Higher Mode Response Research Articles

Proposal for vertical distribution of seismic design load and equivalent isolation ratio for seismically isolated buildings with multiple types of dampers: Vertical distribution of seismic design load for seismically isolated buildings corresponding to diversity of seismic isolation devices, part 2

AbstractAs previously reported, we have proposed a vertical distribution of seismic design load for seismically isolated buildings (SIBs) corresponding to diversity of seismic isolation devices such as hysteretic dampers and velocity‐dependent dampers. This proposed seismic design load is obtained from the relationship between response amplification caused by higher mode responses and the isolation ratio which represents structural characteristics of SIBs. In this paper, we build a concept of the equivalent isolation ratio which has applicability to various dampers in order to simplify an evaluation formula of vertical distribution of seismic design load. Moreover, an effect of the combined application of various dampers on vertical distribution of shear force coefficient of SIBs is analyzed on the basis of the equivalent isolation ratio.

Flow-induced response and wake characteristics of a flexible splitter plate attached to a circular cylinder in laminar flow

This paper reported the numerical results of the flow past a flexible splitter plate attached to the rear of a rigid circular cylinder at a low Reynolds number of 160. The finite-volume method (FVM) in OpenFOAM-9 and the finite-element method (FEM) in deal.ii are utilized to solve the fluid and solid domains of the fluid–structure interaction (FSI) issue, respectively. The effects of the plate length L/D and normalized Young's modulus E* are examined. According to the equilibrium position and bending deformation order, five response modes are identified, including the symmetry-I, symmetry-II, symmetry-III, bifurcation-I, and bifurcation-II. The amplitude of the plate-tip is enhanced as the vortex shedding frequency approaches the natural frequency. Nevertheless, the bifurcation is observed between the symmetry-I and symmetry-II modes, where the vibration amplitude sharply drops. The number of local vortices occurring along the surface of flexible plate increases with the plate length, leading to more local negative pressure regions. Consequently, the higher mode response is excited. The greater shear stress occurs at the position of small curvature radius during the plate deformation. The 2S (a pair of vortices is alternately shed per cycle) vortex shedding mode is recognized in most cases. In contrast, the P + S (a pair of vortices shedding from one side and a single vortex shedding from the other side) mode is observed in the bifurcation-II mode with a relatively large amplitude. Due to the deflection, the wake flow becomes asymmetrical with a significant elongation of the recirculation region. Four interaction behaviors between the boundary layers and the plate are identified. The significant reduction of hydrodynamic forces is achieved when the flexible plate experiences the bifurcation.

Evaluating the impact of higher-mode and inelastic dynamic responses of concrete frames on the performance of seismic intensity measures

The accuracy of seismic risk-based evaluation depends on the selected seismic intensity measures (IMs). The performance of the selected IM is commonly assessed based on efficiency and sufficiency criteria, which reflect the ability of the IM to reduce epistemic uncertainty and avoid bias, respectively. Although various characteristics of structural dynamic response affect IM performance to different extents, the current literature determines IM suitability based on the overall response. This study examines the impact of two dynamic response characteristics, namely higher-mode effect and nonlinearity, on the efficiency and sufficiency of a comprehensive set of common and advanced IMs. Two correlation-based measures are then proposed to explicitly evaluate the effect of higher-mode effect and nonlinearity using statistical tests. The results show that the developed statistical measures can explain the inefficiency and insufficiency of an IM based on dynamic characteristics of response. In addition, while the IM’s efficiency and sufficiency changes for different structures and ground motion sets, vector-valued and energy-based scalar IMs provide more consistent performance. Lastly, the impact of higher-mode response and nonlinearity is more pronounced on IMs efficiency than IM sufficiency.

Seismic design and parametric study of steel modular frames with distributed seismic resistance

Structures in modular buildings typically have some unique characteristics as compared with conventional structures, e.g., discrete connection of modules through inter-module connections, discontinuous floor diaphragms. The behavior of steel modular structures under earthquake excitations has not been fully understood, and no seismic design method specifically tailored for modular building structures is available. Moreover, although various inter-module connections with different rotational connectivity have been proposed, their suitability for seismic application is questionable. In this paper, the distributed seismic design method, which makes use of the lateral resistance inherent in all modules, was proposed for modular buildings with steel frames. A numerical parametric study was conducted on a 9-story prototype building. The effect of three parameters, i.e., the rotational stiffness of inter-module connections, the seismic design force level, and the height-wise distribution of the design base shear, were studied. The results show that the rotational stiffness of inter-module connections has limited impact on the elastic lateral stiffness and the fundamental period of modular steel frames. However, in the inelastic range, the increase in the rotational stiffness will lead to less plastic drift concentration and better collapse prevention performance. Increasing the seismic design force may not result in enhanced collapse prevention performance, as it is also dependent on the height-wise distribution of the design base shear and if significant higher-mode response is involved in the total response of the structure.

