Experimental study on interaction between membrane structures and wind environment

The interaction between membrane structures and their environment can be either static or dynamic. Static interaction refers to interaction with static air, while dynamic interaction refers to wind and its effects. They can be evaluated by two parameters, added mass and radiation /aerodynamic damping, which are experimentally investigated in this study. The study includes the effects of both the static and dynamic interaction on structural dynamic characteristics, and the relationship between the interaction parameters and the covered area of a membrane structure for the static interaction and the relationship between the interaction parameters and wind direction and speed for the dynamic interaction. Experimental data show that the dynamic interaction is strongly correlated with the structural modes, i.e., the interaction of the symmetric modes is much larger than the anti-symmetric modes; and the influence of the dynamic interaction is significant in wind-induced response analysis and cannot be ignored. In addition, it is concluded that the structural natural frequency is remarkably decreased by this interaction, and the frequency band is significantly broadened.     

Frequency dependent ritz vectors

In order to reduce the size of problems involving analysis of the dynamic response of structural systems, a transformatio based on appropriately selected Ritz shapes is commonly employed. The lower mode shapes may at times serve a effective Ritz shapes. However, the computation of mode shapes is a time consuming task; in addition, the mode shapes may not form the best basis for representing the spatial distribution of loads. The recently developed load dependent vectors, which are derived from a static solution for the applied loads, address some of the problems inherent in the use of mode shapes. However, both the natural mode shapes and the load dependent vectors fail to account for the frequency content of the loading, a parameter that may influence strongly the response, particularly for loading with a high frequency content. A procedure is presented here for the generation of frequency dependent vectors. A combination of load dependent and frequency dependent vectors will often form a very efficient basis for the representation of the response, as illustrated by several examples presented here.     

On the stability of colonnade structural systems under static and dynamic loading conditions

The structural behavior of colonnade structural systems subjected to static and dynamic loading is investigated to identify the main factors affecting the stability and to improve our understanding of their behaviour. In particular, the discrete element method of analysis is utilised to study the static and dynamic behaviour of a typical section of the two storey colonnade of the Forum in Pompeii. Static analysis indicated that the failure of colonnade structures occur at higher friction angles as the weight above the structure decreases and so a sudden collapse can occur when parts of the monument are disassembled. For the dynamic analysis, the mechanical behavior of the colonnade was investigated for both harmonic and real seismic excitations. For excitations with relatively low dominant frequencies, the primary response is rocking; as the excitation frequency increases, the response becomes more complicated demonstrating both sliding and rocking movements. It was also shown that the construction methods used in ancient times, such as multi-block segmented trabeations and solid block beam, have quite significant impact on the mechanical response of the structures under static and dynamic loading.     

Mode acceleration-based response spectrum approach for nonclassically damped structures

The paper describes the development of a mode accleration-based response spectrum approach for calculating the seismic design response of the nonclassically damped structures. The response is divided into a pseudo-static part and a dynamic part. The pseudo-static part is calculated by a simple static analysis of the structure for the inertial forces, induced by a unit ground acceleration, applied statically. The dynamic part, of course, pends upon the dynamic characteritics of the structure which are defined in terms of the complex-valued modal characteristics. The correlation between the pseudo-static and dynamic components is properly considered. The design ground input in this approach is defined in terms of the relative acceleration and relative velocity response spectra. The proposed approach has the desired attribute of the mode acceleration approach as the response can be accurately calculated even if only a first few modes are used in the analysis. The approach is computationally more efficient than the convenionally used mode displacement approach. The applicability of the approach is verified by numerical simulation results.     

