Effects of balanced impact damper in structures subjected to walking and vertical seismic excitations

This study investigates whether a balanced impact damper (BID) with a vertically suspended impact body colliding with shock absorbing rubber can suppress vibrations of a floor slab subjected to walking and vertical seismic excitations. The impact body is suspended by coil springs to sustain its deadweight and centralize it within the gap, and collides with the stopper when its amplitude exceeds the specified gap width. The stopper is covered by a shock‐absorbing rubber made of polyurethane gel. The installed BID was evaluated in a single degree‐of‐freedom model of a floor slab subjected to vertical excitations. Simulations revealed that the installed BID properly controls the vibrations. Next, the effects of the BID installed on a steel plate were investigated in shaking table tests. The BID effectively suppressed vertical vibrations of the plate subjected to sinusoidal waves, seismic motions, and walking excitations. In addition, the shaking table tests were accurately simulated by the developed mathematical model of the damper. Copyright © 2015 John Wiley & Sons, Ltd.     

多点激励下自锚式斜拉-悬吊协作体系桥地震反应分析

考虑地震动的空间变化效应,对自锚式斜拉-悬吊协作体系桥进行了随机地震反应分析。研究了P波、SH波和SV波作用下该协作体系内力和位移峰值响应的特点,对比分析了均匀一致地面动和多点非一致地面运动对其地震反应的影响,计算中由于虚拟激励法的引入,计算效率获得极大的提高。结果表明行波效应和部分相干效应对该类超大跨径桥梁地震反应有相当大的影响。     

Dynamic analysis of track nonlinear energy sinks subjected to simple and stochastice excitations

Track nonlinear energy sinks (track NESs) have been shown to be an effective and applicable strategy to mitigate structural response in recent years. However, previous studies on track NESs has mainly focused on demonstrating the benefits of track NESs through numerical simulations and experiments, with relatively little attention paid to the analytical understanding of the unique dynamics of track NESs. This study analyzes the responses of a track NES when subjected to impulsive and harmonic excitations by the harmonic balance method. Special attention is given to the cause and effect of the peaking behavior that is a prominent characteristic of the track NES's restoring force–displacement relationship. Analytical results reveal that the special energy–frequency characteristics of track NESs can be, at times, utilized to enhance the energy robustness that is absent in the conventional cubic NESs. Based on the analytical response expression, an equivalent linearization method (ELM) for the track NESs is developed for stochastic analysis. This ELM is numerically validated on the systems with strong nonlinearities. Stochastic optimization built on the ELM is performed to obtain design parameters of the track NES that can lead to minimum response variances of the primary structure. In particular, the proposed optimization procedure can be applied to seismic optimum design in which the seismic excitations are modeled as filtered white-noise ground motions. The analytical techniques provided in this study lay the groundwork for the practical implementation of track NESs as a robust and effective control strategy for engineering structures.     

Response of secondary systems in structures subjected to transient excitation

An analytical method, based on matrix perturbation theory, is developed whereby a simple estimate can be obtained of the maximum dynamic response of lightly damped, light equipment (modelled as a n(²)-degree-of-freedom system) attached to a structure (modelled as a n(¹)-degree-of-freedom system) subjected to ground motion or impact. A natural frequency of the equipment is considered close or equal to a natural frequency of the structure. It is assumed that the information available to the designer is a time history of the ground motion or impact, or an associated design spectrum; the fixed base modal properties of the structure; and the fixed base modal properties of the equipment. The method employed avoids the direct conventional analysis of a n(²) + n(¹)-degree-of-freedom system either by modal or by matrix time-marching methods; as well as errors in estimates of peak response due to the possible unreliability of numerical schemes because of the lightness of the equipment, or due to uncertainty as to the appropriate procedure for summing the contributions of the two closely spaced modes which occur in the system. The proposed procedure is demonstrated for an example equipment-structure system. Computed results based on the method are in close agreement with results obtained through a Newmark time-integration scheme.     