Steel flexure and shear yielding base-mechanism for enhanced seismic resilience of RC core wall high-rise structures

As a result of rapid urbanization worldwide, there is an increasing demand for high-rise buildings, creating an acute need for more resilient tall structures, especially in regions of high seismicity. One of the main challenges facing design engineers is that buildings become increasingly susceptible to higher-mode effects as they become taller. Although current design practices typically achieve life-safety and collapse-prevention during major earthquake events, there is often extensive structural and non-structural damage, in great part exacerbated by the contribution of higher-mode responses. This article proposes a novel system involving a flexure and shear yielding base-mechanism, designed to limit both the first mode and higher-mode responses of a 42-story benchmark structure. These concepts only make use of well-defined buckling restrained steel braces, which have been extensively tested over many decades now and are currently implemented widely in buildings, to achieve the desired shear and flexural base yielding mechanisms. Nonlinear three-dimensional (3D) models developed in ABAQUS were used to validate key elements while models of the benchmark structure and base-mechanism were developed in ETABS to perform Nonlinear Time-History Analyses (NLTHA) for three hazard levels to investigate the global seismic response of the proposed system. Improvements among key seismic response parameters are observed at all hazard levels. By concentrating inelastic demands in the dedicated base steel yielding braces in the proposed system, quick inspection and potential repair after a major earthquake can be achieved with reduced disruptions to the use and operation of the building above.

Numerical investigation of VIV responses of the flexible riser system modelled as tensioned cable subjected to shear flow

The crossflow vortex-induced vibration (VIV) responses of the tensioned cable subjected to the sheared flow velocity profile are investigated numerically using the wake oscillator model. A comparative study is carried out on the VIV response characteristics between the tensioned cable and beam with an aspect ratio (L/D) of 3000. The study was conducted on tensioned cable having different L/D of 2000 and 3000 achieved by varying both diameter and length of the cable. The effect of top tension on the RMS crossflow displacement responses is investigated. The RMS crossflow displacement response is not sensitive to the boundary conditions for the flexible cylinder modeled as a tensioned cable. In contrast, the RMS crossflow displacement response of the lower L/D flexible cylinder modeled as a beam is sensitive to boundary conditions. The standing wave response pattern is observed for the beam with L/D of 500. The standing and traveling wave response patterns are combined for the tensioned cable with L/D = 500. Unlike finite tensioned beams, the higher mode responses are obtained even in the lower aspect ratio for tensioned cables.

An improved capacity design procedure incorporating the effect of gap-opening on higher mode responses in rocking wall structures

An improved capacity design procedure incorporating the effect of gap-opening on higher mode responses in rocking wall structures

Pseudo-double impulse for simulating critical response of elastic-plastic MDOF model under near-fault earthquake ground motion

A pseudo-double impulse (PDI) is proposed as an extension of the ordinary double impulse (DI) as a substitute of a one-cycle sine wave. PDI is treated as a set of impulsive lateral forces while the ordinary DI was introduced as an impulsive ground acceleration. The deformation and acceleration responses of multi-degree-of-freedom (MDOF) models under DI largely exceed those under the corresponding one-cycle sine wave as a main part of a near-fault ground motion. This is because DI has multiple frequency components and the higher-mode responses are excited. While the influence coefficient vector of the ordinary DI consists of 1 at every component, the influence coefficient vector of PDI is set to be proportional to the undamped fundamental natural mode. Therefore, the fundamental-mode response is mainly excited and the higher-mode responses are hardly excited by PDI. The displacement responses, the velocity responses and the input energy under DI and those under PDI are derived here for both elastic proportionally and non-proportionally damped MDOF models. The critical timing under PDI is also derived. The critical timing can be obtained by the time-history response analysis without repetition. It is demonstrated through the time-history response analysis that the distributions of interstory drifts and floor accelerations under the critical PDI correspond well to those under the critical one-cycle sine wave. Moreover, it is shown that, as far as the input level is large, the critical input period of PDI and that of the one-cycle sine wave correspond well. Since this procedure is not limited to elastic models, the proposed procedure helps to efficiently estimate the critical responses under the one-cycle sine wave for elastic-plastic MDOF models. Finally, the responses under recorded near-fault ground motions are compared with those under PDI. It is shown that the correspondence of the response under PDI and that under the recorded ground motions is fairly good although recorded ground motions are not always critical inputs for elastic-plastic MDOF models.