Static and dynamic stiffness measurements with Opalinus Clay

In this work, an experimental study was carried out with the aim of reconciling static and dynamic stiffness of Opalinus Clay. The static and dynamic stiffness of core plugs from a shaly and a sandy facies of Opalinus Clay were characterized at two different stress states. The measurements included undrained quasi-static loading–unloading cycles from which the static stiffness was derived, dynamic stiffness measurement at seismic frequencies (0.5–150 Hz) and ultrasonic velocity measurements (500 kHz) probing the dynamic stiffness at ultrasonic frequencies. The experiments were carried out in a special triaxial low-frequency cell. The obtained results demonstrate that the difference between static and dynamic stiffness is due to both dispersion and non-elastic effects: Both sandy and shaly facies of Opalinus Clay exhibit large dispersion, that is, a large frequency dependence of dynamic stiffness and acoustic velocities. Especially dynamic Young's moduli exhibit very high dispersion; between seismic and ultrasonic frequencies they may change by more than a factor 2. P-wave velocities perpendicular to bedding are by more than 200 m/s higher at ultrasonic frequencies than at seismic frequencies. The static undrained stiffness of both sandy and shaly facies is strongly influenced by non-elastic effects, resulting in significant softening during both loading and unloading with increasing stress amplitude. The zero-stress extrapolated static undrained stiffness, however, reflects the purely elastic response and agrees well with the dynamic stiffness at seismic frequency.     

Higher mode effects in frame pin‐supported wall structure by using a distributed parameter model

Frame pin‐supported wall structure is a kind of rocking structure, which releases constraints at the bottom of the wall. The wall is affiliated to the frame and can rotate around the hinge. Previous studies have investigated seismic performance (such as deformation pattern and plastic hinge distribution) of frame pin‐supported wall structure. Strength demand of this system was investigated through static pushover analysis. However, dynamic characteristics, especially higher mode effects, remain to be quantified. As demonstrated in several researches, higher mode effects have non‐negligible effects on seismic response. For this purpose, a distributed model for analyzing higher mode effects in frame pin‐supported wall structure was proposed, where the pin‐supported wall and the frame were simplified as a bending beam and a shear beam, respectively. The model was solved by differential equations derived from equilibrium and compatibility. Displacement and inner force distribution of frame pin‐supported wall structure in higher modes were quantified according to the model. Influence of critical parameters, such as wall stiffness and structure period, was assessed on higher mode effects. It was demonstrated that response in higher modes cannot be neglected in the design of frame pin‐supported wall structure. Capacity design based on the fundamental mode is not conservative, especially in the wall. Furthermore, pin‐supported walls tend to force the frame to vibrate in the rocking mode and suppress higher mode effects in the frame. Copyright © 2016 John Wiley & Sons, Ltd.     

Modal methods in the dynamics of systems with non-classical damping

When damping in a system is both significantly high and its distribution is non-classical the solution of dynamical problems by conventional modal analysis is complicated by the presence of coupling between the normal co-ordinates. Further, the convergence of a solution may be erratic with successive modal additions, leading to the need to include a larger number of modes than would otherwise be expected. In this paper methods of modal analysis in structural dynamics are discussed and their derivations briefly given. These include the conventional mode displacement method and the force summation method, employing normal modes, and the analogous procedures with damped modes. In the latter, dynamic response equations are not coupled. Dynamic loading solutions by the four approaches, each taking account of the non-classical damping distribution, are demonstrated with a simple model representing a structure on a compliant foundation. The results strongly suggest that the use of damped modes with force summation could be the most effective procedure when damping is non-classical.     

Higher-mode effect on the seismic responses of buildings with viscoelastic dampers

In conventional modal analysis procedures, usually only a few dominant modes are required to describe the dynamic behavior of multi-degrees-of-freedom buildings. The number of modes needed in the dynamic analysis depends on the higher-mode contribution to the structural response, which is called the higher-mode effect. The modal analysis approach, however, may not be directly applied to the dynamic analysis of viscoelastically damped buildings. This is because the dynamic properties of the viscoelastic dampers depend on their vibration frequency. Therefore, the structural stiffness and damping contributed from those dampers would be different for each mode. In this study, the higher-mode effect is referred to as the response difference induced by the frequency-dependent property of viscoelastic dampers at higher modes. Modal analysis procedures for buildings with viscoelastic dampers distributed proportionally and non-proportionally to the stiffness of the buildings are developed to consider the higher-mode effect. Numerical studies on shear-type viscoelastically damped building models are conducted to examine the accuracy of the proposed procedures and to investigate the significance of the higher-mode effect on their seismic response. Two damper models are used to estimate the peak damper forces in the proposed procedures. Study results reveal that the higher-mode effect is significant for long-period viscoelastically damped buildings. The higher-mode effect on base shear is less significant than on story acceleration response. Maximum difference of the seismic response usually occurs at the top story. Also, the higher-mode effect may not be reduced by decreasing the damping ratio provided by the viscoelastic dampers. For practical application, it is realized that the linear viscous damping model without considering the higher-mode effect may predict larger damper forces and hence, is on the conservative side. Supported by: Science Council, Chinese Taipei, grant no. 88-2625-2-002-006     

