Contribution Of Higher Modes Research Articles

Modified Modal Pushover Design for Asymmetric-Plan RC Shear-Wall Structures

The goal of this research is to provide a new method for designing reinforced concrete wall structures with a one-way asymmetric plan. This presented method is called the modified modal pushover design method (MMPD), which uses assumptions of modified modal pushover analysis (MMPA) for estimating the responses of structures. In summary, the arbitrary distribution of walls’ reinforcements at the beginning of MMPD design steps is modified so that a structure is limited to its selected limit state when analyzed by the MMPA method by knowing that walls’ stiffness is proportional to their corresponding strength. An appropriate hysteretic model (PIVOT model) is selected for the first-mode nonlinear SDOF system so that it estimates the peak and time history displacement response of the roof accurately. Three 8-storey buildings are designed for two different distributions of reinforcement areas to assess their effects on NRHA demands of each story. Higher mode contributions in responses of all structures are calculated by the elastic jagged response spectrum; mean-matched smoothed displacement response spectrum ± standard deviation curve is also used to compare stories’ shear and torsional demands estimated by these two response spectra. The results have shown the accuracy of the MMPD method in calculating the strength and stiffness of seismic-resisting walls.

Prediction of the Influence of Higher Modes on the Dynamic Response of High-Rise Buildings Subjected to Narrow-Banded Ground Motions

This paper presents the results of a study aimed at assessing the effects of higher modes of vibration on the nonlinear dynamic response of tall framed-buildings subjected to narrow-banded motions. For this purpose, analytical models of a 20-story building were developed under the consideration of two types of hysteretic behavior and subjected to 20 seismic excitations having a dominant period of motion of 1[Formula: see text]s. While the fundamental period of vibration of the building equals 2.7[Formula: see text]s, its second period is close to 1[Formula: see text]s; as a result, the selected seismic excitations over-stimulate the participation of the second mode in the overall dynamic response of the building. The circumstances under which the contribution of higher modes gives place to an excessive response of the upper stories are identified, and quantitative measures are presented. From an engineering point of view, parameters that predict an excessive response of higher-level floors are proposed.

An efficient full-wavefield computational approach for seismic testing in a layered half-space

Inversion of subsurface shear-wave velocity profile based on effective dispersion curve or full wavefield is still rare due to the lack of efficient forward computation kernel for the full wavefield in a layered medium. To facilitate exploiting the complete signal content in seismic testing, an efficient new computational framework for modeling synthetic full wavefields in horizontally layered systems is proposed. Dynamic response of an isotropic elastic layered system subjected to vertical loading is implemented and thoroughly validated. The new procedure is based the Fourier-Bessel series expansion (not the traditional Fourier-Bessel transform), and it is at least two-orders faster than the current full wavefield computation method based on integral transformation. It considers survey parameters and models all wave phenomena, including near-field effect and leaky waves, which cannot be captured by the modal summation method. Examples of full wavefield simulation are presented to demonstrate different levels of information provided by the experimentally available fundamental mode, broadband effective dispersion curve, and the full velocity spectrum. Different earth models may have similar fundamental modes or even effective dispersion curves; however, their difference manifests in different higher-mode contributions and can only be exploited by utilizing the entire velocity spectra including the vertical and radial components. The coupling between the vertical and radial components in terms of their spectral ratio and phase difference can provide additional constraints (data) in seismic testing.

Contribution of higher modes in the dynamic response of reinforced concrete member subjected to blast

Response of reinforced concrete structures subjected to blast load of high intensity and short duration is difficult to analyze. P-I (pressure-impulse) curves are one of the approaches for describing structural response against blast load. Design codes also suggest preparing P-I curves based on SDOF for obtaining structural response subjected to blast. Blast load excites higher modes of vibrations. The SDOF analysis does not cover the higher modes effect.The structural dynamic response of RC flexure members under a varying range of explosion scenarios was predicted by carrying out investigations. The linear elastic beam with variable boundary conditions was analyzed using the Modal superposition method based upon Euler-Bernoulli, Rayleigh, Shear, and Timoshenko theories. For various ranges of the blast, Iso-damage (P-I) curves, including the effect of higher modes, were generated, and the types of failure were established. These iso-damage curves differ significantly from those obtained using the SDOF concept for the case of blast in the dynamic and impulsive regime. In the case of near blast, understandably higher modes (both flexure and shear) play a significant role. The present study suggests that the Timoshenko formulation yields an accurate response irrespective of the Flexibility of the structure.

