An extended multiple-support response spectrum method incorporating fluid-structure interaction for seismic analysis of deep-water bridges

The effects of ground motion spatial variability(GMSV)or fluid-structure interaction(FSI)on the seismic responses of deep-water bridges have been extensively examined.However,there are few studies on the seismic performance of bridges considering GMSV and FSI effects simultaneously.In this study,the original multiple-support response spectrum(MSRS)method is extended to consider FSI effect for seismic analysis of deep-water bridges.The solution of hydrodynamic pressure on a pier is obtained using the radiation wave theory,and the FSI-MSRS formulation is derived according to the random vibration theory.The influence of FSI effect on the related coefficients is analyzed.A five-span steel-concrete continuous beam bridge is adopted to conduct the numerical simulations.Different load conditions are designed to investigate the variation of the bridge responses when considering the GMSV and FSI effects.The results indicate that the incoherence effect and wave passage effect decrease the bridge responses with a maximum percentage of 86%,while the FSI effect increases the responses with a maximum percentage of 26%.The GMSV and FSI effects should be included in the seismic design of deep-water bridges.

Response Spectrum Analysis of 7-story Assembled Frame Structure with Energy Dissipation System

Viscoelastic damper is an effective passive damping device,which can reduce the seismic response of the structure by increasing the damping and dissipating the vibration energy of structures.It has a wide application prospect in actual structural vibration control because of simple device and economical material.In view of the poor seismic behaviors of assembled frame structure connections,various energy dissipation devices are proposed to improve the seismic performance.The finite element numerical analysis method is adopted to analyze relevant energy dissipation structural parameters.The response spectrum of a 7-story assembled frame structure combined the ordinary steel support,ordinary viscoelastic damper,and viscoelastic damper with displacement amplification device is analyzed.The analysis results show that the mechanical behavior of assembled frame structure with ordinary steel supports are not significantly different from those without energy dissipation devices.The assembled frame structure with viscoelastic damper has better seismic performance and energy dissipation,especially for the viscoelastic damper with displacement amplification devices.The maximum value of inter-story displacement angle decreases by 32.24%;the maximum floor displacement decreases by 31.91%,and the base shear decreases by 13.62%compared with the assembled frame structures without energy dissipation devices.The results show that the seismic fortification ability of the structure is significantly improved,and the overall structure is more uniformly stressed.The damping structure with viscoelastic damper mainly reduces the dynamic response of the structure by increasing the damping coefficient,rather than by changing the natural vibration period of the structure.This paper provides an effective theoretical basis and reference for improving the energy dissipation system and the seismic performance of assembled frame structures.

Generation of artificial earthquakes for matching target response unsmooth spectrum via wavelet package transform

The seismic records of target response spectrum used in the time-history analysis should be allowed to meet the norms. However, the previous fitting methods of target spectrum are mostly for the situations that the target spectrum is a smooth curve. In many cases, it needs to match unsmooth target spectrum for single determined response spectrum. An adjustment of time history via wavelet packet transform was presented, which is able to fit unsmooth target spectrum. It was found that there is a certain bias between the band center frequency of the component of seismic record after wavelet packet decomposition and the peak frequency of response spectra of wavelet packet components. For this reason, five strategies were presented to select iteration points, and the effects of the five strategies were compared with two calculation examples. It was turned out that the peak frequency of the response spectrum of wavelet packet component can lead to good fitting effect when it is selected as the iteration point. In the iteration process, it shows great promise in fitting non-smooth target spectrum and has a trend of converge.