A Framework with reduced computational burden for Seismic Fragility Assessment of Reinforced Concrete Buildings in High-Intensity Seismic Zones

The current research is targeted to develop the analytical fragility relationships of reinforced concrete (RC) buildings in high-intensity seismic zones by considering the effects of higher structural modes to reduce the computational effort. A new framework is presented in the study to assess the vulnerability in terms of the fragility relationships that can consider the modal response of individual modes in a building structure. The developed methodology considers the uncoupled modes of a structure employing a nonlinear single degree of freedom structures and defines distinct limit states for each mode separately. By using the presented methodology, the response of higher modes can be incorporated in the fragility assessment. For elucidation, a two-story reinforced concrete (RC) school building structure is selected from seismic zone 4 of Pakistan. In the first place, its vulnerability is assessed by developing fragility relationships using dynamic response history analysis of full three Dimensional nonlinear analytical models, subsequently, the fragility relationships are developed using the presented methodology by considering the first two modes of the structure. Afterward, a comparison has been made between the developed fragility curves from both of the methodologies. The results prove the effectiveness, swiftness, and the simplicity of the established methodology for carrying out the vulnerability assessments without compromising any accuracy. The developed framework reduces the computational time of one calculation cycle from 72 h for conventional methods to merely 4 h using a regular computer.

Shake table test of a two‐story steel building seismically retrofitted using gravity‐controlled rocking braced frame system

AbstractThis article describes a shake table test program that was conducted to investigate the seismic behavior of a half‐scale two‐story gravity‐controlled rocking braced steel frame building. In this system, braced frame columns are designed to uplift from the foundation under severe earthquakes to reduce the seismic force demands on the frame members. Self‐centering capacity is solely provided by the gravity loads carried by the rocking frame. Energy dissipative devices are added at the base of the braced frame columns to control drifts. The system can be used for new structures as well as the retrofit of seismically deficient structures. In the test program, the specimen represented a gravity‐controlled rocking frame that had been proposed for seismic retrofit in a previous study. The test structure was subjected to ground motions expected for two site classes in two seismically active regions in Canada. Three different energy dissipative devices located at the rocking interface were studied: friction, friction spring dampers, and steel bars yielding in tension and elastically buckling in compression. The focus of the tests was on peak axial loads in the columns and additional moments and shears in the beams resulting from column impact upon rocking. Axial loads in the braces and columns from higher mode response were also examined. The tests revealed significant increases in beam forces due to column impacts. Large axial forces due to the second vibration mode response were measured in the second story braces. A numerical model is proposed to accurately predict the measured force demands.

Vortex-induced vibrations of a flexible cylinder at subcritical Reynolds number

Abstract

Approximate Analysis for Shear Force Amplification Effect in Ordinary RC Shear Walls

An approximate analysis method is proposed to predict the dynamic amplification of shear forces in ordinary reinforced concrete shear walls as a preliminary study. First, a seismic design for three groups of ordinary reinforced concrete shear walls higher than 60 m was created on the basis of nonlinear dynamic analysis. Causes for the dynamic amplification effect of shear forces were investigated through a detailed evaluation of the nonlinear dynamic analysis result. A new modal combination rule was proposed on the basis of that observation, in which fundamental mode response and combined higher mode response were summed directly. The fundamental mode response was approximated by nonlinear static analysis result, while higher mode response was computed using response spectrum analysis for equivalent linear structural models with the effective stiffness based on the nonlinear dynamic analysis result. The proposed approximate analysis generally predicted vertical distribution of story shear and shear forces of individual walls from the nonlinear dynamic analysis with comparable accuracy.

Effects of diaphragm flexibility on the seismic design acceleration of precast concrete diaphragms

A new seismic design methodology for precast concrete diaphragms has been developed and incorporated into the current American seismic design code. This design methodology recognizes that diaphragm inertial forces during earthquakes are highly influenced by higher dynamic vibration modes and incorporates the higher mode effect into the diaphragm seismic design acceleration determination using a first mode reduced method, which applies the response modification coefficient only to the first mode response but keeps the higher mode response unreduced. However the first mode reduced method does not consider effects of diaphragm flexibility, which plays an important role on the diaphragm seismic response especially for the precast concrete diaphragm. Therefore this paper investigated the effect of diaphragm flexibility on the diaphragm seismic design acceleration for precast concrete shear wall structures through parametric studies. Several design parameters were considered including number of stories, diaphragm geometries and stiffness. It was found that the diaphragm flexibility can change the structural dynamic properties and amplify the diaphragm acceleration during earthquakes. Design equations for mode contribution factors considering the diaphragm flexibility were first established through modal analyses to modify the first mode reduced method in the current code. The modified first mode reduced method has then been verified through nonlinear time history analyses.

