Displacement Response Spectra Research Articles

Influence of velocity pulse directivity on seismic response of cross-fault bridges

Pulse-type ground motions have special destructive effects on structures, and directivity is one of the fundamental characteristics of velocity pulses. In this paper, the impact of the velocity pulse directivity of seismic motions on both sides of the fault on the seismic response of fault-crossing bridges was quantified using the original records from the Chi-Chi earthquake in Taiwan. First, an automatic baseline correction method was applied to restore the permanent ground displacement, and the direction corresponding to the strongest pulse energy on both sides of the fault was identified based on continuous wavelet transformation. On this basis, the variability of the peak intensity of ground motions on the hanging wall and footwall in different directions, as well as the differences in pulse characteristics between the strongest pulse component and the two initial horizontal components, were analysed. Finally, a typical 5 × 30 m continuous girder bridge was considered as the research object to reveal the influence of the velocity pulse directivity on the seismic response of key parts on both sides of the fault. The results showed that the variability in the peak ground-motion intensity on the hanging wall of the fault was higher than that on the footwall. The displacement variability was up to 863 %, velocity was 262 %, and acceleration was 124 %. The pulse characteristics of the strongest pulse component were stronger than those of the parallel and vertical fault components, and its acceleration, velocity, and displacement response spectra were larger. The amplification effects of the velocity pulse directivity on the transverse bending moment, longitudinal bending moment, and torque of the pier bottom reached 1.3, 1.1, and 1.6, respectively. However, the amplification effect of the velocity pulse directivity on the relative displacement of the pier top, displacement of the main beam, and displacement of the bearing was more than 1.6 times, which was more significant than the internal force of the pier bottom.

Evaluation of wavelet decomposition level to enhance numerical analysis of seismic responses

In this study, the discrete wavelet transform (DWT) is used to enhance the efficiency of numerical analysis by decomposing earthquake excitation signals into low- and high-frequency components. The low-frequency components, considered as the main damaging factor in earthquake waves, stored in approximation coefficients have been used to perform time response analysis. In the selection of the ground motions, the special attention is given to the ratio of peak ground acceleration (PGA) to peak ground velocity (PGV). An ensemble of nine earthquake records have been selected and used. For each earthquake, displacement response spectra have been generated for both the original signal and its approximations at different DWT levels. To determine the most accurate decomposition level, the normalized root-mean-squared error (NRMSE) of wavelet energy has been computed in spectral displacement responses. The outcomes reveal a dependency of the decomposition level on the specific characteristics of each earthquake. Subsequently, structural analyses are conducted on base-isolated structures with varying story numbers, to examine the accuracy of decomposed signals. Employing both the original signal and its approximations to the structures, base mat displacements and roof accelerations are computed. The findings of the seismic analyses demonstrate the effectiveness of the proposed decomposition levels.

Effect of soil-building interaction on dynamic earth pressure on basement walls

This study investigates dynamic earth pressure on basement walls by considering soil-structure interaction, a factor that is often overlooked by conventional methods like Mononobe-Okabe, Seed and Whitman, and Wood. Superstructure, basement, and soil were numerically simulated in a single model to evaluate the inertial and kinematic effects of buildings on dynamic earth pressure on the basement walls. The numerical model was validated using data from a centrifuge test and an instrumented building. Then, a parametric study was performed, with the height, width, and basement depth of the building varied with six input motions. The results showed that the inertia of the building increased dynamic thrust. Furthermore, the dynamic thrust showed a similar trend with the displacement response spectrum curve of the ground surface acceleration as the building height increased, while the distribution shape transitioned from triangular to inverted triangular. Additionally, wider buildings had increased dynamic earth pressure, while deeper buildings exhibited smaller normalized dynamic thrust.

Dynamic soil-structure interaction analysis for base-isolated nuclear island building based on the method of external source wave motion

Soil-structure interaction (SSI) is crucial to the dynamic response of nuclear power plants (NPPs), and should be properly considered when analysing the seismic isolation performance of base-isolated NPPs. In this study, a three-dimensional numerical simulation program is developed for the time-domain dynamic analysis of base-isolated NPPs considering SSI effects. The seismic input is realised using the method of external source wave motion, and the nonlinear behavior of isolators is fully considered. Using this program, the SSI effects of the base-isolated nuclear island building under different sites are analysed and compared, including the acceleration, displacement, and floor response spectra. The numerical results show that the SSI effects change the spectral characteristics of the actual seismic input. When the shear wave velocity of the site is relatively large, the SSI effects can increase the dynamic response of base-isolated NPPs. Additionally, the isolation performance of the base-isolated NPPs is weakened when SSI effects are considered, and with a decrease in the shear wave velocity of the site, the isolation capacity is further reduced. The influence of the SSI effects should be fully considered in the base isolation design of NPPs.