Efficient simulation of spatially correlated non-stationary ground motions by wavelet-packet algorithm and spectral representation method

Although the classical spectral representation method(SRM)has been widely used in the generation of spatially varying ground motions,there are still challenges in efficient simulation of the non-stationary stochastic vector process in practice.The first problem is the inherent limitation and inflexibility of the deterministic time/frequency modulation function.Another difficulty is the estimation of evolutionary power spectral density(EPSD)with quite a few samples.To tackle these problems,the wavelet packet transform(WPT)algorithm is utilized to build a time-varying spectrum of seed recording which describes the energy distribution in the time-frequency domain.The time-varying spectrum is proven to preserve the time and frequency marginal property as theoretical EPSD will do for the stationary process.For the simulation of spatially varying ground motions,the auto-EPSD for all locations is directly estimated using the time-varying spectrum of seed recording rather than matching predefined EPSD models.Then the constructed spectral matrix is incorporated in SRM to simulate spatially varying non-stationary ground motions using efficient Cholesky decomposition techniques.In addition to a good match with the target coherency model,two numerical examples indicate that the generated time histories retain the physical properties of the prescribed seed recording,including waveform,temporal/spectral non-stationarity,normalized energy buildup,and significant duration.

Time-frequency response spectrum of rotational ground motion and its application

The rotational seismic motions are estimated from one station records of the 1999 Jiji （Chi-Chi）, Taiwan, earthquake based on the theory of elastic plane wave propagation. The time-frequency response spectrum （TFRS） of the rotational motions is calculated and its characteristics are analyzed, then the TFRS is applied to analyze the damage mechanism of one twelve-storey frame concrete structure. The results show that one of the ground motion components can not reflect the characteristics of the seismic motions completely; the characteristics of each component, especially rotational motions, need to be studied. The damage line of the structure and TFRS of ground motion are important for seismic design, only the TFRS of input seismic wave is suitable, the structure design is reliable.

Artificial ground motion compatible with specified ground shaking peaks and target response spectrum

This article describes a hybrid simulation method to generate artificial ground motion time histories that are compatible with specified peak seismic acceleration, velocity and displacement as well as the target response spectrum of absolute acceleration. First, based on traditional methods that match the target spectrum in the frequency domain, an initial acceleration time history was synthesized to satisfy the specified peak acceleration, target spectral acceleration and intensity envelope. Second, by using the inversion formula of the seismic input to a linear single-degree-of-freedom system and by superimposing a series of narrow-band time histories in the time domain, the initial time history is further modified to allow its peak velocity and displacement to approach the targets and improve its matching precision with the target spectrum. Numerical examples are provided to demonstrate that the proposed method achieves good agreement with the target values.

Attenuation relations for horizontal peak ground acceleration and response spectrum in northeastern Tibetan Plateau region

The seismic intensity attenuation relations in northeastern Tibetan Plateau region are established by a regression analysis on isoseismal data. Then the attenuation relations for horizontal peak ground acceleration and short-period response spectrum for western North America are derived based on the database of HUO Jun-rong and strong mo-tion data from recent earthquakes. The attenuation relations of long-period response spectrum for western North America are developed by analyzing the broadband digital seismic recordings of southern California. By integrat-ing the short-period and long-period attenuation relationships, the attenuation relations for horizontal acceleration response spectrum in the period range of 0.04~6 s for western North America are established. The attenuation equation that accounts for the magnitude saturation and near-field saturation of high frequency ground motion is used. Finally the attenuation relations for horizontal peak ground acceleration and response spectrum for the region of northeastern Tibetan Plateau are developed by using the transforming method.

Generating ground motion by two new techniques of adding harmonic wave in the time domain and approximating to response spectrum as a whole

In this paper,two new methods are introduced to fit response spectrum in generating earthquake acceleration time history.The first method is Adding Harmonic Wave in Time Domain(AHWTD).In this method, a control point of response spectrum is adjusted by adding a harmonic time history to the adjusted one.Three features of the method are that it has small cross interference,small amount of computation and it can give consideration to the amplitude envelope.The second one is Approximating Response Spectrum as a Whole(ARSW).This method has following feature. When adjust a time history that is decided by amplitude spectrum A k and phase spectrum φ k(k =0, 1, 2, …, n ), the mean square root of every relative error E j(j= 1, 2, …, M ) between response spectrum and object spectrum V r=∑Mj=1E 2 j/M is used to decide adjusting direction of any amplitude spectrum A k . Because E j and V r are functions of A k and φ k , the problem of fitting response spectrum in generating earthquake acceleration time history can be changed to a problem of finding minimum point of V r . Restricted by Nyquist frequency, AHWTD is not suitable for high frequencies of response spectrum. Restricted by frequency distribution of FFT, the density of control points in the low frequency part can′t be too dense for ARSW. But two methods can replenish each other and get such a good fitting effect that we can fit the given peak ground acceleration and peak ground velocity well at the same time.

