## SEARCH

#### Institution

##### ( see all 599)

- China Earthquake Administration 81 (%)
- Tongji University 54 (%)
- Harbin Institute of Technology 52 (%)
- Dalian University of Technology 34 (%)
- Tsinghua University 26 (%)

#### Author

##### ( see all 2210)

- Lee, George C. 25 (%)
- Xie, Lili 22 (%)
- Li, Jie 13 (%)
- Chang, Shuenn-Yih 11 (%)
- Liang, Jianwen 10 (%)

#### Subject

##### ( see all 7)

- Vibration, Dynamical Systems, Control 685 (%)
- Civil Engineering 668 (%)
- Earth Sciences 433 (%)
- Geotechnical Engineering 354 (%)
- Geotechnical Engineering & Applied Earth Sciences 314 (%)

## CURRENTLY DISPLAYING:

Most articles

Fewest articles

Showing 1 to 50 of 712 matching Articles
Results per page:

## Modified precise time step integration method of structural dynamic analysis

### Earthquake Engineering and Engineering Vibration (2005-12-01) 4: 287-293 , December 01, 2005

The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method (e.g., an algorithm with an arbitrary order of accuracy) is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix *H*. If the matrix *H* is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.

## Parameter identification of hysteretic model of rubber-bearing based on sequential nonlinear least-square estimation

### Earthquake Engineering and Engineering Vibration (2010-09-01) 9: 375-383 , September 01, 2010

In order to evaluate the nonlinear performance and the possible damage to rubber-bearings (RBs) during their normal operation or under strong earthquakes, a simplified Bouc-Wen model is used to describe the nonlinear hysteretic behavior of RBs in this paper, which has the advantages of being smooth-varying and physically motivated. Further, based on the results from experimental tests performed by using a particular type of RB (GZN110) under different excitation scenarios, including white noise and several earthquakes, a new system identification method, referred to as the sequential nonlinear least-square estimation (SNLSE), is introduced to identify the model parameters. It is shown that the proposed simplified Bouc-Wen model is capable of describing the nonlinear hysteretic behavior of RBs, and that the SNLSE approach is very effective in identifying the model parameters of RBs.

## Application of consequence-based design criteria in regions of moderate seismicity

### Earthquake Engineering and Engineering Vibration (2003-06-01) 2: 35-38 , June 01, 2003

Current design criteria and principles of earthquake engineering design are reviewed, including safety factors, probabilistic approach, and two-level and multi-level functional design ideas. The modern multi-functional idea is discussed in greater details. When designing a structure, its resistance to and the intensity of the earthquake action are considered. The consequence of failure of the structure is considered only through a rough and empirical factor of importance, ranging usually from 1.0 to 1.5. This paper suggests a method of “consequence-based design,” which considers the consequences of malfunctioning instead of simply an importance factor. The main argument for this method is that damage to a structure located in different types of societies may have very different consequences, which are dependant on its value and usefulness to the society and the seismicity in the region.

## Research on seismic performance of shear walls with concrete filled steel tube columns and concealed steel trusses

### Earthquake Engineering and Engineering Vibration (2011-12-01) 10: 535-546 , December 01, 2011

In order to further improve the seismic performance of RC shear walls, a new composite shear wall with concrete filled steel tube (CFT) columns and concealed steel trusses is proposed. This new shear wall is a double composite shear wall; the first composite being the use of three different force systems, CFT, steel truss and shear wall, and the second the use of two different materials, steel and concrete. Three 1/5 scaled experimental specimens: a traditional RC shear wall, a shear wall with CFT columns, and a shear wall with CFT columns and concealed steel trusses, were tested under cyclic loading and the seismic performance indices of the shear walls were comparatively analyzed. Based on the data from these experiments, a thorough elastic-plastic finite element analysis and parametric analysis of the new shear walls were carried out using ABAQUS software. The finite element results of deformation, stress distribution, and the evolution of cracks in each phase were compared with the experimental results and showed good agreement. A mechanical model was also established for calculating the load-carrying capacity of the new composite shear walls. The results show that this new type of shear wall has improved seismic performance over the other two types of shear walls tested.

## Seismic performance of buildings during 2011 Van earthquakes and rebuilding efforts

### Earthquake Engineering and Engineering Vibration (2016-09-01) 15: 591-606 , September 01, 2016

The October 23, 2011 *M*7.2 Tabanli - Van and November 9, 2011 *M*5.2 Edremit–Van earthquakes caused damage in a widespread area across the Van province in Turkey. The ground motions, the damage caused by these earthquakes and the recent progress related to recovery efforts are presented herein. First, the key properties of the recorded strong ground motions like spectral amplitudes and directionality are evaluated. The observed damage in the affected reinforced concrete and masonry structures are discussed. The set of common structural damage mechanisms (i.e., soft story failure, torsional response due to plan irregularity, short column failure, pull out failure, pounding) observed in the damaged buildings were identified. The relationship between the key structural properties and the extent of damage is investigated. The primary loss drivers across the region were identified to be the poor quality of workmanship and improper use of building materials. The results from the investigation suggest that a large portion of the loss could have been prevented if sufficient attention and care were given to the implementation of the design regulations and in particular to the construction practice. Lastly, the recent progress in the ongoing rebuilding activities is presented.

## Nonlinear earthquake response analysis and energy calculation for seismic slit shear wall structures

### Earthquake Engineering and Engineering Vibration (2002-12-01) 1: 227-237 , December 01, 2002

Based on the concept of structural passive control, a new type of slit shear wall, with improved seismic performance when compared to an ordinary solid shear wall, was proposed by the authors in 1996. The idea has been verified by a series of pseudo-static and dynamic tests. In this paper a macro numerical model is developed for the wall element and the energy dissipation device. Then, nonlinear time history analysis is carried out for a 10-story slit shear wall model tested on a shaking table. Furthermore, the seismic input energy and the individual energy dissipated by the components are calculated by a method based on Newmark-β assumptions for this shear wall model, and the advantages of this shear wall are further demonstrated by the calculation results from the viewpoint of energy. Finally, according to the seismic damage criterion on the basis of plastic accumulative energy and maximum response, the optimal analysis is carried out to select design parameters for the energy dissipation device.