Predominant Frequency in Near-Field Strong Ground Motion by Analysis of Displacement Response Spectra

A literature review on the spectral content of seismic ground motion indicates that a clear predominant frequency in earthquakes is very difficult to define. Here, it is considered that this has been so because the usual seismic record or response quantity is always employed: acceleration. In this work, an attempt is made to define a single predominant frequency for strong seismic ground motion in the near field with a different idea. It is considered that this is possible if the concentration is on displacement rather than on ordinary acceleration. In particular, relative displacement response spectra will be studied, instead of the common acceleration one, and the existence of clear and neat maximum spectral displacements around, statistically, a single and general proposed predominant frequency will be investigated for a set of twenty very strong (magnitude larger than 6.5 MW) world events.

Validation of One Predominant Frequency Presence in Seismic Ground Displacement by Means of Deformation Response Spectra

There are very few results in the literature on spectral content of seismic ground displacement; nonetheless, these results are singular as most of the spectral content is limited to a very narrow low frequency band, contrary to ground acceleration. These few spectral characterizations have been obtained, expectedly, by means of power spectral or Fourier analyses of ground displacement records, only. As these records are not as reliable as ground acceleration records, the existence of a clear predominant frequency in ground displacement warrants confirmation through a different procedure. We propose a corroboration method of this highly narrow-band characteristic that is based on the more dependable acceleration signal, rather than on the same ground displacement record that is the subject of study. Specifically, displacement response spectra are analyzed (which rely on acceleration records) to verify previously observed neat predominant frequencies in ground displacement, which is a novelty.

AN INVESTIGATION OF DAMPING MODIFICATION FACTORS CORRESPONDING TO DIFFERENT DAMPING RATIOS FOR SDOF SYSTEMS

The damping ratio is an important parameter in dynamic analyses and plays a key role in the design of building structures. Elastic response spectra are widely used in this design to describe the earthquake action in specific site classes. 5% damped response spectra are generally used for most of the conventional structures. However, other types of structures may not have a damping ratio of 5% and can have much lower or much larger damping ratios. The damping ratio is recommended at about 5% for concrete structures whereas it is estimated at 2% for steel structures. Tall slender buildings may have much lower damping ratios and low-rise buildings may be designed using much larger damping ratios than 5%. For these types of buildings, elastic response spectra are modified to account for different levels of damping ratios. This study proposes the damping modification factors (DMFs) which are computed using 5% response spectra as the benchmark. A strong ground motion set has been selected for the stiff site class and the displacement, pseudo-velocity, and pseudo-acceleration response spectra have been computed for single-degree-of-freedom (SDOF) systems. DMFs have been obtained in terms of these spectra and 3%, 10%, 20%, and 30% damping ratios have been considered. Variations of DMFs with different damping ratios have been obtained graphically. It can be seen from the results that DMFs are sensitive to the vibration period of the SDOF system.

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.

Dynamic Characteristics Analysis of Magnetic Levitation Rotor Considering Unbalanced Magnetic Pull

The working principle of the motor can cause unbalanced magnetic pull (UMP) between stator and rotor unavoidably. Previous research about nonlinear vibration excited by UMP was focused on the rotor supported by traditional mechanical bearings or gas bearings. However, the magnetic levitation rotor is particular due to the low rigidity provided by the active magnetic bearing (AMB). UMP amplifies rotor vibration in the resonant zone and further excites the nonlinear electromagnetic force, thus producing different vibration phenomena. The paper calculates rotor orbit, spectra analysis, and time-history plot with numerical methods and studies the influence of the rotation speed, eccentricity, key control parameters, and UMP on rotor dynamics in detail. Results illustrate displacement response spectra of the magnetic levitation rotor are quite different from previous research results. The appearing frequency components are inducted by universal formulas in this paper. Furthermore, research shows a slight adjustment of the control parameters affect significantly harmonic components and vibration characteristics. The research results have practical reference significance for fault diagnosis, feature recognition, and controller optimization of the AMB-rotor system.