A comparison of IBC with 1997 UBC for modal response spectrum analysis in standard-occupancy buildings

This paper presents a comparison of the seismic forces generated from a Modal Response Spectrum Analysis （MRSA） by applying the provisions of two building codes, the 1997 Uniform Building Code （UBC） and the 2000-2009 International Building Code （IBC）, to the most common ordinary residential buildings of standard occupancy. Considering IBC as the state of the art benchmark code, the primary concern is the safety of buildings designed using the UBC as compared to those designed using the IBC. A sample of four buildings with different layouts and heights was used for this comparison. Each of these buildings was assumed to be located at four different geographical sample locations arbitrarily selected to represent various earthquake zones on a seismic map of the USA, and was subjected to code-compliant response spectrum analyses for all sample locations and for five different soil types at each location. Response spectrum analysis was performed using the ETABS software package. For all the cases investigated, the UBC was found to be significantly more conservative than the IBC. The UBC design response spectra have higher spectral accelerations, and as a result, the response spectrum analysis provided a much higher base shear and moment in the structural members as compared to the IBC. The conclusion is that ordinary office and residential buildings designed using UBC 1997 are considered to be overdesigned, and therefore they are quite safe even according to the IBC provisions.

A simplified multisupport response spectrum method

A simplified multisupport response spectrum method is presented.The structural response is a sum of two components of a structure with a first natural period less than 2 s.The first component is the pseudostatic response caused by the inconsistent motions of the structural supports,and the second is the structural dynamic response to ground motion accelerations.This method is formally consistent with the classical response spectrum method,and the effects of multisupport excitation are considered for any modal response spectrum or modal superposition.If the seismic inputs at each support are the same,the support displacements caused by the pseudostatic response become rigid body displacements.The response spectrum in the case of multisupport excitations then reduces to that for uniform excitations.In other words,this multisupport response spectrum method is a modification and extension of the existing response spectrum method under uniform excitation.Moreover,most of the coherency coefficients in this formulation are simplified by approximating the ground motion excitation as white noise.The results indicate that this simplification can reduce the calculation time while maintaining accuracy.Furthermore,the internal forces obtained by the multisupport response spectrum method are compared with those produced by the traditional response spectrum method in two case studies of existing long-span structures.Because the effects of inconsistent support displacements are not considered in the traditional response spectrum method,the values of internal forces near the supports are underestimated.These regions are important potential failure points and deserve special attention in the seismic design of reticulated structures.

Artificial ground motion compatible with specified peak velocity and target spectrum

In this paper, a method, which synthesizes the artificial ground motion compatible with the specified peak velocity as well as the target acceleration response spectrum, was proposed. In this method, firstly, an initial acceleration time history α8^（0） （t）, which satisfies the prescribed peak ground acceleration, the target spectral acceleration ST（ω, ζ）,and the specified intensity envelope, is generated by the traditional method that generates the requency domain; secondly,α8^（0） （t）is further modulated by superimposing narrow-band time histories upon it in the time domain to make its peak velocity, approach the target peak ground velocity, and at the same time to improve its fitting precision to the target spectrum. Numerical examples show that this algorithm boasts high calculation precisions.

The relation between the response spectrum and the phase diference spectrum

The relation between the phase difference spectrum and the response spectrum is studied in this paper. It is found that the phase difference spectrum influences the response spectrum through affecting the response motion′s envelope function shape of a single degree of freedom system. Decreasing the variance of phase difference spectrum causes the increasing of response spectrum when its mean value curve keeps the same, otherwise the situation is opposite. As the increase of the tangent of the mean value curve, the response spectrum decreases, otherwise it increases. The damping plays an important role while the phase difference spectrum influences the response spectrum. The effect of the phase difference spectrum on the absolute acceleration response spectrum becomes more and more obvious with the increase of the damping. On the other hand, the increase of damping weakens the effect of the phase difference spectrum on the amplification factor spectrum.