## Experimental study on full-scale steel beam-to-column moment connections

### Earthquake Engineering and Engineering Vibration (2005-12-01) 4: 311-323 , December 01, 2005

Ten full-scale steel beam-to-column moment connections used in moment-resisting frames (MRFs) were tested to study the failure process, failure mode, strength and plastic rotation capacity. The specimens include one traditional welded flange-bolted web connection, one traditional fully welded connection, four beam flange strengthened connections, three beam flange weakened connections, and one through-diaphragm connection. The test results show that the connections with flange cover plates or with partly cut beam flanges satisfy the beam plastic rotation demand for ductile MRFs. From the measured stress profiles along the beam flange and beam web depth, the mechanics of brittle fracture at the end of the beam is discussed. Design recommendations for steel beam-to-column moment connections are proposed.

## Delay-dependent stability and added damping of SDOF real-time dynamic hybrid testing

### Earthquake Engineering and Engineering Vibration (2010-09-01) 9: 425-438 , September 01, 2010

It is well-recognized that a transfer system response delay that reduces the test stability inevitably exists in real-time dynamic hybrid testing (RTDHT). This paper focuses on the delay-dependent stability and added damping of SDOF systems in RTDHT. The exponential delay term is transferred into a rational fraction by the Padé approximation, and the delay-dependent stability conditions and instability mechanism of SDOF RTDHT systems are investigated by the root locus technique. First, the stability conditions are discussed separately for the cases of stiffness, mass, and damping experimental substructure. The use of root locus plots shows that the added damping effect and instability mechanism for mass are different from those for stiffness. For the stiffness experimental substructure case, the instability results from the inherent mode because of an obvious negative damping effect of the delay. For the mass case, the delay introduces an equivalent positive damping into the inherent mode, and instability occurs at an added high frequency mode. Then, the compound stability condition is investigated for a general case and the results show that the mass ratio may have both upper and lower limits to remain stable. Finally, a high-emulational virtual shaking table model is built to validate the stability conclusions.

## Diffraction of plane SV waves by a cavity in poroelastic half-space

### Earthquake Engineering and Engineering Vibration (2009-03-01) 8: 29-46 , March 01, 2009

This paper presents an indirect boundary integration equation method for diffraction of plane SV waves by a 2-D cavity in a poroelastic half-space. The Green’s functions of compressive and shear wave sources are derived based on Biot’s theory. The scattered waves are constructed using fictitious wave sources close to the boundary of the cavity, and their magnitudes are determined by the boundary conditions. Verification of the accuracy is performed by: (1) checking the satisfaction extent of the boundary conditions, (2) comparing the degenerated solutions of a single-phased case with well-known solutions, and (3) examining the numerical stability of the solutions. The nature of diffraction of plane SV waves around a cavity in a poroelastic half-space is investigated by numerical examples.

## New lumped-mass-stick model based on modal characteristics of structures: development and application to a nuclear containment building

### Earthquake Engineering and Engineering Vibration (2013-06-01) 12: 307-317 , June 01, 2013

In this study, a new lumped-mass-stick model (LMSM) is developed based on the modal characteristics of a structure such as eigenvalues and eigenvectors. The simplified model, named the “frequency adaptive lumped-massstick model,” hasonly a small number of stick elements and nodes to provide the same natural frequencies of the structure and is applied to a nuclear containment building. To investigate the numerical performance of the LMSM, a time history analysis is carried out on both the LMSM and the finite element model (FEM) for a nuclear containment building. A comparison of the results shows that the dynamic responses of the LMSM in terms of displacement and acceleration are almost identical to those of the FEM. In addition, the results in terms of fl oor response spectra at certain elevations are also in good agreement.

## 3-D consistency dynamic constitutive model of concrete

### Earthquake Engineering and Engineering Vibration (2010-06-01) 9: 233-246 , June 01, 2010

Based on the consistency-viscoplastic constitutive model, the static William-Warnke model with threeparameters is modified and a consistency-viscoplastic William-Warnke model with three-parameters is developed that considers the effect of strain rates. Then, the tangent modulus of the consistency viscoplastic model is introduced and an implicit backward Elure iterative algorithm is developed. Comparisons between the numerical simulations and experimental data show that the consistency model properly provides the uniaxial and biaxial dynamic behaviors of concrete. To study the effect of strain rates on the dynamic response of concrete structures, the proposed model is used in the analysis of the dynamic response of a simply-supported beam and the results show that the strain rate has a significant effect on the displacement and stress magnitudes and distributions. Finally, the seismic responses of a 278 m high arch dam are obtained and compared by using the linear elastic model, as well as rate-independent and rate-dependent William-Warnke three-parameter models. The results indicate that the strain rate affects the first principal stresses, and the maximal equivalent viscoplastic strain rate of the arch dam. Numerical calculations and analyses reveal that considering the strain rate is important in the safety assessments of arch dams located in seismically active areas.

## A new model for analyzing nonlinear torsion behavior of concrete filled steel tube columns with rectangular section

### Earthquake Engineering and Engineering Vibration (2016-06-01) 15: 269-282 , June 01, 2016

An experimental study on concrete filled steel tube columns with rectangular section subjected to compressionflexure-torsion combined action has been carried out. The failure modes and load-deformation hysteretic relations were obtained. Based on the principles of classical material mechanics, the relations between the torsion curvature of the section and the shear strain of the fiber on the section were established. Then the strain distribution on the rectangular section of concrete filled steel tube columns subjected to torsion was analyzed. The three-dimensional refined finite element model was also built, in order to make the precision verification. The matrix forms of the relation between the torsion curvature of the section and the shear strain of the fiber on the section were derived, and introduced into the fiber beam model considering nonlinear torsion effect on the section. The comparison between test results and calculation results showed that the fiber beam model considering nonlinear torsion effect had high modeling efficiency and solution precision for predicting the torsion behavior of concrete filled steel tube columns with rectangular sections, and was suitable for analyzing the dynamic response of various structures subjected to the combined cyclic load caused by the earthquake load.