The Effect of the Yield Strength Coefficient and Natural Vibration Period on the Damage Potential Ranking of Ground Motions

To analyze the effect of structural parameters on the damage potential ranking of ground motions, the effect of the yield strength coefficient (Cy) and natural vibration period (T) on the damage potential ranking of ground motions is analyzed based on the bilinear model and the modified Clough model, which are the most commonly used hysteretic models in structural dynamic analysis. The displacement response (Sd) spectrum under nonlinear conditions is taken as the damage potential intensity measure (IM) of ground motions, and the effect of the Cy and T on the Sd mean spectrum is also analyzed for comparative analysis. The results show that: (1) in the short-period range, Cy has a great effect on the displacement response ranking. On the other hand, in the medium- and long-period ranges, Cy has little effect on the Sd ranking; (2) with the change of T in medium- and long-period ranges, the variation of Sd values is obvious when the change of T is small, but the variation of Sd ranking is very small. This conclusion can provide a theoretical basis for evaluating the damage potential of ground motions and selecting input ground motions.

Research on Vibration Control of Power Transmission Lines-TMDI Based on Colliding Bodies Optimization

To investigate the vibration control capability of a tuned mass damper inerter (TMDI) on a transmission line, the motion equations of the transmission line with TMDI under harmonic excitation were derived. Thus, the closed-form solutions of the displacement response spectrum were obtained by Fourier transform. Based on the colliding bodies optimization (CBO), one of the metaheuristic algorithms, the TMDI parameters, was optimized to minimize the displacement of the transmission line-TMDI system. The research results show that the response of the transmission line was reduced by at least half for different mass ratio and frequency ratio conditions, which indicates that the TMDI can effectively control the displacement response of the transmission line. In addition, the TMDI parameters were optimized by CBO, and the vibration control efficiency was significantly improved. The results of the study show that the data converge quickly with fewer iterations in collision body optimization. On the one hand, CBO avoids getting into local optimization compared to other metaheuristic algorithms. On the other hand, it is cheaper in terms of the cost of its calculations compared to the methods of mathematical derivation. It plays an active role in the optimization of complex structures. The vibration suppression performance of the TMDI after optimization reaches 56–96%.

Application of the Lagrange Equation for Intelligent Sensor Vibration Control for Power Network Monitoring

Objective. In order to control the vibration of the beam structure more effectively and improve the safety and availability of the beam structure, an application study of the Lagrange equation for vibration control of smart sensors for power grid monitoring is proposed. The vibration of the beam structure, the displacement of the beam structure under the excitation of seismic acceleration, the response analytical electrical formula, and the displacement response formula of the beam structure under the action of the kinematic force are deduced. The optimal parameters of the beam-TMDI system are given, and the parameter sensitivity analysis is carried out. Then, the control effect of the TMDI system is studied by numerical analysis, and the vibration reduction effect of the TMDI system and the tuned mass damper (TMD) system is compared. Experimental results show that when the mass ratio μ of the TMDI system and the TMD system are both set to a fixed value of 0.005, and the parameter β of the TMDI system is set to 0, namely β = b = 0 , at this time, the TMDI system degenerates into a TMD system. The TMD natural frequency is 14.179 rad/s and the damping ratio is 0.0432 by the DH optimization method, while the TMD natural frequency is 14.1812 rad/s, and the damping ratio is 0.0436 by the augmented Lagrangian optimization algorithm. Conclusion. The vibration displacement response spectrum of a beam structure obtained by the frequency domain method can effectively reflect electricity in the displacement response of a beam structure. The parameters that minimize the vibration response of the beam structure can be accurately obtained by using the augmented Lagrangian parameter optimization method. The sensitivity of the TMDI system is controlled by the inertial device, and the inertial device has a significant impact on its robustness. The vibration reduction performance of the TMDI system is obviously better than in the conventional TMD systems.