Sound Source Localization Based on SRP-PHAT Spatial Spectrum and Deep Neural Network

Microphone array-based sound source localization(SSL)is a challenging task in adverse acoustic scenarios.To address this,a novel SSL algorithm based on deep neural network(DNN)using steered response power-phase transform(SRP-PHAT)spatial spectrum as input feature is presented in this paper.Since the SRP-PHAT spatial power spectrum contains spatial location information,it is adopted as the input feature for sound source localization.DNN is exploited to extract the efficient location information from SRP-PHAT spatial power spectrum due to its advantage on extracting high-level features.SRP-PHAT at each steering position within a frame is arranged into a vector,which is treated as DNN input.A DNN model which can map the SRP-PHAT spatial spectrum to the azimuth of sound source is learned from the training signals.The azimuth of sound source is estimated through trained DNN model from the testing signals.Experiment results demonstrate that the proposed algorithm significantly improves localization performance whether the training and testing condition setup are the same or not,and is more robust to noise and reverberation.

Consecutive combined response spectrum

Appropriate estimates of earthquake response spectrum are essential for design of new structures, or seismic safety evaluation of existing structures. This paper presents an alternative procedure to construct design spectrum from a combined normalized response spectrum （NRSc） which is obtained from pseudo-velocity spectrum with the ordinate scaled by different peak ground amplitudes （PGA, PGV, PGD） in different period regions. And a consecutive function./（/） used to normalize the ordinates is defined. Based on a comprehensive study of 220 strong ground motions recorded during recent eleven large worldwide earthquakes, the features of the NRSc are discussed and compared with the traditional normalized acceleration, velocity and displacement response spectra （NRSA, NRSv, NRSD）. And the relationships between ground amplitudes are evaluated by using a weighted mean method instead of the arithmetic mean. Then the NRSc is used to define the design spectrum with given peak ground amplitudes. At last, the smooth spectrum is compared with those derived by the former approaches, and the accuracy of the proposed spectrum is tested through an analysis of the dispersion of ground motion response spectra.

Response Spectrum Method for Extreme Wave Loading With Higher Order Components of Drag Force

Response spectra of fixed offshore structures impacted by extreme waves are investigated based on the higher order components of the nonlinear drag force. In this way, steel jacket platforms are simplified as a mass attached to a light cantilever cylinder and their corresponding deformation response spectra are estimated by utilizing a generalized single degree of freedom system. Based on the wave data recorded in the Persian Gulf region, extreme wave loading conditions corresponding to different return periods are exerted on the offshore structures. Accordingly, the effect of the higher order components of the drag force is considered and compared to the linearized state for different sea surface levels. When the fundamental period of the offshore structure is about one third of the main period of wave loading, the results indicate the linearized drag term is not capable of achieving a reliable deformation response spectrum.

Response spectrum of seismic design code for zones lack of near-fault strong earthquake records

It was shown from the study on the recently near-fault earthquake ground motions that the near-fault effects were seldom considered in the existing Chinese seismic code. Referring to the UBC97 design concept for near-fault factors, based on the collected world-widely free-site records of near-fault earthquakes ground motions classified by earthquake magnitude and site condition, the attenuation relationship expressions of the acceleration spectrum demand at the key points within the long period and moderate period were established in term of the earthquake magnitude and the site condition. Furthermore, the near-fault factors＇ expressions about the earthquake magnitude and the fault distance were deduced for the area lack of near-fault strong earthquake records. Based on the current Chinese Building Seismic Design Code, the near-fault effect factors and the modified design spectral curves, which were valuable for the seismic design, were proposed to analyze the seismic response of structures.