Stability of elastic frames subjected to earthquake excitations

Dynamic stability of elastic multistorey frame structures subjected to vertical earthquake ground accelerations is studied. Different stationary, non-stationary, white and non-white random models for earthquake strong motion are considered. The concepts of mean-square and almost-sure stability are reviewed and the corresponding stability theorems are presented. Several general criteria regarding the dynamic stability of the equilibrium state of multistorey frames subjected to random excitations are developed. A few examples concerning the stability of single and multi-degree-of-freedom structures under earthquake excitations are presented. The stability of motion of frames under combined horizontal–vertical acceleration is also briefly discussed.     

Response spectrum analysis of structures subjected to spatially varying motions

An important aspect of earthquake loads exerted on extended structures, or structures founded on several foundations, is the spatial variability of the seismic motion. Hence, a rigorous earthquake resistant design of lifeline structures should account for the spatial character of the seismic input, at least in an approximate way. A procedure is proposed which enables addressing the problem of multiply supported structures, subjected to imperfectly correlated seismic excitations, by means of an extension to the response spectrum method. A modified response spectrum model is developed for the design of extended facilities subjected to single and multicomponent ground motion. The modification procedure is based on adjusting each spectral value of the given design response spectrum by means of a correction factor, which depends on the structural properties and on the characteristics of the wave propagation phenomenon. Finally, the theoretical model is validated through digital simulation of seismic ground motion, whereby model predictions are found to be in good agreement with exact results.     

Arch responses to correlated multiple excitations

This paper analyses the in-plane stochastic responses of incompressible circular arches to spatially correlated multiple excitations. The dynamic, quasi-static and total structural displacements, moments, shear and axial forces are calculated. The results are compared with those obtained by various simplified excitations. The effects of the ground motion spatial variations on arch responses are examined. The results indicate that the responses may be underestimated or overestimated by neglecting the ground motion spatial variations, depending upon the structure and ground motion properties, the locations where the responses are evaluated, and the response quantity under consideration.     

大跨度结构TMD减震系统多点激励的地震随机响应分析

众多研究表明，对大跨度结构进行抗震分析时，必须采用非一致地震激励模型。本文对带TMD系统的大跨度结构考虑地震行波效应后的随机地震响应问题进行了研究。文中建立了结构的动力方程，并利用虚拟激励法求解。研究结果表明，对于大跨度结构装设TMD子结构以后可显著地降低结构的位移、速度和加速度响应，但在设计TMD减震系统时，必须考虑到地震激励的非一致性，否则可能会使预期的减震效果失效。     

近断层脉冲型地震动作用下隔震结构地震反应分析

隔震结构在远震场地减震效果良好，但是近断层地震动的明显的长周期速度和位移脉冲运动可能对隔震建筑等长周期结构的抗震性能和设计带来不利影响，需要深入探讨。本文首先讨论近断层地震动的长周期脉冲运动特征，然后以台湾集集地震8条典型近震记录和其它4条常用近震记录以及4条远震记录作为地震动输入，对两幢安装铅芯橡胶隔震支座的钢筋混凝土框架隔震结构进行非线性地震反应时程分析，通过比较探讨了算例计算结果，定量说明隔震结构的近震脉冲效应显著，是隔震设计不容忽视的问题。     

Stochastic considerations in seismic analysis of structures

A method is presented for stochastic modelling of a design earthquake by a power spectral density function for seismic analysis of structures. The method can be adopted with information currently available in the form of design response spectra for earthquake motion. Accurate seismic responses of structures can be easily obtained using such stochastic models. The methods for accurate response analysis of structures with closely spaced modes and for generation of floor response spectra of a building using a prescribed ground response spectrum directly are also presented. The hypothesis that a design earthquake can be modelled by a power spectral density function is used only implicitly in developing these methods.     