Method for solving dynamic equilibrium equations based on displacement excitation

Mode superposition is a widely used method for solving the dynamic equilibrium equation in structural dynamic analysis. However, the accuracy of this method may be reduced when the dynamic equilibrium equations are set up using displacement excitation. A new method for developing solutions for dynamic equilibrium equations based on displacement excitation is introduced. The dynamic equilibrium equation is decomposed into two parts, namely displacement excitation and velocity excitation, and precise integration and mode superposition methods are combined to solve the equation. Ritz vectors are then used to calculate the static response of the truncated modes of the structure, and a method for determining the number of participating modes is obtained. Using multi-degree-of-freedom systems as two computational examples, the differences in the structural responses obtained from the displacement excitation and acceleration excitation are compared and analyzed. It is shown that the new solution method generates consistent accuracy between the displacement excitation and acceleration excitation.     

应力、应变控制下压实黄土动力特性研究

基于动三轴试验研究了不同围压条件下,加载控制方式对压实黄土动应力应变关系的影响规律,对比了不同控制方式下压实黄土的动应力应变时程曲线的差异。研究表明:压实黄土的动应力应变关系符合双曲线模型;加载控制方式不会改变压实黄土骨干曲线的类型,但会显著影响拟合参数的大小。相同围压下,采用应变控制测定的初始动模量较小;随着围压的增大,应变控制下初始动模量随围压的增长速率反而越小,二者之间的差距越来越大。应力控制和应变控制加载过程中,动模量在某一振级下随着动循环次数的增加而逐渐衰减,且应力控制方式下衰减的幅度较大。对于土体结构受力较为敏感的原状土,使用应变控制加载方式可能会获得更为准确的试验结果。     

伸缩缝刚度对大跨度悬索桥动力特性的影响

伸缩缝作为大跨度桥梁与引桥之间的重要连接构件,其抗推刚度及可能存在的变异性对主桥及引桥动力特性的影响不可忽略。本文建立了大跨度悬索桥及引桥的有限元模型,采用弹簧单元模拟加劲梁与引桥箱梁之间的伸缩缝,分析伸缩缝刚度对悬索桥及引桥自振特性及其地震响应的影响规律。分析结果表明:伸缩缝刚度对加劲梁的横弯振型、竖弯与纵飘耦合振型的频率有明显的影响;伸缩缝刚度的变化会导致加劲梁与引桥的振型相互耦合,同时这些振型的频率发生相应的突变,当伸缩缝刚度较大时,加劲梁两个竖弯与纵飘的耦合振型解耦成为独立的竖弯和纵飘振型;当引桥与悬索桥加劲梁的纵飘振型发生耦合时,在纵向和竖向地震作用下的悬索桥及引桥的地震响应达到最小。伸缩缝刚度对悬索桥动力特性影响的分析可为悬索桥的模态参数确认、损伤识别、抗震性能分析提供有价值的借鉴。     

弦支穹顶结构动力反应分析

以天津开发区商务中心大堂的弦支穹顶为研究对象,分析了弦支穹顶结构体系的自振特性,分别运用随机模拟风振分析方法和时间历程分析方法,对其进行了风振和地震反应分析,得到了结构在动力荷载作用下的响应时程,并对分析结果进行了频谱分析和统计分析。研究发现弦支穹顶结构的自振频率呈密集型分布,且振型复杂;结构的风振响应基本以受迫振动为主,没有出现明显的峰值共振现象;结构的地震响应在前几阶基频处出现了较为明显的峰值共振现象;从振动的幅值角度看,风荷载的动力作用效应相对于地震荷载要显著。     