Higher mode effects of multistorey substructures on the seismic response of double-layered steel gridshell domes

The seismic response of gridshell roofs with substructures is strongly influenced by the relative mass and stiffness of the roof and substructure, and particularly by how close the periods of the dominant roof and substructure modes are. Multistorey substructures may exhibit a significant higher-mode acceleration response, primarily due to the contribution of the shorter second translational substructure mode to the roof response. This paper presents parametric studies conducted on steel gridshell domes with 60, 100 and 150 m spans and six-storey substructures to investigate the interaction between the higher substructure modes and dominant roof modes. The contribution of each substructure mode to the overall response was characterised by a newly proposed dominance response ratio. In contrast to previous studies of long-period single-storey substructures, which only minimally excited the roof modes, the higher modes of the long-period multistorey substructures investigated in this study significantly contributed to the roof response. The roof vertical accelerations were amplified by up to three times the substructure roofline acceleration, as the curved roof geometry couples the horizontal substructure and vertical roof response. The substructure higher-mode contribution was quantified using amplification factors and developed into equivalent static loads that were found to be in good agreement with response spectrum analysis results. The proposed equivalent static loads provide insight into the complex dynamic characteristics of gridshell roofs with multistorey substructures and offer an efficient method for preliminary seismic design.

Evolution of initial stage fluctuations in the glasma

We perform a calculation of the one- and two-point correlation functions of energy density and axial charge deposited in the glasma in the initial stage of a heavy ion collision at finite proper time. We do this by describing the initial stage of heavy ion collisions in terms of freely evolving classical fields whose dynamics obey the linearized Yang-Mills equations. Our approach allows us to systematically resum the contributions of high momentum modes that would make a power series expansion in proper time divergent. We evaluate the field correlators in the McLerran-Venugopalan model using the glasma graph approximation, but our approach for the time dependence can be applied to a general four-point function of the initial color fields. Our results provide analytical insight into the preequilibrium phase of heavy ion collisions without requiring a numerical solution to the Yang-Mills equations.

Reflection of K1 Internal Tides at the Continental Slope in the Northern South China Sea

AbstractReflection of the K1 internal tides (ITs) in the northern South China Sea (SCS) is investigated using a high‐resolution three‐dimensional numerical model. The simulated results indicate that the westward K1 ITs generated at the Luzon Strait (LS) first impact the continental slope in the northern SCS, and thereafter are reflected. There is a total of 0.31 GW of K1 energy that are reflected, suggesting a weak reflection considering 3.54 GW of westward K1 energy from the LS. Two reflected K1 beams are revealed. The southeast one is the more energetic and can propagate across the deep basin, agreeing with that extracted from satellite altimeter data. The eastward one propagates toward the LS, but it is absent in altimeter results because of its lower intensity. Both the two reflected beams are radiated from the supercritical region in shallow water. Different from the incident waves that are dominated by mode‐1, the reflected waves exhibit a multimodal structure. Contribution of high modes to reflected waves is comparable to that of mode‐1. Moreover, modal content is different for the two reflected beams, with higher proportion of high‐mode energy flux for eastward reflected beam. In contrast to the K1 ITs, no remarkable reflected O1 ITs are detected from either simulated or altimeter results. This is due to the weak generation of O1 ITs at the LS, which leads to less O1 energy reaching the continental slope. The results of this work can provide essential insight on IT dynamics in the SCS.