## Karhunen-Loéve expansion for random earthquake excitations

### Earthquake Engineering and Engineering Vibration (2015-03-01) 14: 77-84 , March 01, 2015

This paper develops a trigonometric-basis-function based Karhunen-Loéve (KL) expansion for simulating random earthquake excitations with known covariance functions. The methods for determining the number of the KL terms and defining the involved random variables are described in detail. The simplified form of the KL expansion is given, whereby the relationship between the KL expansion and the spectral representation method is investigated and revealed. The KL expansion is of high efficiency for simulating long-term earthquake excitations in the sense that it needs a minimum number of random variables, as compared with the spectral representation method. Numerical examples demonstrate the convergence and accuracy of the KL expansion for simulating two commonly-used random earthquake excitation models and estimating linear and nonlinear random responses to the random excitations.

## Modal parameter identification and damping ratio estimation from the full-scale measurements of a typical Tibetan wooden structure

### Earthquake Engineering and Engineering Vibration (2016-12-01) 15: 681-695 , December 01, 2016

Tibetan heritage buildings have a high historical and cultural value. They have endured adverse environmental loadings over hundreds of years without significant damage. However, there are few reports on their structural characteristics under normal environmental loadings and their behavior under dynamic loadings. In this research, a typical Tibetan wooden wall-frame building is selected to study its dynamic characteristics. Field measurements of the structure were conducted under environmental excitation to collect acceleration responses. The stochastic subspace identification (SSI) method was adopted to calculate the structural modal parameters and obtain the out-of-plane vibration characteristics of the slab and frames. The results indicated that the wall-frame structure had a lower out-of-plane stiffness and greater in-plane stiffness due to the presence of stone walls. Due to poor identified damping ratio estimates from the SSI method, a method based on the variance upper bound was proposed to complement the existing variance lower bound method for estimating the modal damping ratio to address the significant damping variability obtained from different points and measurements. The feasibility of the proposed method was illustrated with the measured data from the floor slab of the structure. The variance lower and upper bound methods both provided consistent results compared to those from the traditional SSI method.

## Research on the random seismic response analysis for multi- and large-span structures to multi-support excitations

### Earthquake Engineering and Engineering Vibration (2015-09-01) 14: 527-538 , September 01, 2015

The pseudo excitation method (PEM) has been improved into a more practical form, on which the analytic formulae of seismic response power spectral density (PSD) of simplified large-span structural models have been derived. The analytic formulae and numerical computing results of seismic response PSD have been derived to study the mechanism of multi-support excitation effects, such as the wave-passage effect and incoherence effect, for the seismic response of multiand large-span structures. By using a multi-span truss as an example, the influence of multi-support excitation effects on the seismic response of such structures is studied.

## Double deck bridge behavior and failure mechanism under seismic motions using nonlinear analyzes

### Earthquake Engineering and Engineering Vibration (2013-09-01) 12: 447-461 , September 01, 2013

This paper investigates the behavior and the failure mechanism of a double deck bridge constructed in China through nonlinear time history analysis. A parametric study was conducted to evaluate the influence of different structural characteristics on the behavior of the double deck bridge under transverse seismic motions, and to detect the effect of bidirectional loading on the seismic response of this type of bridge. The results showed that some characteristics, such as the variable lateral stiffness, the foundation modelling, and the longitudinal reinforcement ratio of the upper and lower columns of the bridge pier bents have a major impact on the double deck bridge response and its failure mechanism under transverse seismic motions. It was found that the soft story failure mechanism is not unique to the double deck bridge and its occurrence is related to some conditions and structural characteristics of the bridge structure. The analysis also showed that the seismic vulnerability of the double deck bridge under bi-directional loading was severely increased compared to the bridge response under unidirectional transverse loading, and out-of-phase movements were triggered between adjacent girders.

## Ground motion spatial variability effects on seismic response control of cable-stayed bridges

### Earthquake Engineering and Engineering Vibration (2011-03-25) 10: 37-49 , March 25, 2011

The spatial variability of input ground motion at supporting foundations plays a key role in the structural response of cable-stayed bridges (CSBs); therefore, spatial variation effects should be included in the analysis and design of effective vibration control systems. The control of CSBs represents a challenging and unique problem, with many complexities in modeling, control design and implementation, since the control system should be designed not only to mitigate the dynamic component of the structural response but also to counteract the effects of the pseudo-static component of the response. The spatial variability effects on the feasibility and efficiency of seismic control systems for the vibration control of CSBs are investigated in this paper. The assumption of uniform earthquake motion along the entire bridge may result in quantitative and qualitative differences in seismic response as compared with those produced by uniform motion at all supports. A systematic comparison of passive and active system performance in reducing the structural responses is performed, focusing on the effect of the spatially varying earthquake ground motion on the seismic response of a benchmark CSB model with different control strategies, and demonstrates the importance of accounting for the spatial variability of excitations.

## Quasi-real time inversion method of three-dimensional epicenter coordinate, trigger time, and magnitude based on CORS

### Earthquake Engineering and Engineering Vibration (2016-09-01) 15: 425-433 , September 01, 2016

This study explores the quasi-real time inversion principle and precision estimation of three-dimensional coordinates of the epicenter, trigger time and magnitude of earthquakes with the aim to improve traditional methods, which are flawed due to missing information or distortion in the seismograph records. The epicenter, trigger time and magnitude from the Lushan earthquake are inverted and analyzed based on high-frequency GNSS data. The inversion results achieved a high precision, which are consistent with the data published by the China Earthquake Administration. Moreover, it has been proven that the inversion method has good theoretical value and excellent application prospects.

## From the editors

### Earthquake Engineering and Engineering Vibration (2005-06-01) 4: iii , June 01, 2005

## Twin lintel belt in steel for seismic strengthening of brick masonry buildings

### Earthquake Engineering and Engineering Vibration (2004-12-01) 3: 215-222 , December 01, 2004

A single-room, single-storey full-scale brick masonry building with precast RC roofing system was tested thrice under displacement controlled lateral cyclic loading, to assess the effectiveness of the basic repair and seismic strengthening techniques. Initially, the virgin building specimen was loaded laterally to failure. In the second stage, the damaged building was repaired by stitching across the cracks, and tested under the same lateral loading. In the third stage, the twice-damaged structure was repaired once more by stitching and strengthened by twin lintel belt in steel and vertical corner reinforcement, and re-tested. The building strengthened by*twin lintel belt in steel* showed about 28% higher strength under lateral loading than the virgin building.