Extension of modal pushover analysis to seismic assessment of bridges

Nonlinear static (pushover) analysis has become a popular tool during the last decade for the seismic assessment of buildings. Nevertheless, its main advantage of lower computational cost compared to nonlinear dynamic time‐history analysis (THA) is counter‐balanced by its inherent restriction to structures wherein the fundamental mode dominates the response. Extension of the pushover approach to consider higher modes effects has attracted attention, but such work has hitherto focused mainly on buildings, while corresponding work on bridges has been very limited. Hence, the aim of this study is to adapt the modal pushover analysis procedure for the assessment of bridges, and investigate its applicability in the case of an existing, long and curved, bridge, designed according to current seismic codes; this bridge is assessed using three nonlinear static analysis methods, as well as THA. Comparative evaluation of the calculated response of the bridge illustrates the applicability and potential of the modal pushover method for bridges, and quantifies its relative accuracy compared to that obtained through other inelastic methods. Copyright © 2006 John Wiley & Sons, Ltd.     

考虑坝体材料非线性的混凝土拱坝地震反应分析

本文基于可信概率水准的破坏性强震作用,针对小湾高拱坝进行了考虑坝体材料非线性的拱坝地震反应分析。在分析模型中,同时考虑了无约束域地震能量辐射效应和近域地基材料非均匀性的影响。为了实现非线性条件下的静、动力组合分析,利用显式有限元结合修正的黏弹性人工边界的开放系统时域静、动力统一分析方法进行了求解,对在自重作用下的初始静力解计算采用了动力松弛技术。     

Results from field testing A curved box girder bridge using simulated earthquake loads

This paper presents the results of a unique field test on a curved highway overpass. In the test, large horizontal loads were applied to the superstructure of the bridge and quickly released, causing the bridge to vibrate. The resulting large-amplitude vibrations were intended to be similar to the vibrations caused by earthquakes (horizontal accelerations of up to 25 per cent of gravity were measured on the bridge deck). Well-defined lateral, longitudinal, vertical and torsional vibration modes were identified from the test data. The vibration modes were used to verify an analytical model of the bridge's dynamic response. For this paper, the model was verified using only the fundamental vibration mode, which was primarily a horizontal vibration mode. Using a system identification procedure, the dynamic response model was adjusted until its frequency and mode shape matched the measured frequency and mode shape. Parameters in the verified model were compared with the same parameters calculated from information in the structural drawings. Because the fundamental mode represents a horizontal mode, the bridge parameters identified in this paper were those parameters which strongly influence the horizontal response of the bridge.     

Higher modes in simplified inelastic seismic analysis of single column bent viaducts

The influence of the higher modes and their consideration in the pushover analysis of reinforced concrete single column bent viaducts with different degree of irregularity is discussed. Typical multimode pushover‐based methods (modal pushover analysis, modal adaptive non‐linear static procedure and incremental response spectrum analysis) are addressed and compared with a single mode procedure (N2) and inelastic time history analysis. If in the transverse direction the substructure of the viaduct is flexible in comparison with the superstructure, the influence of higher modes is small (the structure is regular) and single mode procedure works well. This typically occurs when the columns are high or considerably damaged. Conversely, for the analysis of irregular structures having short and slightly damaged columns, the multimode methods are needed. In most cases, all the analysed multimode pushover‐based methods have given the results comparable with time history analysis, with the exception of cases where torsional sensitivity is varying during the response. All the methods have limitations (discussed in detail in the paper), which should be fully recognized by the user. Copyright © 2005 John Wiley & Sons, Ltd.     