Fragility curves for seismic damage assessment in regular and irregular MRFs using improved wavelet-based damage index

In the conventional performance‐based earthquake engineering framework, fragility curves are mapped to a function of story drift ratio or spectral acceleration corresponding to the first mode. Based on the fragility curves, the probability of structural healthy status can be estimated. Practically, it is difficult to measure story drift and expensive to develop an automative measuring system. Therefore, this paper strives to develop fragility curves by using wavelet-based refined damage-sensitive feature (rDSF), considering higher mode contributions. These fragility curves can be obtained from absolute acceleration responses recorded at each story of buildings. As irregularities have important and significant effects on behaviour and seismic performance of Moment Resisting Frames (MRFs) especially in the field of structural health monitoring, in the next step, we extend the fragility curves for irregular MRFs. To this end, an efficient and more precise rDSF using Morlet and cmorfb-fc wavelets are extended to map fragility curves. The correlation coefficient between rDSF and maximum story drift ratio is evaluated as a criterion to determine the effects of irregularity. The 6-story steel benchmark MRF was manufactured to consider a stiffness reduction irregularity caused by the deference in story height and ductility of beam-column members. To assemble rDSFs, acceleration responses recorded both from the regular and irregular MRFs were analyzed by using incremental dynamic analysis, subjected to different ground motion sets. Moreover, a system identification method is used to identify the natural frequencies of each MRF. Based on the acquired results, it can be concluded that the MRFs including higher first story and weak columns-strong beams changes with a higher probability of damages lead to damage occurrence at lower seismic intensities and also lower maximum story drift ratios as compared with those of reference MRF. Moreover, the results show that the fragility curves estimated by wavelets-based rDSF, especially by using cmorfb-fc wavelet-based rDSF, due to lower probability of damages (varied between 27% and 81% for different damage states) have more efficiency than the fragility curves derived from Morlet wavelet-based DSF, considering only the first mode, for all the MRFs of interest. Furthermore, global fragility curves lead to a total assessment of the MRFs, while for a more accurate damage diagnosis, the rDSF-base fragility curves computed for each story can be used.

Study on vibration response of submerged floating tunnel considering vehicle eccentric load

The submerged floating tunnel (SFT) is a novel traffic structure for crossing long channels and deep waterways. The moving vehicles within the SFT have a remarkable influence on structural vibration response. To analyze the eccentric load effect of vehicles in the SFT, the structure is simplified as a spatial beam on elastic foundation, while the vehicle is simulated as a seven-DOF model with three dimensions. Using the Morison equation to express the effect of nonlinear fluid resistance, the vehicle-tunnel coupling vibration equations under the action of a motorcade running on one lane of the roadway are derived using the Hamilton Principle. Then, with the help of the mode superposition method and the fourth-order Runge–Kutta method, the solution for the equation is obtained. The accuracy of the proposed theoretical derivation and corresponding programming are verified by the finite element method. Based on the analysis, the SFT with a total span of 1000 m is selected as the research object to explore the spatial behavior of the SFT under vehicle-tunnel coupling vibration. The results show that the vertical displacement peak appears at the quarter-span of the tube, whereas the peaks of horizontal displacement and torsional angle appear at the mid-span under the eccentric load of a motorcade. The contribution of high order modes on the structural displacement should be considered. Moreover, the form of the motorcade affects the vertical displacement and torsional angle of the tube, and with the change of motorcade layout and vehicle speed, the resonance effect and vibration elimination effect will appear in the vehicle-tunnel coupling vibration system. Furthermore, the design parameters of the cable have a significant effect on the deformation resistance of the tube, therefore the selection and layout of the cable should take both the anchoring stiffness and material cost into account. For controlling the eccentric load effect, the inclined angle and installation angle of the cable are recommended to be 60° and 75°, respectively.

Proposal of lateral forces for capacity design of controlled rocking steel cores considering higher mode effects

Controlled rocking steel cores (CRSCs) may suffer progressive collapse because of inadequate structural design and loss of re-centering action. While the CRSCs displace in the first-mode frequency, the demands of their members are strongly affected by higher modes. Conventional lateral load distributions, such as the uniform and inverted triangular, cannot predicate the design forces of CRSCs. This paper proposes new lateral loads for the design of CRSCs. Continuum cantilever beam analogy is utilized to formulate the higher-mode contribution. The application of the lateral loads is validated through illustrative examples of low- and mid-rise CRSCs. Results supported by nonlinear time response analyses demonstrate the effectiveness of proposed formulae for reliable estimation of seismic demands. The proposed lateral forces are readily applicable in commercial software without gap modeling at the base boundary conditions of CRSCs.

