Decoupled dynamic analysis of combined systems by iterative determination of interface accelerations

A dynamic analysis technique is presented that can be used to determine the response of a discrete model of a large linear structural system composed of multiple substructures. The technique circumvents the costly computation of the modal characteristics of the combined system. This is accomplished by relying on a predictor-corrector scheme to converge iteratively to the interface accelerations of the combined system, while the equations of motions of the individual structures are integrated separately. In this regard, the temporal slopes of the interface accelerations (jerks) are computed at each time point of integration to predict the interface accelerations at the next time point. The proposed technique is exemplified by conducting a space shuttle landing loads analysis; the obtained numerical data demonstrate its reliability and efficiency.     

Seismic shear vibration of embankment dams in semi-cylindrical valleys

A rigorous analytical solution is developed for the lateral linear shear response of embankment dams in semi-cylindrical valleys. Closed-form algebraic expressions are presented pertaining to both free and base-induced oscillations, and extensive parametric and comparative studies elucidate the prominent effects of canyon geometry (shape and aspect ratio) on dynamic response. Harmonic steady-state as well as earthquake-induced accelerations, displacements and shear strains in the dam are studied and compared with those obtained from 3-Dimensional analyses for other canyon geometries, as well as from 2-Dimensional (2-D) analyses of the dam mid-section. It is shown that such 2-D analyses may provide significantly lower values of near-crest accelerations, but slightly higher values of shear strains and stresses than the 3-D analyses. The proposed method of analysis is at least three orders of magnitude less expensive than other presently available numerical procedures.     

Non-linear seismic response analysis using vector superposition methods

Computational algorithms based on the pseudo-force method (PFM) and the tangent spectrum method (TSM) for the seismic analysis of elasto-plastic MDOF structures by mode superposition are presented. The emphasis is put on the effect of the truncation of higher modes on the convergence of the ductility demand and energy dissipated during the earthquake. Eigenvectors and load-dependent vectors have been used in comparative analyses. Applications on a flexible 25-storey building and a stiff, 5-storey shear building indicate that, for a flexible structure, the ductility demand computed from the PFM is more sensitive to basis truncation than that computed from the TSM. However, for the stiff structure, the opposite behaviour is observed. The results indicate that the use of load-dependent vectors in inelastic analyses maintains the computational advantages found for elastic analyses in previous investigations. Although the PFM is more stable and computationally more effective than the TSM, it does not provide any information on the evolution of tangent modal properties in time that reflects dynamic response modification as the structure becomes inelastic.     

云南漾濞地震大理某高层建筑结构地震响应观测数据初步分析

2021年5月21日21时21分至22时32分,云南漾濞先后发生了M5.6级、M6.4级、M5.0级和M5.2级地震,位于大理的某高层建筑结构地震反应观测台阵获取了这4次地震的结构动力响应,观测数据同步性好,数据质量高。该高层建筑为框架剪力墙结构,地上26层,地下1层,三分量加速度测点共8个分别位于建筑的第1层、4层、7层、10层、13层、17层、20层和25层,数据实时传输至中国地震局工程力学研究所燕郊数据中心。本文对结构台阵的观测记录进行了初步分析,绘制建筑结构观测楼层的三向绝对加速度及其傅里叶幅值谱,检验数据同步性和质量,通过滤波和积分得到相对速度和相对位移,利用功率谱方法分析得到频率响应函数,并利用复模态指数函数方法得到两水平方向前三阶模态频率和振型。通过4次地震结构模态频率和振型的初步对比结果表明:主体结构基本完好,这与现场调查结果吻合。该结构台阵获取的前震、主震和余震反应记录,为后续开展深入的模态参数分析、地震损伤识别以及研究框架剪力墙结构的振动特性和抗震性能提供了宝贵数据。     

Static versus modal analysis: influence on inelastic response of multi-storey asymmetric buildings

The paper investigates the influence of design procedures on the seismic response of multi-storey asymmetric buildings. To this end, some structures are designed according to methods based on either static or modal analysis, with or without design eccentricities. The seismic response of these systems is determined by means of inelastic dynamic analyses and the design is thoroughly examined in order to explain the results of the dynamic analyses. Attention is basically focused on the ability of design methods to prevent asymmetric buildings from experiencing ductility demands much larger than those of the corresponding torsionally balanced systems. Numerical analyses underline that while design procedures based on either static or modal analysis are suitable for the design of torsionally rigid structures only those based on modal analysis lead to the satisfactory performance of torsionally flexible buildings. Furthermore, the study highlights the qualities of a design method proposed by the Authors. Its application does not require any explicit calculation of design eccentricities and leads to proper seismic response of both torsionally rigid and flexible asymmetric buildings.     

