of studies demonstrating the possibility to have a direct access to in situ soil damping, exploiting the thermal dissipation due to irreversible mechanical phenomena under severe seismic conditions. The introduction provides a background to the three steps of such a study: instrumentation, modelling and inverse identification problem. Section 2 recalls the principle of the Seismic Harmonic System, equipment able to generate powerful in situ soil accelerations in the vicinity of a well. Evidence of a significant in situ soil temperature elevation is given under such seismic conditions. Section 3 reviews the mechanical and related thermal simulations for the prediction by a direct problem procedure of the mean temperature elevation in the vicinity of the borehole, using a two- or three-parameter behaviour model depending on the intensity of the actions. Section 4 is a synthesis of the possibilities offered by thermal in situ measurements to contribute, in parallel with mechanical measurements, to the identification and/or the validation of the damping characteristics of an in situ soil.     

悬挂阻尼控制结构体系巨型框架地震响应分析

提出一种巨型悬挂阻尼控制结构体系，采用结构动力学有限元方法对结构体系进行了地震随机振动分析、时程分析和地震反应谱分析，分析结果表明，这种结构体系能有效地减小结构的地震响应。最后讨论了影响控制效果的参数。     

Dynamic response analysis of nonlinear secondary oscillators to idealised seismic pulses

The paper deals with the seismic response analysis of nonlinear secondary oscillators. Bilinear, sliding and rocking single-degree-of-freedom dynamic systems are analysed as representative of a wide spectrum of secondary structures and nonstructural components. In the first stage, the equations governing their full dynamic interaction with linear multi-degree-of-freedom primary structures are formulated, and then conveniently simplified using primary-secondary two-degree-of-freedom systems and dimensionless coefficients. In the second stage, the cascade approximation is applied, whereby the feedback action of the secondary oscillator on the primary structure is neglected. Owing to the piecewise linearity of the secondary systems being considered, efficient semi-analytical and step-by-step numerical solutions are presented. The semi-analytical solutions allow the direct evaluation of the seismic response under pulse-type ground excitations and are also used to validate step-by-step numerical schemes, which in turn can be used for general-type seismic excitations. In the third stage, a set of decoupling criteria are proposed for the pulse-type base excitations, identifying the conditions under which a cascade analysis is admissible from an engineering standpoint. Finally, the influence and relative dependencies between the input parameters of the ground motion and the primary-secondary assembly are quantified on the response of the secondary systems through nonlinear floor response spectra, and general trends are identified and discussed.