Seismic Fragility Assessment for Korean High-Rise Non-Seismic RC Shear Wall Apartment Buildings

Seismic fragility was assessed for non-seismic reinforced concrete shear walls in Korean high-rise apartment buildings in order to implement an earthquake damage prediction system. Seismic hazard was defined with an earthquake scenario, in which ground motion intensity was varied with respect to prescribed seismic center distances given an earthquake magnitude. Ground motion response spectra were computed using Korean ground motion attenuation equations to match accelerograms. Seismic fragility functions were developed using nonlinear static and dynamic analysis for comparison. Differences in seismic fragility between damage state criteria including inter-story drifts and the performance of individual structural members were investigated. The analyzed building had an exceptionally long period for the fundamental mode in the longitudinal direction and corresponding contribution of higher modes because of a prominently insufficient wall quantity in such direction. The results showed that nonlinear static analyses based on a single mode tend to underestimate structural damage. Moreover, detailed assessments of structural members are recommended for seismic fragility assessment of a relatively low performance level such as collapse prevention. On the other hand, inter-story drift is a more appropriate criterion for a relatively high performance level such as immediate occupancy.

Developing a method for multi-modal shear-based pushover analysis

The nonlinear static seismic analysis has become the focus of many research works because of its simplicity compared with dynamic time history analysis. Procedures have been proposed to include the effect of higher modes in pushover analysis. In this study, a combinatory procedure of two independent modal pushover analyses is presented. The proposed method uses the story shear force. Essentially, the elastic relative stiffness of each story along with the story drifts are used to calculate the story shear force. Two different ways are utilized to estimate the contributions of higher modes to the story shear force. As confirmed by representative examples, it is shown that a combinatory approach of picking up the maximum values of responses between the two presented pushover procedures results in minimum RMS errors in comparison to the exact nonlinear dynamic analysis. In other words, always the maximum response between the two methods is nearest to the exact value calculated as the average of nonlinear time history analysis with earthquakes. Moreover, the combinatory method is shown to be considerably more accurate than previous methods including the modal pushover (MPA) and a recent method of pushover analysis (SSAP) on the basis of story shear force. This is true while the proposed method is much easier to carry out than both MPA and SSAP approaches.

Seismic damage assessment using improved wavelet-based damage-sensitive features

In this paper, acceleration responses of steel MRFs under different ground motions using incremental dynamic analysis (IDA) are used for nonlinear damage diagnosis. In the first step, auto-regressive moving-average with exogenous input (ARX) model, along with stabilization diagram, is utilized to assess the natural frequencies of MRFs. In the second step, complex Morlet (cmorfb-fc) wavelet-based refined damage-sensitive features (rDSFs), as new DSFs considering higher mode contributions and end-effect modifications, are proposed. Improved efficiency and accuracy of the proposed rDSFs are presented through benchmark steel MRFs. Results indicate that the damage pattern (DP) causing first plastic hinge formation and also the damaged story can be accurately recognized using the proposed wavelet-based rDSFs. In addition, the damage extent (severity) for each DP at each story can be assessed using the cumulative sum of wavelet energy at time-shift b (or sum of scalogram for each time) over the refined effective time of vibration (refined ETV) for each output acceleration when compared with that over the refined ETV for the input ground acceleration. Finally, results also indicate improvement over the DSFs existing in the technical literature.