Stochastic earthquake response of secondary systems in base-isolated structures

This paper studies the stochastic responses of secondary systems in base-isolated shear beam structures. A number of base isolation systems such as the laminated rubber bearing (LRB), the resilient-friction base isolator (R-FBI) with or without sliding upper plate, and the EDF system are considered. The stochastic models for the El Centro 1940 and the Mexico City 1985 earthquakes which preserve the non-stationary evolutions of amplitude and frequency content of ground accelerations are used as earthquake excitations. The technique of equivalent linearization is utilized and the mean-square response statistics of secondary systems and primary structure are evaluated. The accuracy of the linearization scheme is verified by comparison with the Monte Carlo simulation results. Statistically estimated peak responses of the secondary system are evaluated and the results are compared with the response spectra for actual earthquake accelerograms. It is shown that the use of base isolation systems, generally, provides considerable protection for structural contents. In particular, the LRB system is remarkably effective in reducing responses of secondary systems. Results for the Mexico City earthquake show that the base-isolated structures are sensitive to long period ground excitations.     

Dynamic analysis of train–bridge system subjected to non‐uniform seismic excitations

Based on the theory of dynamic wheel–rail interactions, a dynamic model of coupled train–bridge system subjected to earthquakes is established, in which the non‐uniform characteristics of the seismic wave input from different foundations are considered. The bridge model is based on the modal comprehension analysis technique. Each vehicle is modelled with 31 degrees of freedom. The seismic loads are imposed on the bridge by using the influence matrix and exerted on the vehicles through the dynamic wheel–rail interaction relationships. The normal wheel–rail interaction is tackled by using the Hertzian contact theory, and the tangent wheel–rail interaction by the Kalker linear theory and the Shen–Hedrick–Elkins theory. A computer code is developed. A case study is performed to a continuous bridge on the planned Beijing–Shanghai high‐speed railway in China. Through input of typical seismic waves with different propagation velocities to the train–bridge system, the histories of the train running through the bridge are simulated and the dynamic responses of the bridge and the vehicles are calculated. The influences of train speed and seismic wave propagation velocity on the dynamic responses of the bridge–vehicle system are studied. The critical train speeds are proposed for running safety on high‐speed railway bridges under earthquakes of various intensities. Copyright © 2006 John Wiley & Sons, Ltd.     

Statistical analysis of the inelastic response of shear structures subjected to earthquakes

Inelastic deformations of structures subjected to strong earthquakes are commonly accepted by Aseismic Codes; some discrepancies exist in the different procedures proposed to design a structure for which the ductility demand is to be limited within acceptable values. To have a better insight into the seismic behaviour of multi-degree-of-freedom structures beyond the elastic range, the dynamic elasto-plastic response of a ten-storey shear system under two sets of artificial and recorded accelerograms is studied considering different stiffness-strength distributions and constitutive laws. Statistics of the results are presented, demonstrating the dependence of the overall and storey ductility values and of their ratio on the characteristics of the structure and excitation.     

埋地双排复合式管体结构在SH波作用下的动力分析

以波动理论为基础,采用复变函数法,给出了地下双排复合式管体结构在SH波作用下的解析解。分析了入射波角度、频率变化,管体埋深、内管的厚度变化等参数对管体动应力集中的影响。结果表明:复合式管体内侧的动应力集中峰值明显高于外侧;高频入射时,双排管体在给定距离之间的相互影响较大,动应力集中峰值向邻侧偏移;复合式管体内管越薄,动应力集中峰值越大;垂直入射时,动应力集中峰值受埋深的影响呈周期性变化。     

Random vibration analysis of long-span structures subjected to spatially varying ground motions

On the basis of the pseudo-excitation method (PEM), a random vibration methodology is formulated for the seismic analysis of multi-supported structures subjected to spatially varying ground motions. The ground motion spatial variability consists of the wave passage, incoherence and site–response effects. Advantages of this method are that less computation effort is required and that the cross-correlations both between normal modes and between excitations are automatically included. Random seismic responses of a realistic long-span bridge due to the wave passage, incoherence and site–response effects are extensively investigated. It is shown that all these effects have significant influence on the seismic response of the structure.     