## Identification of acceleration pulses in near-fault ground motion using the EMD method

### Earthquake Engineering and Engineering Vibration (2005-12-01) 4: 201-212 , December 01, 2005

In this paper, response spectral characteristics of one-, two-, and three-lobe sinusoidal acceleration pulses are investigated, and some of their basic properties are derived. Furthermore, the empirical mode decomposition (EMD) method is utilized as an adaptive filter to decompose the near-fault pulse-like ground motions, which were recorded during the September 20, 1999, Chi-Chi earthquake. These ground motions contain distinct velocity pulses, and were decomposed into high-frequency (HF) and low-frequency (LF) components, from which the corresponding HF acceleration pulse (if existing) and LF acceleration pulse could be easily identified and detected. Finally, the identified acceleration pulses are modeled by simplified sinusoidal approximations, whose dynamic behaviors are compared to those of the original acceleration pulses as well as to those of the original HF and LF acceleration components in the context of elastic response spectra. It was demonstrated that it is just the acceleration pulses contained in the near-fault pulse-like ground motion that fundamentally dominate the special impulsive dynamic behaviors of such motion in an engineering sense. The motion thus has a greater potential to cause severe damage than the far-field ground motions, i.e. they impose high base shear demands on engineering structures as well as placing very high deformation demands on long-period structures.

## Suboptimal Rayleigh damping coefficients in seismic analysis of viscously-damped structures

### Earthquake Engineering and Engineering Vibration (2014-12-01) 13: 653-670 , December 01, 2014

An optimization method for the consistent evaluation of two Rayleigh damping coefficients is proposed. By minimizing an objective function such as an error term of the peak displacement of a structure, the two coefficients can be determined with response spectral analysis. The optimization method degenerates into the conventional method used in current practices when only two modes of vibration are included in the objective function. Therefore, the proposed method with all significant modes included for simplicity in practical applications results in suboptimal damping coefficients. The effects of both spatial distribution and frequency content of excitations as well as structural dynamic characteristics on the evaluation of Rayleigh damping coefficients were investigated with a five-story building structure. Two application examples with a 62-story high-rise building and a 840 m long cable-stayed bridge under ten earthquake excitations demonstrated the accuracy and effectiveness of the proposed method to account for all of the above effects.

## Health monitoring of time-varying stochastic structures by latent components and fuzzy expert system

### Earthquake Engineering and Engineering Vibration (2008-05-01) 7: 91-106 , May 01, 2008

In this paper, a novel parametric model-based decomposition method is proposed for structural health monitoring of time-varying structures. For this purpose, the advanced Functional-Series Time-dependent Auto Regressive Moving Average (FS-TARMA) technique is used to estimate the parameters and innovation variance used in the parametric signal decomposition scheme. Additionally, a unique feature extraction and reduction method based on the decomposed signals, known as Latent Components (LCs), is proposed. To evaluate the efficiency of the proposed method, numerical simulation and an experimental study in the laboratory were conducted on a time-varying structure, where various types of damage were introduced. The Fuzzy Expert System (FES) was used as a classification tool to demonstrate that the proposed method successfully identifies different structural conditions when compared with other methods based on non-reduced and ordinary feature extraction.

## Stochastic seismic response of structures with added viscoelastic dampers modeled by fractional derivative

### Earthquake Engineering and Engineering Vibration (2003-06-01) 2: 133-139 , June 01, 2003

Viscoelastic dampers, as supplementary energy dissipation devices, have been used in building structures under seismic excitation or wind loads. Different analytical models have been proposed to describe their dynamic force deformation characteristics. Among these analytical models, the fractional derivative models have attracted more attention as they can capture the frequency dependence of the material stiffness and damping properties observed from tests very well. In this paper, a Fourier-transform-based technique is presented to obtain the fractional unit impulse function and the response of structures with added viscoelastic dampers whose force-deformation relationship is described by a fractional derivative model. Then, a Duhamel integral-type expression is suggested for the response analysis of a fractional damped dynamic system subjected to deterministic or random excitation. Through numerical verification, it is shown that viscoelastic dampers are effective in reducing structural responses over a wide frequency range, and the proposed schemes can be used to accurately predict the stochastic seismic response of structures with added viscoelastic dampers described by a Kelvin model with fractional derivative.

## Site effects by generalized inversion technique using strong motion recordings of the 2008 Wenchuan earthquake

### Earthquake Engineering and Engineering Vibration (2013-06-01) 12: 165-184 , June 01, 2013

The generalized inversion of S-wave amplitude spectra from the free-field strong motion recordings of the China National Strong Motion Observation Network System (NSMONS) are used to evaluate the site effects in the Wenchuan area. In this regard, a total of 602 recordings from 96 aftershocks of the Wenchuan earthquake with magnitudes of *M*3.7-*M*6.5 were selected as a dataset. These recordings were obtained from 28 stations at a hypocenter distance ranging from 30 km to 150 km. The inversion results have been verified as reliable by comparing the site response at station 62WUD using the Generalized Inversion Technique (GIT) and the Standard Spectral Ratio method (SSR). For all 28 stations, the site predominant frequency *F*_{p} and the average site amplification in different frequency bands of 1.0–5.0 Hz, 5.0–10.0 Hz and 1.0–10.0 Hz have been calculated based on the inversion results. Compared with the results from the horizontal-to-vertical spectral ratio (HVSR) method, it shows that the HVSR method can reasonably estimate the site predominant frequency but underestimates the site amplification. The linear fitting between the average site amplification for each frequency band and the *V*_{s20} (the average uppermost-20 m shear wave velocity) shows good correlation. A distance measurement called the asperity distance *D*_{Aspt} is proposed to reasonably characterize the source-to-site distance for large earthquakes. Finally, the inversed site response is used to identify the soil nonlinearity in the main shock and aftershocks of Wenchuan earthquake. In ten of the 28 stations analyzed in the main shock, the soil behaved nonlinearly, where the ground motion level is apparently beyond a threshold of PGA > 300 cm/s^{2} or PGV > 20 cm/s, and only one station coded 51SFB has evidence of soil nonlinear behavior in the aftershocks.