Influence of Incoherence and Wave Passage Effects on Seismic Performances of Long Immersed Tunnel

This paper conducts time history analysis to explore the influence of spatially varying earthquake ground motion (SVEGM) on seismic responses of the long immersed tunnel. Incoherence effect and wave passage effect are mainly focused here. Moreover, three coherency models are adopted to investigate the sensitivity of the computed responses to the models. The calculation results show that SVEGM enlarges seismic responses of the immersed tunnel significantly than uniform excitation. Considering wave passage effect and incoherence effect simultaneously makes the seismic responses increase more sharply than considering the latter only. The deformation of Gina gasket is barely sensitive to coherency model, while the axial compression force is sensitive to coherency model. It indicates suppressing that the fundamental mode and dominating higher-mode response are the hallmark of multi-support excitation. The great differences of three models decay with separation at low frequencies and their coherency in frequency domain are the main reasons that cause the variations of the axial compression forces.

Assessment Method for Inelastic Higher Mode Effects in Outrigger Braced Tall Building Under Seismic Loads

Outrigger system is a more popular structural system in tall buildings and higher mode participation in such buildings is an important aspect in design. During severe earthquake impacts, buildings undergo inelastic deformations, and this can lead to lengthening of modal periods of the building. Since higher mode effects have a significant impact on the overall behavior in tall buildings, the impact due to lengthening of modal periods needs to be addressed in the design. In this study, a simple assessment method is presented to quantify the effect of higher mode response on the behavior of outrigger braced buildings under seismic loads. The method comprises of simplifying the building to vertical cantilever with lateral degrees of freedom equal to number of stories and rotational springs with equivalent spring stiffness at corresponding outrigger locations. A pin-based structure was assumed to limit the first mode response to represent the transition from elastic to inelastic status of the building. The proposed method is capable of estimating the inelastic lengthened periods for higher modes and their responses in outrigger braced tall buildings. The developed method was applied to a case study outrigger braced tall building and reasonable results are predicted.

Incorporation of Torsional & Higher-Mode Responses in Displacement-Based Seismic Design of Asymmetric RC Frame Buildings

Direct displacement-based design (DDBD) is currently a widely used displacement-based seismic design method. DDBD accounts for the torsional response of reinforced concrete (RC) frame buildings by using semi-empirical equations formulated for wall-type buildings. Higher-mode responses are incorporated by using equations obtained from only a few parametric studies of regular planar frames. In this paper, there is an attempt to eliminate torsional responses by proportioning frames’ secant stiffnesses so that the centers of rigidity and supported mass (the mass on and above each story) coincide. Once the torsional rotations are significantly reduced and only translational motions are achieved, higher-mode responses are included using a technique developed by the authors in their recent paper. The efficiency of the proposed design procedure in fulfilling the intended performance objective is checked by two plan-asymmetric 20-story RC frame building cases. Case-I has the same-plan configuration while Case-II has a different-plan configuration along the height. Both cases have different bay widths in orthogonal directions. Verification of the case studies by nonlinear time history analysis (NTHA) has shown that the proposed method results in designs that satisfy the performance objective with reasonable accuracy without redesigning members. It is believed that a step forward is undertaken toward rendering design verification by NTHA less necessary, thereby saving computational resources and effort.

Rational Design Approach for Enhancing Higher-Mode Response of a Microcantilever in Vibro-Impacting Mode.

This paper proposes an approach for designing an efficient vibration energy harvester based on a vibro-impacting piezoelectric microcantilever with a geometric shape that has been rationally modified in accordance with results of dynamic optimization. The design goal is to increase the amplitudes of higher-order vibration modes induced during the vibro-impact response of the piezoelectric transducer, thereby providing a means to improve the energy conversion efficiency and power output. A rational configuration of the energy harvester is proposed and it is demonstrated that the new design retains essential modal characteristics of the optimal microcantilever structures, further providing the added benefit of less costly fabrication. The effects of structural dynamics associated with advantageous exploitation of higher vibration modes are analyzed experimentally by means of laser vibrometry as well as numerically via transient simulations of microcantilever response to random excitation. Electrical characterization results indicate that the proposed harvester outperforms its conventional counterpart (based on the microcantilever of the constant cross-section) in terms of generated electrical output. Reported results may serve for the development of impact-type micropower generators with harvesting performance that is enhanced by virtue of self-excitation of large intensity higher-order mode responses when the piezoelectric transducer is subjected to relatively low-frequency excitation with strongly variable vibration magnitudes.