Inerter Location-Based Vibration Suppression Study of a Transmission Line Equipped with Tuned-Mass-Damper-Inerter (TMDI) under Harmonic Excitation

This paper proposes a novel ungrounded TMDI to improve the vibration suppression performance of the transmission line under harmonic excitation. This type of inerter-based damper may transform a translational motion into a rotational motion, greatly increasing the efficiency of vibration suppression. In the present study, the differential equations of motion are first derived based on the transmission line with an ungrounded TMDI structure. Then the closed-form solution of the displacement response spectrum considering the influence of the suspension location of the inerter is developed. The impact of the inerter location on vibration suppression performance is investigated in depth by defining the suspension location factor (υ) and tuning the damping ratio and frequency ratio. The results demonstrate that the suspension location of the inerter has a substantial impact on the damping ratio, frequency ratio, and vibration suppression performance. When the connection location of the inerter is near to the mass of the damper, it degrades the vibration suppression performance of the system. The failure phenomenon of the inerter occurs in the range of 0.2 < υ < 0.3, indicating that the presence of the inerter in this range does not enhance vibration suppression performance. The modal coordinate difference has a considerable impact on the vibration suppression efficacy of the TMDI. With increasing modal coordinate differences, the vibration suppression performance of the TMDI grows dramatically.

Empirical predictive models for fling step and displacement response spectra based on the NESS database

The characterization of the fling-step represents a challenging task due to the shortage of near-source records with permanent tectonic displacement and the limitation in retrieving the fling-amplitude from accelerometric waveforms. In recent years, innovative ground-motion processing techniques have been developed for a more accurate estimation of both fling-displacements and spectral displacements in contrast to traditional bandpass filtering, although their application is still unusual. In this paper, we exploit the newly released dataset of the Near-Source Strong-motion records (NESS2) uniformly processed with the extended BASeline COrrection technique (eBASCO), against which we propose: (1) a new empirically-based ground motion model (GMM) for the prediction of the fling-step, and (2) an adjustment factor of the spectral displacements predicted by a reference GMM to account for the contribution of the fling-step at long periods. Such models are in agreement with observations and existing GMMs, and thus could be advantageously employed in seismic hazard analyses.

Sourcemap: a graphical representation to enhance the low frequency source radiation

SUMMARY Data from dense seismic arrays allow nowadays to map directly the radiation of the seismic source in space. However, the main features observed on these maps are usually linked to the propagation, its attenuation and some site effects. Only few parameters like the magnitude or fault extension may be inferred through the shape and the size of the epicentral area. In this work, we propose a new strategy able to produce fast qualitative maps, ‘Sourcemaps’, that highlight directly some basic characteristics of the seismic source. They are based on a parameter which is robust and fast to compute with a minimal processing: the displacement response spectrum (DRS) computed at low frequency. In order to highlight the source effects, we correct the DRS by the geometrical spreading. We have applied this strategy to some earthquakes occurred in Japan in the last 25 yr using K-NET/KiK-net data. In these examples, we show that the source parameters such as the focal mechanism (nodal planes) and the directivity may be clearly seen on the Sourcemaps. Some site effects at large scale are still visible. The strategy proposed in this work is completely automatic without the need of a visual inspection of the input data. Thus it provides a robust assessment of key parameters of the source. We suggest a systematic computation of these ‘Sourcemaps’ after each event inside a dense network.

Tuned-Mass-Damper-Inerter Performance Evaluation and Optimal Design for Transmission Line under Harmonic Excitation

To investigate vibration control and optimal design of transmission lines with tuned-mass-damper-inerter (TMDI), the motion equation of transmission lines with TMDI is established in the paper, and the closed-form solutions of the response spectrum of transmission line displacement are derived by the frequency domain analysis method. The design parameters of TMDI are optimized by fixed-point theory, and the vibration control performance of TMDI is discussed. The results show that the increase in apparent mass ratio has a positive effect on the vibration control performance of TMDI; the vibration control performance is greatly affected by frequency ratio and limited by damping ratio; the increase in both mass ratio and apparent mass ratio reduces the peak values of the displacement response spectra of transmission line with TMDI; however, blindly increasing the apparent mass and mass ratio (β > 0.2 or μ > 0.4) has a limited effect on improving the vibration control performance of TMDI; compared with conventional TMD, the peak values of the controlled displacement response spectrum of the transmission line with TMDI can be reduced by about 12%, and TMDI has a better vibration suppression effect on the transmission lines.