Impact of Traffic-Induced Vibrations on Residential Buildings and Their Occupants in Metropolitan Cities

This paper evaluates and quantifies the adverse impact of traffic-induced vibrations on the structural systems of residential buildings and their occupants. To do this, İstanbul, one of the world’s most populous and traffic-congested cities, was selected as a case study. Firstly, a survey was conducted on 100 occupants of six neighbourhoods to understand human perception of vibrations and the physical condition of typical buildings. Then, train-induced ground vibrations were measured near a busy railway. Using the survey data and the measured train vibrations, time-history analyses were applied to five typical residential buildings. The results showed that there is a considerable contribution of higher modes to overall building response. Peak particle velocities calculated on the buildings are predominantly intolerable. Critically, 95% of the occupants would like authorities to reorganize traffic regulations to reduce the effects of this global problem. Therefore, human response to traffic-induced vibrations should be consideration of serviceability limit state and site-specific analysis should be incorporated into the codes of practice.

Features of internal tides observed near the shelf break in the northern South China Sea

Features of internal tides in the northern South China Sea are investigated using measurements of two moorings at 506 m (MR1) and 260 m (MR2) working between April and November of 2014. The diurnal internal tides at MR1 are significantly enhanced in June–July and display a regular fortnight modulation, whereas at shallower MR2, the June–July intensification is absent and the fortnight cycle becomes irregular. Fortnight cycle peaks of diurnal internal tides have a regular time-lag of ~ 2.8 days after those of diurnal barotropic tides (at MR1). We derive a mathematical relationship indicating that this time-lag of fortnight cycle peaks is around twice the time for the diurnal internal tides propagating from the generation place to the mooring site. Semidiurnal internal tides are dominated by the mode-1 (~ 70%), while diurnal internal tides exhibit multi-modal structures, with the contribution of ~ 20–30% for each of the first three modes. The diurnal mode-1 contribution varies fortnightly, and eddy passages are highly correlated with the increasing contribution of semidiurnal high modes (at MR1). Furthermore, we find that the nonlinear interaction between internal tides and near-inertial motions is weak in summer, even during periods of strong near-inertial motions (at MR2), because in summer, the shear of near-inertial currents is maximum at a depth shallower than the depth of maximum internal tide shear.

Response of structure with controlled uplift using footing weight

Allowing structures to uplift in earthquakes can significantly reduce or even avoid the development of plastic hinges within the structure. The permanent deformations in the structure can thus be minimized. However, uplift of footings can cause additional horizontal movements of a structure. With an increase in movement relative to adjacent structures, the probability of pounding between structures increases. This experimental study reveals that the footing mass can be used to control the vertical displacement of footing and thus reduce the horizontal displacements of an upliftable structure. A four storey model structure with plastic hinges and uplift capability was considered. Shake table tests using ten different earthquake records were conducted. Three different footing masses were considered. It is found that the amplitude of footing uplift can be greatly reduced by increasing the mass of the footing. As a result, allowing structural uplift does not necessary increase the horizontal displacement of the structure. The results show that with increasing footing weight, the interaction between structural and footing response can increase the contribution of the higher modes to the structural response. Consequently, the induced vibrations on secondary structure increase.

Protein Fluctuations and Cavity Changes Relationship.

Protein cavities and tunnels are critical for function. Ligand recognition and binding, transport, and enzyme catalysis require cavities rearrangements. Therefore, the flexibility of cavities should be guaranteed by protein vibrational dynamics. Molecular dynamics simulations provide a framework to explore conformational plasticity of protein cavities. Herein, we present a novel procedure to characterize the dynamics of protein cavities in terms of their volume gradient vector. For this purpose, we make use of algorithms for calculation of the cavity volume that result robust for numerical differentiations. Volume gradient vector is expressed in terms of principal component analysis obtained from equilibrated molecular dynamics simulations. We analyze contributions of principal component modes to the volume gradient vector according to their frequency and degree of delocalization. In all our test cases, we find that low frequency modes play a critical role together with minor contributions of high frequency modes. These modes involve concerted motions of significant fractions of the total residues lining the cavities. We make use of variations of the potential energy of a protein in the direction of the volume gradient vector as a measure of flexibility of the cavity. We show that proteins whose collective low frequency fluctuations contribute the most to changes of cavity volume exhibit more flexible cavities.