## Design spectra including effect of rupture directivity in near-fault region

### Earthquake Engineering and Engineering Vibration (2006-12-01) 5: 159-170 , December 01, 2006

In order to propose a seismic design spectrum that includes the effect of rupture directivity in the near-fault region, this study investigates the application of equivalent pulses to the parameter attenuation relationships developed for near-fault, forward-directivity motions. Near-fault ground motions are represented by equivalent pulses with different waveforms defined by a small number of parameters (peak acceleration, *A*, and velocity *V*; and pulse period, *T*_{v}). Dimensionless ratios between these parameters (e.g., *AT*_{v}/*V*, *VT*_{v}/*D*) and response spectral shapes and amplitudes are examined for different pulses to gain insight on their dependence on basic pulse waveforms. Ratios of *AT*_{v}/*V*, *VT*_{v}/*D*, and the ratio of pulse period to the period for peak spectral velocity (*T*_{v-p}) are utilized to quantify the difference between rock and soil sites for near-fault forward-directivity ground motions. The *AT*_{v}/*V* ratio of recorded near-fault motions is substantially larger for rock sites than that for soil sites, while *T*_{v-p}/*T*_{v} ratios are smaller at rock sites than at soil sites. Furthermore, using simple pulses and available predictive relationships for the pulse parameters, a preliminary model for the design acceleration response spectra for the near-fault region that includes the dependence on magnitude, rupture distance, and local site conditions are developed.

## Earthquake damage potential and critical scour depth of bridges exposed to flood and seismic hazards under lateral seismic loads

### Earthquake Engineering and Engineering Vibration (2015-12-01) 14: 579-594 , December 01, 2015

Many bridges located in seismic hazard regions suffer from serious foundation exposure caused by riverbed scour. Loss of surrounding soil significantly reduces the lateral strength of pile foundations. When the scour depth exceeds a critical level, the strength of the foundation is insufficient to withstand the imposed seismic demand, which induces the potential for unacceptable damage to the piles during an earthquake. This paper presents an analytical approach to assess the earthquake damage potential of bridges with foundation exposure and identify the critical scour depth that causes the seismic performance of a bridge to differ from the original design. The approach employs the well-accepted response spectrum analysis method to determine the maximum seismic response of a bridge. The damage potential of a bridge is assessed by comparing the imposed seismic demand with the strengths of the column and the foundation. The versatility of the analytical approach is illustrated with a numerical example and verified by the nonlinear finite element analysis. The analytical approach is also demonstrated to successfully determine the critical scour depth. Results highlight that relatively shallow scour depths can cause foundation damage during an earthquake, even for bridges designed to provide satisfactory seismic performance.

## Dynamic shear modulus of undisturbed soil under different consolidation ratios and its effects on surface ground motion

### Earthquake Engineering and Engineering Vibration (2013-12-01) 12: 561-568 , December 01, 2013

The dynamic shear modulus for three types of undisturbed soil under different consolidation ratios is presented by using the resonant column test method. Its effects on surface ground motion is illustrated by calculation. The test results indicate that the power function is a suitable form for describing the relationship between the ratio of the maximum dynamic shear modulus due to anisotropic and isotropic consolidations and the increment of the consolidation ratio. When compared to sand, the increment of the maximum dynamic shear modulus for undisturbed soil due to anisotropic consolidation is much larger. Using a one-dimensional equivalent linearization method, the earthquake influence factor and the characteristic period of the surface acceleration are calculated for two soil layers subjected to several typical earthquake waves. The calculated results show that the difference in nonlinear properties due to different consolidation ratios is generally not very notable, but the degree of its influence on the surface acceleration spectrum is remarkable for the occurrence of strong earthquakes. When compared to isotropic consolidation, the consideration of actual anisotropic consolidation causes the characteristic period to decrease and the earthquake influence factor to increase.

## Damage characteristics and seismic capacity of buildings during Nepal M s 8.1 earthquake

### Earthquake Engineering and Engineering Vibration (2015-09-01) 14: 571-578 , September 01, 2015

The extensive damage to buildings caused by the Nepal *M*_{s} 8.1 earthquake has attracted much attention by the international community. After the preliminary scientific investigations on the different affected areas in Nepal, the construction and damage characteristics of five different types of buildings commonly existing in Nepal were discussed and the reasons of their disaster performance were analyzed. Types of buildings investigated include reinforced concrete (RC) frame structures, rubble structures, brick-wood structures, raw soil structures, and brick-wood structures of historic buildings. In addition, the weak links of the seismic design were pointed out, which was very important for the post-earthquake reconstruction and recovery, and gave a preliminary explanations for the damage experienced.

## Control devices incorporated with shape memory alloy

### Earthquake Engineering and Engineering Vibration (2007-06-01) 6: 159-169 , June 01, 2007

Shape Memory Alloy (SMA) is a type of material that offers some unique characteristics for use in devices for vibration control applications. Based on SMA’s material properties, four types of control devices that incorporate NiTiSMA wires are introduced in this paper, which include three types of dampers (SMA damper, SMA-MR damper and SMA-friction damper) and one kind of isolation bearing (SMA-rubber bearing). Mechanical models of these devices and their experimental verifications are presented. To investigate the control performance of these devices, the SMA-MR damper and SMA-rubber bearing are applied to structures. The results show that the control devices could be effective in reducing the seismic response of structures.

## Seismic reliability analysis of large electric power systems

### Earthquake Engineering and Engineering Vibration (2004-06-01) 3: 51-55 , June 01, 2004

Based on the De.Morgan laws and Boolean simplification, a recursive decomposition method is introduced in this paper to identify the main exclusive safe paths and failed paths of a network. The reliability or the reliability bound of a network can be conveniently expressed as the summation of the joint probabilities of these paths. Under the multivariate normal distribution assumption, a conditioned reliability index method is developed to evaluate joint probabilities of various exclusive safe paths and failed paths, and, finally, the seismic reliability or the reliability bound of an electric power system. Examples given in the paper show that the method is very simple and provides accurate results in the seismic reliability analysis.