Displacement response spectra for active seismic regions in India

Displacement response spectra for active seismic regions in India

A moving load amplitude spectrum for analyzing the resonance and vibration cancellation of simply supported bridges under moving loads

A novel method for analyzing the resonance and vibration cancellation of simply supported bridges in the frequency domain by using moving load amplitude spectrum (MLAS) is presented in this paper. Firstly, the Fourier transform for the motion equation of simply supported bridge under equidistant moving loads is carried out to derive the bridge's moving load spectrum and displacement response spectrum. The MLAS, which can be obtained by taking the modulus of the moving load spectrum, is related to the moving loads and the vibration modes of the bridge. Surprisingly, the MLAS can effectively reflect the displacement amplitude laws of the bridge free vibration excited by the moving loads. Then, the resonance and vibration cancellation of the simply supported bridge under equidistant moving loads are analyzed respectively based on the proposed MLAS. It is noted that the corresponding resonance speed obtained by the proposed MLAS is a supplement to the traditional resonance speed which sometimes doesn't cause the maximum displacement response of simply supported bridges. What's more, the vibration cancellation of the simply supported bridge under equidistant moving loads is divided into two types in this paper.The corresponding cancellation speeds vc1-can and vc2-can are determined simply by the proposed MLAS in the frequency domain. The time-domain analysis in many references only gives the cancellation speeds vc1-can but not the cancellation speeds vc2-can presented in this paper. Therefore, the cancellation speeds vc1-can and vc2-can presented in this paper can provide a more comprehensive understanding of the influence factors of vibration cancellation. Finally, the relevant theoretical researches on the proposed MLAS are validated with several examples by comparing the results of the time-domain analysis.

Nonlinear soil effects on observed and simulated response spectra

AbstractSoil effects are collectively referred to the influences that local geology and morphology of soil deposits have on ground motions coming from bedrock. The quantification of soil effects in building codes has a great impact in the design of structures because soil factors amplify the reference seismic input, which is typically defined for rock‐type soil class from probabilistic seismic hazards analysis. This topic, within earthquake engineering, represents one of the typical interfaces between structural engineering, geotechnical engineering and engineering seismology. In fact, this issue is generally addressed with different approaches depending on the background of the researchers. This article investigates soil effects combining the viewpoints of structural and geotechnical engineers and seismologists. It is shown that the averaging technique adopted for the definition of ground motion predictive models for spectral ordinates does not play a significant role in defining the results of rock‐like soil classes. However, for other soil classes characterized by soil effects, different methods of averaging the spectral ordinates produce significant differences. The main result of this study is the proposal of a new analytical formulation for the quantification of soil amplification factors for both acceleration and displacement response spectra. The proposed formulation is based on a database of real ground motions and simulated accelerograms. The latter have been obtained through stochastic ground response analyses, with the propagation of natural ground motions on rock‐like soil class through randomly generated soil deposits representative of different soil classes of Eurocode 8 and the Italian Building Code. The comparison between real and simulated data revealed the crucial role of soil nonlinearity in the definition of soil effects, which is also in relation with the variation of magnitude, fault distance and the intensity measures expected on outcropping rock.

Design and analysis of isolation effectiveness for three-dimensional base-seismic isolation of nuclear island building

In order to investigate the application of 3D base-seismic isolation system in nuclear power plants (NPPs), comprehensive analysis of constitution and design theory for 3-dimensional combined isolation bearing (3D-CIB) was presented and derived. Four different vertical stiffness of 3D-CIB was designed to isolate the nuclear island (NI) building. This paper aimed at investigating the isolation effectiveness of 3D-CIB through modal analysis and dynamic time-history analysis. Numerical results in terms of dynamic response of 3D-CIB, relative displacement response, acceleration and floor response spectra (FRS) of the superstructure were compared to validate the reliability of 3D-CIB in mitigating seismic response. The results showed that 3D-CIB can significantly attenuate the horizontal acceleration response, and a fair amount of the vertical acceleration response reduction of the upper structure was still observed. 3D-CIB plays a significant role in reducing the horizontal and vertical FRS, the vertical FRS basically do not vary with the floor height. The smaller the vertical stiffness of 3D-CIB is, the better the vertical isolation effectiveness is, whereas, it will increase the displacement and the rocking effect of superstructure. Although the advantage of 3D-CIB is that the vertical stiffness can be flexibly adjusted, it should be designed by properly accounting for the balance between the isolation effectiveness and displacement control including rocking effect. The results of this study can provide the technical basis and guidance for the application of 3D-CIB to engineering structure.