The dependence of response spectrum on the tectonic ambient shear stress field

It has been analyzed the influence of the tectonic ambient shear stress value on response spectrum based on the previous theory. Based on the prediction equation BJF94 presented by the famous American researchers, CLB20, a new prediction formula is proposed by us, where it is introduced the influence of tectonic ambient shear stress value on response spectrum. BJF94 is the prediction equation, which mainly depends on strong ground motion data from western USA, while the prediction equation SEA99 is based on the strong ground motion data from exten-sional region all over the world. Comparing these two prediction equations in detail, it is found that after BJF94′s prediction value lg(Y) minus 0.16 logarithmic units, the value is very close to SEA99′s one. This case demonstrates that lg(Y) in extensional region is smaller; the differences of prediction equation are mainly owe to the differences of tectonic ambient shear stress value. If the factor of tectonic ambient shear stress value is included into the pre-diction equation, and the magnitude is used seismic moment magnitude to express, which is universal used around the world, and the distance is used the distance of fault project, which commonly used by many people, then re-gional differences of prediction equation will become much less, even vanish, and it can be constructed the uni-versal prediction equation proper to all over the world. The error in the earthquake-resistant design in China will be small if we directly use the results of response spectrum of USA (e.g. BJF94 or SEA99).

Nonlinear response spectrums for cable-supported glass curtain walls

Aiming at the seismic-resistant performance of cable-supported glass curtain walls,the methods for formulating nonlinear single degree of freedom system and calculating the nonlinear response spectrums are proposed. Taking pretension effect in cables and geometrical nonlinearity into account,the nonlinear acceleration spectrums are calculated under given conditions,such as site and different seismic fortification intensities. The seismic design response spectrums are developed. During vibrating,varying period due to the influence of pretension effect in cables and geometrical nonlinearity drives the maximum period of plateau in nonlinear response spectrums to move towards the long period zone,and the maximum of seismic effect coefficient is larger than that of current seismic code. The theoretical analysis and the example demonstrate that using the nonlinear response spectrums is safe and economical.

Comparison of DSHA-based response spectrum with design response spectrum of building code of Pakistan(BCP-SP-2007)for a site in Muzaffargarh area,Pakistan

The building code of any country is considered to be a basic technical guidance document for the seismic design of structures.However,building codes are typically developed for the whole country,without considering site specific models that incorporate detailed site-specific data.Therefore,the adequacy of the design spectrum for building codes may sometimes be questionable.To study the sufficiency of the building codes of Pakistan(BCP-SP-2007),a deterministic seismic hazard analysis(DSHA)based spectrum was developed for a site in the Muzaffargarh area,Pakistan,using an updated earthquake catalogue,seismic source model,and a next generation attenuation model(NGA-WEST-2).Further,an International Building Code(IBC-2000)spectrum was developed for the study area to compare the results.The DSHA-based response spectrum resulted in a peak ground acceleration(PGA)value of 0.21 g for the Chaudwan fault.The evaluation of BCP-SP-2007 and IBC-2000 spectra provided a critical assessment for analyzing the associated margins.A comparison with the DSHA-based response spectrum showed that the BCP-SP-2007 design spectrum mostly overlapped with the DSHA spectrum unlike IBC-2000.However,special attention is needed for designing buildings in the study area when considering earthquake periods longer than 1 s,and the BCP-SP-2007 spectrum can be enhanced when considering a period range of 0.12-0.64 s.Finally,BCP-SP-2007 is based on a probabilistic approach and its comparison with deterministic results showed the significance of both methods in terms of design.

Comparison of Design Response Spectrum for Long Period Structures Based on Scenario Earthquakes

Two kinds of determining methods for scenario earthquakes are presented in this paper,namely the weighted average method and maximum probability method. This paper briefly introduces the two methods,then taking a high-rise building in the Yantai area as a case study,we use the weighted average method and maximum probability method to realize seismic hazard analysis, determine earthquake magnitude, the epicenter and specific space position,and then give two response spectrums of the two methods. By comparing the differences of response spectrums between the two methods,we find that the weighted average method is more suitable for long period structures,while considering long period safety. The maximum probability method is more suitable for short period structures. It is reasonable to choose a corresponding different method when the structures have different natural vibration periods.