## Seismic vulnerability evaluation of axially loaded steel built-up laced members II: evaluations

### Earthquake Engineering and Engineering Vibration (2008-06-01) 7: 125-136 , June 01, 2008

The test results described in Part 1 of this paper (Lee and Bruneau, 2008) on twelve steel built-up laced members (BLMs) subjected to quasi-static loading are analyzed to provide better knowledge on their seismic behavior. Strength capacity of the BLM specimens is correlated with the strength predicted by the AISC LRFD Specifications. Assessments of hysteretic properties such as ductility capacity, energy dissipation capacity, and strength degradation after buckling of the specimen are performed. The compressive strength of BLMs is found to be relatively well predicted by the AISC LRFD Specifications. BLMs with smaller *kl/r* were ductile but failed to reach the target ductility of 3.0 before starting to fracture, while those with larger *kl/r* could meet the ductility demand in most cases. The normalized energy dissipation ratio, *E*_{C}/*E*_{T} and the normalized compressive strength degradation, *C*_{r}″/*C*_{r} of BLMs typically decrease as normalized displacements *δ*/*δ*_{b,exp} increase, and the ratios for specimens with larger *kl/r* dropped more rapidly than for specimens with smaller *kl/r*; similar trends were observed for the monolithic braces. The BLMs with a smaller slenderness ratio, *kl/r*, and width-to-thickness ratio, *b/t*, experienced a larger number of inelastic cycles than those with larger ratios.

## Parallel finite element modeling of earthquake ground response and liquefaction

### Earthquake Engineering and Engineering Vibration (2004-06-01) 3: 23-37 , June 01, 2004

Parallel computing is a promising approach to alleviate the computational demand in conducting large-scale finite element analyses. This paper presents a numerical modeling approach for earthquake ground response and liquefaction using the parallel nonlinear finite element program, ParCYCLIC, designed for distributed-memory message-passing parallel computer systems. In ParCYCLIC, finite elements are employed within an incremental plasticity, coupled solid-fluid formulation. A constitutive model calibrated by physical tests represents the salient characteristics of sand liquefaction and associated accumulation of shear deformations. Key elements of the computational strategy employed in ParCYCLIC include the development of a parallel sparse direct solver, the deployment of an automatic domain decomposer, and the use of the Multilevel Nested Dissection algorithm for ordering of the finite element nodes. Simulation results of centrifuge test models using ParCYCLIC are presented. Performance results from grid models and geotechnical simulations show that ParCYCLIC is efficiently scalable to a large number of processors.

## A SPH simulation on large-amplitude sloshing for fluids in a two-dimensional tank

### Earthquake Engineering and Engineering Vibration (2013-03-01) 12: 135-142 , March 01, 2013

Smoothed particle hydrodynamics (SPH) is a mesh-free adaptive Lagrangian particle method with attractive features for dealing with the free surface flow. This paper applies the SPH method to simulate the large-amplitude lateral sloshing both with and without a floating body, and the vertical parametrically-excited sloshing in a two-dimensional tank. The numerical results show that the SPH approach has an obvious advantage over conventional mesh-based methods in handling nonlinear sloshing problems such as violent fluid-solid interaction, and flow separation and wave-breaking on the free fluid surface. The SPH method provides a new alternative and an effective way to solve these special strong nonlinear sloshing problems.

## Improving the seismic torsional behavior of plan-asymmetric, single-storey, concrete moment resisting buildings with fluid viscous dampers

### Earthquake Engineering and Engineering Vibration (2016-03-01) 15: 61-78 , March 01, 2016

The optimal distribution of fluid viscous dampers (FVD) in controlling the seismic response of eccentric, single-storey, moment resisting concrete structures is investigated using the previously defined center of damping constant (CDC). For this purpose, a number of structural models with different one-way stiffness and strength eccentricities are considered. Extensive nonlinear time history analyses are carried out for various arrangements of FVDs. It is shown that the arrangement of FVDs for controlling the torsional behavior due to asymmetry in the concrete structures is very dependent on the intensity of the peak ground acceleration (PGA) and the extent of the structural stiffness and strength eccentricities. The results indicate that, in the linear range of structural behavior the stiffness eccentricity es which is the main parameter in determining the location of optimal CDC, is found to be less or smaller than the optimal damping constant eccentricity *e**_{d}, i.e., |e*_{d}| > |e_{s}|. But, in the nonlinear range of structural behavior where the strength eccentricity er is the dominant factor in determining the location of optimal CDC, |e*_{d}| > |e_{r}|. It is also concluded that for the majority of the plan-asymmetric, concrete structures considered in this study with e_{r} ≠ 0, the optimal CDC approaches the center of mass as e_{r} decreases.

## Numerical analysis on seismic response of Shinkansen bridge-train interaction system under moderate earthquakes

### Earthquake Engineering and Engineering Vibration (2011-03-01) 10: 85-97 , March 01, 2011

This study is intended to evaluate the influence of dynamic bridge-train interaction (BTI) on the seismic response of the Shinkansen system in Japan under moderate earthquakes. An analytical approach to simulate the seismic response of the BTI system is developed. In this approach, the behavior of the bridge structure is assumed to be within the elastic range under moderate ground motions. A bullet train car model idealized as a sprung-mass system is established. The viaduct is modeled with 3D finite elements. The BTI analysis algorithm is verified by comparing the analytical and experimental results. The seismic analysis is validated through comparison with a general program. Then, the seismic responses of the BTI system are simulated and evaluated. Some useful conclusions are drawn, indicating the importance of a proper consideration of the dynamic BTI in seismic design.

## On time-step in structural seismic response analysis under ground displacement/acceleration

### Earthquake Engineering and Engineering Vibration (2009-09-01) 8: 341-347 , September 01, 2009

There are two models in use today to analyze structural responses when subjected to earthquake ground motions, the Displacement Input Model (DIM) and the Acceleration Input Model (AIM). The time steps used in direct integration methods for these models are analyzed to examine the suitability of DIM. Numerical results are presented and show that the time-step for DIM is about the same as for AIM, and achieves the same accuracy. This is contrary to previous research that reported that there are several sources of numerical errors associated with the direct application of earthquake displacement loading, and a very small time step is required to define the displacement record and to integrate the dynamic equilibrium equation. It is shown in this paper that DIM is as accurate and suitable as, if not more than, AIM for analyzing the response of a structure to uniformly distributed and spatially varying ground motions.