Influence of squeeze-film damping on higher-mode microcantilever vibrations in liquid

The functionality of atomic force microscopy (AFM) and nanomechanical sensing can be enhanced using higher-mode microcantilever vibrations. Both methods require a resonating microcantilever to be placed close to a surface, either a sample or the boundary of a microfluidic channel. Below a certain cantilever-surface separation, the confined fluid induces squeeze-film damping. Since damping changes the dynamic properties of the cantilever and decreases its sensitivity, it should be considered and minimized. Although squeeze-film damping in gases is comprehensively described, little experimental data is available in liquids, especially for higher-mode vibrations. We have measured the flexural higher-mode response of photothermally driven microcantilevers vibrating in water, close to a parallel surface with gaps ranging from ~200 μm to ~1 μm. A modified model based on harmonic oscillator theory was used to determine the modal eigenfrequencies and quality factors, which can be converted into co-moving fluid mass and dissipation coefficients. The range of squeeze-film damping between the cantilever and surface decreased for eigenfrequencies (inertial forces) and increased for quality factors (dissipative forces) with higher mode number. The results can be employed to improve the quantitative analysis of AFM measurements, design miniaturized sensor fluid cells, or benchmark theoretical models. PACS: 07.10.Cm (Micromechanical devices and systems), 46.40.Ff (Resonance and damping of mechanical waves), 07.79.-v (Scanning probe microscopes and components), 07.07.Df (Sensors (chemical, optical, electrical, movement, gas, etc.); remote sensing).

Effect of higher modes on the seismic response and design of moment-resisting RC frame structures

Recently, extensive research has been conducted regarding higher-mode effects on the response of multi degree-of-freedom (MDOF) systems. The research has been focused mainly on structures with a lateral force resisting system consisting of slender walls, since these types of buildings are expected to be mostly affected by higher-mode phenomena according to structural dynamics, and simplified expressions have been proposed for slender-wall structures to account for higher-mode response in estimating shear forces. Current seismic design practice assumes the same reduction factor for all modes, even though there is strong evidence that inelasticity affects higher modes of vibration unequally. Additionally, simplified design methods are based only on the fundamental mode of vibration neglecting the effect of higher modes or considering them as elastic. In this paper, higher-mode contributions on the overall response of a nine-storey moment resisting frame (MRF), for which a domination of the first mode is expected, are investigated. The accuracy of a modified Modal Response Spectrum Analysis (mMRSA) method and other available methods is evaluated by comparing the results with the ones of the nonlinear response history analysis. Modal behaviour (reduction) factors are directly calculated for the first three modes and the validity of common assumptions is examined. The assessment of the methods is not restricted to deformations, but is extended to storey inertial forces and shears as well, which have attracted less interest from structural engineers, even though they are considered responsible for numerous structural and non-structural failures during major recent earthquakes and are critical for the design of several structures, such as precast buildings. The results suggest that the storey inertial forces and accelerations at all storeys and shear forces at higher storeys are significantly underestimated by methods neglecting or non-properly accounting for higher modes, even for first-mode dominated structures. The contribution of higher modes depends on the ground motion characteristics, the overstrength associated with each mode and the response quantity examined.

Simplified analysis of mid‐story seismically isolated buildings

AbstractThe mid‐story isolation design method is recently gaining popularity for the seismic protective design of buildings located in the areas of high population. In a mid‐story isolated building, the isolation system is incorporated into the mid‐story rather than the base of the building. In this paper, the dynamic characteristics and seismic responses of mid‐story isolated buildings are investigated using a simplified three‐lumped‐mass structural model for which equivalent linear properties are formulated. From the parametric study, it is found that the nominal frequencies of the superstructure and the substructure, respectively, above and below the isolation system have significant influences on the isolation frequency and equivalent damping ratio of a mid‐story isolated building. Moreover, the mass and stiffness of the substructure are of greater significance than the superstructure in affecting the dynamic characteristics of the isolated building. Besides, based on the response spectrum analysis, it is noted that the higher mode responses may contribute significantly to the story shear force of the substructure. Consequently, the equivalent lateral force procedure of design codes should carefully include the effects of higher modes. Copyright © 2010 John Wiley & Sons, Ltd.