Generation of floor response spectra including oscillator-structure interaction

A method is presented for generating floor response spectra for aseismic design of equipment attached to primary structures. The method accurately accounts for tuning, interaction and non-classical damping, which are inherent characteristics of composite oscillator-structure systems. Modal synthesis and perturbation techniques are used to derive the modal properties of the composite system in terms of the known properties of the structure and the oscillator. Floor spectra are generated directly in terms of these derived properties and the input ground response spectrum using modal combination rules that account for modal correlations and non-classical damping. The computed spectra, in general, are considerably lower than conventional floor response spectra due to the effect of interaction. They provide more realistic and economical criteria for design of equipment. The method is accurate to the order of perturbation and is computationally efficient, as it avoids time-history analysis and does not require numerical eigenvalue evaluation of the composite oscillator-structure system. The results of a parametric study demonstrate the accuracy of the method and illustrate several key features of floor response spectra.     

立交桥曲线箱梁动力分析模型

提出了1种双脊骨空间有限元模型,用来模拟和分析立交桥曲线箱梁的固有振动特性和动力反应。将曲线箱梁分别看作是由空间梁或壳组成的空间结构,并分别采用分段空间直梁模型、壳元模型和实体元模型进行模拟,分析相同曲线箱梁的振动特性和地震时程反应,通过与双脊骨模型的计算结果的比较验证双脊骨模型的可靠性。初步研究了在相同曲率半径下不同跨度的曲线箱梁的固有振动特性,分析了双脊骨模型的脊骨间距、横向连接间距等参数对模型计算结果的影响。研究结果可为曲线梁桥抗震性能和地震反应分析提供参考。     

Effects of infill walls and floor diaphragms on the dynamic characteristics of a narrow‐rectangle building

Most buildings in Singapore are lightly reinforced concrete structures, which are mainly designed for gravity loading only, because Singapore is an island country located in a low‐to‐moderate seismic region. The dynamic properties of a typical high‐rise residential building with a long, narrow rectangular floor plan are studied using both experimental and numerical methods. The effects of the brick infill walls and the flexible diaphragms on the dynamic characteristics of the building are discussed in detail. The results from the ambient vibration tests are correlated with the numerical results of three different finite element models with different levels of sophistication. They include a bare frame model, a frame model with brick infill walls, and a frame model with both brick infill walls and flexible diaphragms. The dynamic properties of the third model match very well with the measured results in terms of both the natural frequencies and the mode shapes. The correlation results demonstrate the respective effects of the brick infill walls and the flexible diaphragms on the dynamic characteristics of the narrow‐rectangle building structure. Copyright © 2006 John Wiley & Sons, Ltd.     

Modal time history analysis of non-classically damped structures for seismic motions

The step-by-step modal time history integration methods are developed for dynamic analysis of non-classically damped linear structures subjected to earthquake-induced ground motions. Both the mode displacement and mode acceleration-based algorithms are presented for the calculation of member and acceleration responses. The complex-valued eigenvectors are used to effect the modal decoupling of the equations of motion. However, the recursive step-by-step algorithms are still in terms of real quantities. The numerical results for the acceleration response and floor response spectra, obtained with these approaches, are presented. The mode acceleration approach is observed to be decidedly better than the mode displacement approach in as much as it alleviates the so-called missing mass effect, caused by the truncation of modes, very effectively. The utilization of the mode acceleration-based algorithms is, thus, recommended in all dynamic analyses for earthquake-induced ground motions.     

Performance of a transparent Flexible Shear Beam container for geotechnical centrifuge modeling of dynamic problems

A transparent Flexible Shear Beam (FSB) container was designed and constructed to simulate the dynamic response of a stratum of soil under horizontal, one-dimensional (1-D) earthquake shaking in a geotechnical centrifuge. A stack of four rectangular, acrylic frames separated by layers of flexible, high-strength rubber was used to form the transparent container. The fundamental natural frequency of the container was estimated to be similar to a layer of sand in its softened or liquefied state. The suitability of the container in simulating 1-D site response with minimal boundary effects was evaluated by monitoring the uniformity of the induced accelerations and settlements across the soil specimen. Further, the measured lateral displacements were compared with equivalent-linear site response analyses. The new FSB container was found to provide satisfactory boundary conditions for studying complex Soil–Structure-Interaction problems, while simultaneously enabling researchers to visualize deformations of the soil and buried structures during shaking.     