## Structural health monitoring of long-span suspension bridges using wavelet packet analysis

### Earthquake Engineering and Engineering Vibration (2007-09-01) 6: 289-294 , September 01, 2007

During the service life of civil engineering structures such as long-span bridges, local damage at key positions may continually accumulate, and may finally result in their sudden failure. One core issue of global vibration-based health monitoring methods is to seek some damage indices that are sensitive to structural damage. This paper proposes an online structural health monitoring method for long-span suspension bridges using wavelet packet transform (WPT). The WPT-based method is based on the energy variations of structural ambient vibration responses decomposed using wavelet packet analysis. The main feature of this method is that the proposed wavelet packet energy spectrum (WPES) has the ability to detect structural damage from ambient vibration tests of a long-span suspension bridge. As an example application, the WPES-based health monitoring system is used on the Runyang Suspension Bridge under daily environmental conditions. The analysis reveals that changes in environmental temperature have a long-term influence on the WPES, while the effect of traffic loadings on the measured WPES of the bridge presents instantaneous changes because of the nonstationary properties of the loadings. The condition indication indices *V*_{D} reflect the influences of environmental temperature on the dynamic properties of the Runyang Suspension Bridge. The field tests demonstrate that the proposed WPES-based condition indication index *V*_{D} is a good candidate index for health monitoring of long-span suspension bridges under ambient excitations.

## Seismic analysis of structures with a fractional derivative model of viscoelastic dampers

### Earthquake Engineering and Engineering Vibration (2002-12-01) 1: 251-260 , December 01, 2002

Viscoelastic dampers are now among some of the preferred energy dissipation devices used for passive seismic response control. To evaluate the performance of structures installed with viscoelastic dampers, different analytical models have been used to characterize their dynamic force deformation characteristics. The fractional derivative models have received favorable attention as they can capture the frequency dependence of the material stiffness and damping properties observed in the tests very well. However, accurate analytical procedures are needed to calculate the response of structures with such damper models. This paper presents a modal analysis approach, similar to that used for the analysis of linear systems, for solving the equations of motion with fractional derivative terms for arbitrary forcing functions such as those caused by earthquake induced ground motions. The uncoupled modal equations still have fractional derivatives, but can be solved by numerical or analytical procedures. Both numerical and analytical procedures are formulated. These procedures are then used to calculate the dynamic response of a multi-degree of freedom shear beam structure excited by ground motions. Numerical results demonstrating the response reducing effect of viscoelastic dampers are also presented.

## Pushover analysis procedure for systems considering SSI effects based on capacity spectrum method

### Earthquake Engineering and Engineering Vibration (2007-09-01) 6: 269-279 , September 01, 2007

This paper presents a new procedure to transform an SSI system into an equivalent SDOF system using twice equivalence. A pushover analysis procedure based on the capacity spectrum method for buildings with SSI effects (PASSI) is then established based on the equivalent SDOF system, and the modified response spectrum and equivalent capacity spectrum are obtained. Furthermore, the approximate formulas to obtain the dynamic stiffness of foundations are suggested. Three steel buildings with different story heights (3, 9 and 20) including SSI effects are analyzed under two far-field and two near-field historical records and an artificial seismic time history using the two PASSI procedures and the nonlinear response history analysis (NL-RHA) method. The results are compared and discussed. Finally, combined with seismic design response spectrum, the nonlinear seismic response of a 9-story building with SSI effects is analyzed using the PASSI procedures, and its seismic performance is evaluated according to the Chinese ‘Code for Seismic Design of Buildings.’ The feasibility of the proposed procedure is verified.

## Field testing of stiffened deep cement mixing piles under lateral cyclic loading

### Earthquake Engineering and Engineering Vibration (2013-06-01) 12: 261-265 , June 01, 2013

Construction of seaside and underground wall bracing often uses stiffened deep cement mixed columns (SDCM). This research investigates methods used to improve the level of bearing capacity of these SDCM when subjected to cyclic lateral loading via various types of stiffer cores. Eight piles, two deep cement mixed piles and six stiffened deep cement mixing piles with three different types of cores, H shape cross section prestressed concrete, steel pipe, and H-beam steel, were embedded though soft clay into medium-hard clay on site in Thailand. Cyclic horizontal loading was gradually applied until pile failure and the hysteresis loops of lateral load vs. lateral deformation were recorded. The lateral carrying capacities of the SDCM piles with an H-beam steel core increased by 3–4 times that of the DCM piles. This field research clearly shows that using H-beam steel as a stiffer core for SDCM piles is the best method to improve its lateral carrying capacity, ductility and energy dissipation capacity.

## Displacement-based seismic design of flat slab-shear wall buildings

### Earthquake Engineering and Engineering Vibration (2016-06-01) 15: 209-221 , June 01, 2016

Flat slab system is becoming widely popular for multistory buildings due to its several advantages. However, the performance of flat slab buildings under earthquake loading is unsatisfactory due to their vulnerability to punching shear failure. Several national design codes provide guidelines for designing flat slab system under gravity load only. Nevertheless, flat slab buildings are also being constructed in high seismicity regions. In this paper, performance of flat slab buildings of various heights, designed for gravity load alone according to code, is evaluated under earthquake loading as per ASCE/SEI 41 methodology. Continuity of slab bottom reinforcement through column cage improves the performance of flat slab buildings to some extent, but it is observed that these flat slab systems are not adequate in high seismicity areas and need additional primary lateral load resisting systems such as shear walls. A displacement-based method is proposed to proportion shear walls as primary lateral load resisting elements to ensure satisfactory performance. The methodology is validated using design examples of flat slab buildings with various heights.

## Strength and stiffness reduction factors for infilled frames with openings

### Earthquake Engineering and Engineering Vibration (2014-09-01) 13: 437-454 , September 01, 2014

Framed structures are usually infilled with masonry walls. They may cause a significant increase in both stiffness and strength, reducing the deformation demand and increasing the energy dissipation capacity of the system. On the other hand, irregular arrangements of the masonry panels may lead to the concentration of damage in some regions, with negative effects; for example soft story mechanisms and shear failures in short columns. Therefore, the presence of infill walls should not be neglected, especially in regions of moderate and high seismicity. To this aim, simple models are available for solid infills walls, such as the diagonal no-tension strut model, while infilled frames with openings have not been adequately investigated. In this study, the effect of openings on the strength and stiffness of infilled frames is investigated by means of about 150 experimental and numerical tests. The main parameters involved are identified and a simple model to take into account the openings in the infills is developed and compared with other models proposed by different researchers. The model, which is based on the use of strength and stiffness reduction factors, takes into account the opening dimensions and presence of reinforcing elements around the opening. An example of an application of the proposed reduction factors is also presented.