System identification of linear structures based on Hilbert–Huang spectral analysis. Part 2: Complex modes

A method, based on the Hilbert–Huang spectral analysis, has been proposed by the authors to identify linear structures in which normal modes exist (i.e., real eigenvalues and eigenvectors). Frequently, all the eigenvalues and eigenvectors of linear structures are complex. In this paper, the method is extended further to identify general linear structures with complex modes using the free vibration response data polluted by noise. Measured response signals are first decomposed into modal responses using the method of Empirical Mode Decomposition with intermittency criteria. Each modal response contains the contribution of a complex conjugate pair of modes with a unique frequency and a damping ratio. Then, each modal response is decomposed in the frequency–time domain to yield instantaneous phase angle and amplitude using the Hilbert transform. Based on a single measurement of the impulse response time history at one appropriate location, the complex eigenvalues of the linear structure can be identified using a simple analysis procedure. When the response time histories are measured at all locations, the proposed methodology is capable of identifying the complex mode shapes as well as the mass, damping and stiffness matrices of the structure. The effectiveness and accuracy of the method presented are illustrated through numerical simulations. It is demonstrated that dynamic characteristics of linear structures with complex modes can be identified effectively using the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.     

Earthquake response of tension-leg-platforms in steady currents

Dynamic response of tethers of tension-leg-platforms to current and horizontal earthquake excitations is investigated. The static deflected shape of tether under a steady current is firstly identified. Next dynamic analysis for earthquake input is carried out for this deflected tether. The fluid loading due to surrounding water is included in the analysis as an added mass term and a hydrodynamic damping term. The tether is discretized by lumping masses at selected nodes. The platform is represented by a mass at the top end of the tether. The effect of pretension in the tether is taken into account in the form of a geometric stiffness term. At each node three degrees of freedom corresponding to surge, heave and pitch motion are considered. As the vibration modes and hence the responses are likely to be affected by the foundation characteristics, the study is extended to include the dynamic soil–structure interaction. The dynamic equations of motion for the tether–pile–soil system are derived using the substructure method. The natural frequencies and the vibration mode shapes of the total system are determined by eigenvalue analysis. The input ground acceleration is represented by Tajimi–Kanai's power spectrum for stationary conditions. The response analysis is carried out using the frequency-domain random-vibration approach. The coupled axial and lateral responses are evaluated for horizontal ground excitations. Numerical results indicate that the horizontal displacements of the tether increase with the input ground acceleration, but are nearly equal for all the cases of current velocities considered in the study; the vertical displacements however increase rapidly with the increase in current velocity. For the model considered in the present study, the responses are reduced when soil–structure interaction is included in the analysis.     

Using accidental eccentricity in code-specified static and dynamic analyses of buildings

The differences between the increase in building response due to accidental eccentricity predicted by code-specified static and dynamic analyses are studied for symmetric and unsymmetric single and multistorey buildings. The increase in response computed from static analysis of the building is obtained by applying the equivalent static forces at distance e_a, equal to the storey accidental eccentricity, from the centre of mass at each floor. Alternatively, this increase in response is computed by dynamic analysis of the building with the centre of mass of each floor shifted through a distance e_a from its nominal position. A parametric study is performed on single-storey systems in order to evaluate the differences in response predicted by both analysis procedures. It is shown that these results are essentially the same as the ones obtained for a special class of multistorey systems. Upper and lower bounds for the differences in response computed from static and dynamic analyses are obtained for general multistorey systems. These differences in response depend primarily on the ratio of the fundamental torsional and lateral frequencies of the building. They are larger for small values of the frequency ratio and decrease to zero as the frequency ratio becomes large. Further, these discrepancies are in many cases of the same order as the code-intended increase in response due to accidental eccentricity. This implies that the code-specified static and dynamic analyses to account for accidental torsion should be modified to be mutually consistent.     

An improved response spectrum method for calculating seismic design response. Part 2: Non-classically damped structures

A response spectrum method which combines the analytical advantage of the mode acceleration formulation and the practical advantage of the mode displacement formulation is developed for seismic response calculation of non-classically damped structures. It reduces the error associated with the truncation of the high frequency modes without explicitly using them in the analysis. The method is especially effective for calculating the response of stiff structural systems and also for calculating the response quantities which are strongly affected by high frequency modes. Even with flexible structures, it is shown to provide more accurate response results than the results obtained with the mode displacement approach.