Displacement-based Mode Pushover Analysis of Self-anchored Cable-stayed Suspension Bridge

As being a typical multi-freedom degree system structure, self-anchored cablestayed suspension bridge is significantly affected by higher modes in the earthquake response. Traditional force-based pushover analysis of reverse triangle or uniform distribution patterns will lead* to a certain error for the results of pushover analysis of self-anchored cable-stayed suspension bridge. An improved method of displacement-based mode pushover analysis is presented in this paper by combining the two stage horizontal displacement pattern with mode pushover. This improved method can take the contributions of higher modes into account. And the applicability of the method can be verified commendably by the selected examples. Traditional force-based pushover analysis considers the seismic load is equivalent to lateral load. And it judges whether the deformation ability of the structure and component can meet the need of design and use function by analysing nonlinear response of structures under the monotonic increasing horizontal lateral load applied to the structure with a certain distribution mode. The selection of the lateral load distribution mode can directly affect the analysis results of the pushover method on the seismic performance of whole structure in traditional force-based pushover analysis. Moreover, the problem of stiffness degradation after failure is not taken into account in this traditional wide application method. Seismic hazard, experiment and theoretical analysis indicate structural collapse is mainly due to the lack of deformation capacity and energy dissipation capacity during severer earthquake. In this case, the deformation capacity and the displacement response of structure will have an certain impact on the damage degree of structural members. Therefore, it is more reasonable to use displacement control on structural seismic response during severer earthquake[4]. Compared with the traditional force-based design, the displacement of structure can reflect the nonlinear reactive state more during severer earthquake, it also can control the behavior of structure better in earthquake. Consequently, the displacement-based seismic design method has been greatly developed[5-10]. There are three commonly used displacement-based seismic design method: ductility factor design, capacity spectrum and direct displacement-based design method. The basic thought of displacement-based mode pushover analysis is as follows: first, put monotonic increasing lateral displacement to bear on structure directly according to a certain horizontal displacement distribution mode, second, the final failure pattern of structure is obtained by pushover the structure to the target displacement, after that, whether the deformation ability of structure and component can meet the need of design and use function can be analyzed.

Optimal intensity measure based on spectral acceleration for P-delta vulnerable deteriorating frame structures in the collapse limit state

This study proposes an “optimal” spectral acceleration based intensity measure (IM) to assess the collapse capacity of generic moment frames vulnerable to the P-delta effect. The IM is derived from the geometric mean of the spectral pseudo-acceleration over a certain period interval. The optimized IM includes for first time a flexible lower limit for the period interval, corresponding to the structural period associated with the exceedance of 95% of the total effective mass. This flexible lower limit bound provides an efficient IM, independently of the contribution of higher modes to the total response. The upper bound period is 1.6 times the fundamental period to account for period elongation due to inelastic deformations and gravity loads. In a parametric study on generic frames, structural parameters are varied to quantify the performance of this IM compared to classical benchmark IMs. The “optimal” IM provides minimum, or close to the minimum, dispersion for the entire set of frames with different fundamental periods of vibration, number of stories, and P-delta vulnerability.

Seismic Assessment of Masonry Towers by Means of Nonlinear Static Procedures

The paper presents some FE analyses conducted through advanced techniques for the seismic assessment of existing masonry towers. Traditionally, masonry towers were conceived to withstand vertical loads only, but in recent years national and international standards have imposed the evaluation of their structural performance even in presence of horizontal forces. Eight towers are chosen deliberately very different in geometry and a number of linear and non-linear structural analyses are performed. Their behavior under horizontal loads (mimicking earthquake actions) is investigated by means of traditional static nonlinear procedures. Modal participations in pushover analyses are considered in order to have an insight into the role played by the higher modes in the local and global behavior of the structure. A non-conventional pushover approach, hereafter called EPA-Extended Pushover Analysis-based on modal combinations is utilized. Some comparative analyses between standard and non-conventional pushover are reported. It is found that EPA is reasonable when the contribution of higher modes is significant. EPA turns out to have a reasonable resemblance in terms of capacity and deformation pattern with non-linear dynamic results, highlighting the significant role of the higher modes in such structures, where for instance the presence of the bell cell can play a certain role. Further vulnerability considerations for the towers deduced by the performed analyses are also reported.