## Calendar of events

### Earthquake Engineering and Engineering Vibration (2004-12-01) 3: 307-309 , December 01, 2004

## Principal axes of M-DOF structures part I: Static loading

### Earthquake Engineering and Engineering Vibration (2002-12-01) 1: 293-302 , December 01, 2002

This paper is the first in a two-part series that discusses the principal axes of M-DOF structures subjected to static and dynamic loads. The primary purpose of this series is to understand the magnitude of the dynamic response of structures to enable better design of structures and control modification devices/systems. Under idealized design conditions, the structural responses are obtained by using single direction input ground motions in the direction of the intended control devices/systems, and by assuming that the responses of the structure is decoupleable in three mutually perpendicular directions. This standard practice has been applied to both new and retrofitted structures using various seismic protective systems. Very limited information is available on the effects of neglecting the impact of directional couplings (cross effects - of which torsion is a component) of the dynamic response of structures. In order to quantify such effects, it is necessary to examine the principal axes of structures under both static and dynamic loading. This first paper deals with quantitative definitions of principal axes and “cross effects” of three-dimensional structures under static load by using linear algebra. It shows theoretically that, for three-dimensional structures, such principal axes rarely exist. Under static loading conditions, the cross effect is typically small and negligible from the viewpoint of engineering applications. However, it provides the theoretical base for subsequent quantification of the response couplings under dynamic loads, which is reported in part II of this series.

## A method for computing interstory drift spectra with consideration of gravity effects

### Earthquake Engineering and Engineering Vibration (2010-12-01) 9: 513-521 , December 01, 2010

Vertical loads such as gravity may have an important influence on the seismic response of buildings. In this paper, the continuous shear-beam model is extended to study the seismic demand of shear buildings with consideration of the gravity load effect under near-field ground motions. An analytical solution of the free motion equation of as gravity shear beam model is provided in terms of a Bessel series. A method for computing interstory drift spectra is proposed. The interstory drift spectra for two near-field records with distinct pulses are presented to illustrate the effects of gravity and the damping ratio. The interstory drift spectra are also used to analyze the spectral characteristics of near fault ground motion during the 2008 Wenchuan earthquake. The effects of the gravity load ratio, damping ratio and higher modes are investigated and discussed.

## Simulation of large-scale numerical substructure in real-time dynamic hybrid testing

### Earthquake Engineering and Engineering Vibration (2014-12-01) 13: 599-609 , December 01, 2014

A solution scheme is proposed in this paper for an existing RTDHT system to simulate large-scale finite element (FE) numerical substructures. The analysis of the FE numerical substructure is split into response analysis and signal generation tasks, and executed in two different target computers in real-time. One target computer implements the response analysis task, wherein a large time-step is used to solve the FE substructure, and another target computer implements the signal generation task, wherein an interpolation program is used to generate control signals in a small time-step to meet the input demand of the controller. By using this strategy, the scale of the FE numerical substructure simulation may be increased significantly. The proposed scheme is initially verified by two FE numerical substructure models with 98 and 1240 degrees of freedom (DOFs). Thereafter, RTDHTs of a single frame-foundation structure are implemented where the foundation, considered as the numerical substructure, is simulated by the FE model with 1240 DOFs. Good agreements between the results of the RTDHT and those from the FE analysis in ABAQUS are obtained.

## Hilbert spectrum and intrinsic oscillation mode of dynamic response of a bilinear SDOF system: influence of harmonic excitation amplitude

### Earthquake Engineering and Engineering Vibration (2005-06-01) 4: 17-26 , June 01, 2005

Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the steady response and the transient response when the system behaves linearly, or (2) the intra-wave modulation mechanism embedded in one intrinsic mode function (IMF) component when the system behaves nonlinearly. The temporal variation of the instantaneous frequency of the IMF component is consistent with the system nonlinear behavior of yielding and unloading. As a thorough study of this fundamental structural dynamics problem, this article investigates the influence of the amplitude of the harmonic wave excitation on the Hilbert spectrum and the intrinsic oscillatory mode of the dynamic response of a bilinear SDOF system.

## Seismic performance of an existing bridge with scoured caisson foundation

### Earthquake Engineering and Engineering Vibration (2014-08-01) 13: 151-165 , August 01, 2014

This paper presents in-situ seismic performance tests of a bridge before its demolition due to accumulated scouring problem. The tests were conducted on three single columns and one caisson-type foundation. The three single columns were 1.8 m in diameter, reinforced by 30-D32 longitudinal reinforcements and laterally hooped by D16 reinforcements with spacing of 20 cm. The column height is 9.54 m, 10.59 m and 10.37 m for Column P2, P3, and P4, respectively. Column P2 had no exposed foundation and was subjected to pseudo-dynamic tests with peak ground acceleration of 0.32 g first, followed by one cyclic loading test. Column P3 was the benchmark specimen with exposed length of 1.2 m on its foundation. The exposed length for Column P4 was excavated to 4 m, approximately 1/3 of the foundation length, to study the effect of the scouring problem to the column performance. Both Column P3 and Column P4 were subjected to cyclic loading tests. Based on the test results, due to the large dimension of the caisson foundation and the well graded gravel soil type that provided large lateral resistance, the seismic performance among the three columns had only minor differences. Lateral push tests were also conducted on the caisson foundation at Column P5. The caisson was 12 m long and had circular cross-sections whose diameters were 5 m in the upper portion and 4 m in the lower portion. An analytical model to simulate the test results was developed in the OpenSees platform. The analytical model comprised nonlinear flexural elements as well as nonlinear soil springs. The analytical results closely followed the experimental test results. A parametric study to predict the behavior of the bridge column with different ground motions and different levels of scouring on the foundation are also discussed.

## Precise integration method without inverse matrix calculation for structural dynamic equations

### Earthquake Engineering and Engineering Vibration (2007-03-01) 6: 57-64 , March 01, 2007

The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.