Stochastic seismic response of multiply-supported secondary systems in flexible-base structures

A formulation has been proposed for the transfer function of a secondary system response while the primary system is supported on a compliant soil and the excitation comprises of translational ground motion at its base. For this purpose, the earlier formulation of the authors for the fixed-base case, which exactly considers the interaction between the two sub-systems and is based on the use of their individual modal properties, has been extended. Also, the concept of modifying the input excitation for the interaction accelerations (associated with the soil–structure interaction) has been used. An example P–S system and three example earthquake excitations have been considered to illustrate the proposed formulation and to estimate the expected response peak amplitudes in the secondary system. This study shows that ‘detuning’ of the tuned systems may occur in case of significant soil–structure interaction. Further, for the reasons of both safety and economy, ignoring the interaction effects in designing the secondary systems may not always be justified. Copyright © 1999 John Wiley & Sons, Ltd.     

Research on the random seismic response analysis for multi- and large-span structures to multi-support excitations

The pseudo excitation method(PEM) has been improved into a more practical form,on which the analytic formulae of seismic response power spectral density(PSD) of simplified large-span structural models have been derived.The analytic formulae and numerical computing results of seismic response PSD have been derived to study the mechanism of multi-support excitation effects,such as the wave-passage effect and incoherence effect,for the seismic response of multiand large-span structures.By using a multi-span truss as an example,the influence of multi-support excitation effects on the seismic response of such structures is studied.     

Stochastic seismic response analysis of hysteretic multi-degree-of-freedom structures

Analytical study of random vibration of non-linear mutli-degree-of-freedom (MDF) systems is generally difficult. This is particularly true for MDF inelastic systems due to the highly non-linear and hereditary behaviour of the restoring force. On the other hand, to obtain the response statistics using a step-by-step Monte Carlo simulation requires a large sample, and it could be very costly. The purpose of this paper is to present a practical analytical-empirical method for an MDF yielding system. The method is based on a substitute structure (SS) concept in which the SS parameters are determined from empirical results of single-degree-of-freedom systems, i.e. each element in the system is replaced by a linear counterpart with ductility-dependent stiffness and damping. Based on a linear random vibration response analysis, the statistics of the maximum response (ductility) of each element are obtained by iteration. Numerical examples are given for multi-storey buildings with deteriorating (reinforced concrete frame) or non-deteriorating (steel frame) restoring forces. Comparisons with empirical results are satisfactory qualitatively. The main advantage of this method is that it requires relatively insignificant computation time, e.g. 1 s of execution time on the IBM 360–75 system for an eight-storey steel frame.     

Optimum viscous damper for connecting adjacent SDOF structures for harmonic and stationary white‐noise random excitations

The dynamic behaviour of two adjacent single‐degree‐of‐freedom (SDOF) structures connected with a viscous damper is studied under base acceleration. The base acceleration is modelled as harmonic excitation as well as stationary white‐noise random process. The governing equations of motion of the connected system are derived and solved for relative displacement and absolute acceleration responses of connected structures. The response of structures is found to be reduced by connecting with a viscous damper having appropriate damping. For undamped SDOF structures, the closed‐form expressions for optimum damping of viscous damper for minimum steady state as well as minimum mean square relative displacement and absolute acceleration of either of the connected SDOF structures are derived. The optimum damper damping is found to be functions of mass and frequency ratio of two connected structures. Further, numerical results had indicated that the damping of the connected structures does not have noticeable effects on the optimum damper damping and the corresponding optimized response. This implies that the derived closed‐form expressions for optimum damper damping of undamped structures can also be used in practical applications for damped structures. Copyright © 2006 John Wiley & Sons, Ltd.