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.     

多层选煤厂房的受振层楼板振动分析

非设备层楼板的振动问题是工程中一种易发的振动事故,本文就多层选煤厂的非设备层楼板振动问题进行了研究,探讨了楼板振动产生的机理。文中提出了非设备层楼板振动分析的两步骤法:(1)通过对局部楼板有限元模型的模态分析,来定性判断楼板是否在设备的共振区,从而对楼板是否出现共振进行初步判断;(2)采用结构-设备复合系统三维动力有限元分析模型,对非设备层楼板的动力响应进行分析。实际工程算例的分析证明了该方法的有效性和合理性,该方法为选煤厂的非设备层的楼板振动研究提供了思路。最后,本文对多层选煤厂的非设备层楼板的设计提出了一些参考建议。     

Extension of N2 method to plan irregular buildings considering accidental eccentricity

The paper deals with the topic of analyses performed according to modern code provisions, in particular Eurocode 8 (EC8) rules. Non linear static and non linear dynamic analyses of a plan irregular multi-storey r/c frame building designed according to Eurocode 2 (EC2) and EC8 provisions are carried out.The extension of the N2 method to torsionally flexible structures, as applied in previous papers, does not consider the accidental eccentricity, which is prescribed by EC8 also in the case of non linear static analysis. In this paper, three methods combining the accidental eccentricity prescribed by EC8 to the procedure which extends the N2 method to torsionally flexible structures are proposed and discussed. Each of them provides four modal response spectrum analyses (one for each model, corresponding to each position of centre of mass) and eight non linear static analyses (two signs for four models). NLSA(meth. n.2) seems to be the more reliable method of the three proposed, because it better fits absolute displacements obtained by non linear dynamic analysis.In the paper it is also observed that the value of the behaviour factor assigned by EC8 to torsionally flexible systems seems too conservative.     

Vibration control of cable-stayed bridges—part 1: modeling issues

The objective of the research presented here is to increase the understanding of how the complexities associated with modeling cable-stayed bridges, such as non-linear behaviour and the participation of highly coupled, high-order vibration modes in the overall dynamic response, affect the overall effectiveness of active control schemes. The 316-degree-of-freedom analytical model studied here is based on the Jindo Bridge located in South Korea. Computational considerations associated with control analyses require the size of the model to be significantly reduced, without loss of the important vibration characteristics and complexities. Three separate reduced-order modelling techniques for creating effective control models are studied here: the IRS method, the internal balancing method, and a modal reduction method. These methods are studied and compared on their ability to capture the complex dynamic response of cable-stayed bridges subjected to multiple-support excitation and their ability to create viable and computationally sound state-space models for control analyses. Results show that the modal reduction technique, because of the ability to select only those modes causing the largest force and displacement response, is most effective for control applications. © 1998 John Wiley & Sons, Ltd.     

Modal analysis of circular flexible foundations under vertical vibration

A methodology using modal analysis is presented to evaluate dynamic displacements of a circular flexible foundation on soil media subjected to vertical vibration. The interaction effects between the foundation and the underlying soil are represented using modal soil impedance functions determined by an efficient procedure developed. The displacements of the foundation can then be easily solved by modal superposition. Comparing with existing solutions, the presented method is found to provide accurate results with less computational effort using only a few vibration modes. In addition, parametric studies for modal responses of the flexible foundation indicate that the response of the foundation are significantly influenced by relative stiffness between the foundation and the soil medium, load distributions, vibration frequency range, and the foundation mass. Besides, justification for flexible foundations to be considered as rigid are investigated.     

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.     

Evaluation of predictors of non‐linear seismic demands using ‘fishbone’ models of SMRF buildings

Predictors (or estimates) of seismic structural demands that are less computationally time‐consuming than non‐linear dynamic analysis can be useful for structural performance assessment and for design. In this paper, we evaluate the bias and precision of predictors that make use of, at most, (i) elastic modal vibration properties of the given structure, (ii) the results of a non‐linear static pushover analysis of the structure, and (iii) elastic and inelastic single‐degree‐of‐freedom time‐history analyses for the specified ground motion record. The main predictor of interest is an extension of first‐mode elastic spectral acceleration that additionally takes into account both the second‐mode contribution to (elastic) structural response and the effects of inelasticity. This predictor is evaluated with respect to non‐linear dynamic analysis results for ‘fishbone’ models of steel moment‐resisting frame (SMRF) buildings. The relatively small number of degrees of freedom for each fishbone model allows us to consider several short‐to‐long period buildings and numerous near‐ and far‐field earthquake ground motions of interest in both Japan and the U.S. Before doing so, though, we verify that estimates of the bias and precision of the predictor obtained using fishbone models are effectively equivalent to those based on typical ‘full‐frame’ models of the same buildings. Copyright © 2003 John Wiley & Sons, Ltd.     

Damping‐adjusted combination rule for the response spectrum analysis of base‐isolated buildings

The classical response spectrum method continues to be the most popular approach for designing base‐isolated buildings, therefore avoiding computationally expensive nonlinear time‐history analyses. In this framework, a new method for the seismic analysis and design of building structures with base isolation system (BIS) is formulated and numerically validated, which enables one to overcome the main shortcomings of existing techniques based on the response spectrum method. The main advantages are the following: first, reduced computational effort with respect to an exact complex‐valued modal analysis, which is obtained through a transformation of coordinates in two stages, both involving real‐valued eigenproblems; second, effective representation of the damping, which is pursued by consistently defining different viscous damping ratios for the modes of vibration of the coupled BIS‐superstructure dynamic system; and third, ease of use, because a convenient reinterpretation of the combination coefficients leads to a novel damping‐adjusted combination rule, in which just a single response spectrum is required for the reference value of the viscous damping ratio. The proposed approach is specifically intended for design situations where (i) the dynamic behaviour of seismic isolators can be linearised and (ii) effects of nonproportional damping, as measured by modal coupling indexes, are negligible in the BIS‐superstructure assembly. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis of biodegradation in a 3-D heterogeneous porous medium using nonlinear stochastic finite element method

Probabilistic analysis by Monte Carlo Simulation method (MCSM) is a computationally prohibitive task for a reactive solute transport involving coupled PDEs with nonlinear source/sink terms in 3-D heterogeneous porous media. The perturbation based stochastic finite element method (SFEM) is an attractive alternative method to MCSM as it is computationally efficient and accurate. In the present study SFEM is developed for solving nonlinear reactive solute transport problem in a 3-D heterogeneous medium. Here the solution of the biodegradation problem involving a single solute by a single class of microorganisms coupled with dynamic microbial growth is attempted using this method. The SFEM here produces a second-order accurate solution for the mean and a first-order accurate solution for the standard deviation of concentrations. In this study both the physical parameters (hydraulic conductivity, porosity, dispersivity and diffusion coefficient) and the biological parameters (maximum substrate utilization rate and the coefficient of cell decay) are considered as spatially varying random fields. A comparison between the MCSM and SFEM for the mean and standard deviation of concentration is made for 1-D and 3-D problem. The effects of heterogeneity on the degradation of substrate and growth of biomass concentrations for a range of variances of input parameters are discussed for both 1-D and 3-D problems.     

PART I: Theoretical Site Response Estimation for Microzoning Purposes

— We estimate the theoretical site response along seven cross sections located in the city of Thessaloniki (Greece). For this purpose the 2-D structural models used are based on the known geometry and the dynamic soil properties derived from borehole measurements and other geophysical techniques. Several double-couple sources have been employed to generate the seismic wavefield, and a hybrid method that combines the modal summation with finite differences, has been deployed to produce synthetic accelerograms to a maximum frequency of 6 Hz for all components of motion. The ratios between the response spectra of signals derived for the 2-D local model and the corresponding spectra of signals derived for the 1-D bedrock reference model at the same site, allow us to estimate the site response due to lateral heterogeneities. We interpret the results in terms of both geological and geometrical features of the models and of the characteristics of the wave propagation. The cases discussed confirm that the geometry and depth of the rock basement, along with the impedance contrast, are responsible for ground amplification phenomena such as edge effects and generation and entrapment of local surface waves. Our analysis also confirms that the peak ground acceleration is not well correlated with damage and that a substantially better estimator for possible damage is the spectral amplification.