• International Journal of Automotive Technology
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• v.8 no.1
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• pp.33-38
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• 2007

Since it is difficult to analytically express the Melnikov function when a dynamic system possesses multiple saddle fixed points with homoclinic and/or heteroclinic orbits, this paper investigates a vehicle model with nonlinear suspension spring and hysteretic damping element, which exhibits multiple heteroclinic orbits in the unperturbed system. First, an algorithm for Melnikov integrals is developed based on the Melnikov method. And then the amplitude threshold of road excitation at the onset of chaos is determined. By numerical simulation, the existence of chaos in the present system is verified via time history curves, phase portrait plots and $Poincar{\acute{e}}$ maps. Finally, in order to further identify the chaotic motion of the nonlinear system, the maximal Lyapunov exponent is also adopted. The results indicate that the numerical method of estimating chaotic threshold is an effective one to complicated vehicle systems.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.107-116
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• 2005

A suspension bridge is an example of a nonlinear dynamical system, especially systems with the so called jumping nonlinearity. The fact that we deal with a serious and topical problem is demonstrated for example by the collapse of the Tacoma Narrow suspension bridge. So it would be very contributive to determine under what conditions a similar situation cannot occur and find out safe parameters of the bridge construction. In this paper, we show various possibilities how to model the behaviour of suspension bridge. Then we introduce our own results concerning existence and uniqueness of time-periodic solutions.

• Earthquakes and Structures
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• v.26 no.4
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• pp.285-297
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• 2024

Due to the imbalanced vibration of the adjacent buildings, the pounding phenomenon occurs as a result of an insufficient gap between them. Providing enough gap between adjacent structures is the most efficient approach to preventing the pounding effect. This paper calculated the required separation gaps between adjacent buildings, including two, four, eight, twelve and twenty stories steel moment-resisting frames, and investigated their related influencing parameters such as time periods, damping ratios, and the number of bays. The linear and nonlinear dynamic time-history analyses under real seismic event records were conducted to calculate the required separation gaps by obtaining relative displacement and velocity functions of two adjacent frames. The results showed that the required separation gap increased when the time periods of adjacent frames were not the same. The resulting separation gaps values of linear and nonlinear analyses were similar only for two and four stories frames. In other frames, the resulting separation gap values of linear analyses surpassed the corresponding nonlinear analyses. Although increasing the damping ratios in adjacent frames causes a decrease in the required separation gaps, the number of bays had no significant effect on them.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.1
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• pp.49-62
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• 1994

An analysis method for the time-dependent nonlinear analysis of segmentally erected planar prestressed concrete cable-stayed bridges was described. To account for the time-dependent effects, load history, creep, shrinkage. aging of concrete and relaxation of prestress were considered. Changes in boundary conditions and loads, installing and removing frame elements, stressing, restressing and removing cables and prestressing tendons were incorporated for modeling segmental erection operations. One typical example on segmentally erected prestressed concrete cable-stayed bridge was presented to illustrate the analysis method. Results of this example show that it is important to follow the development of stresses and deformations at all stages of construction to predict the true response of the bridge through its various load history.

• Earthquakes and Structures
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• v.12 no.1
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• pp.35-45
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• 2017

The current paper investigates the effect of the seismic pounding of neighboring buildings on the response of structures isolated by Triple Friction Pendulum Bearing (TFPB). To this end, a symmetric three-dimensional single story building is modeled for analysis with two specified levels of top deck and base deck, to capture the seismic response of the base isolators and building's roof. Linear elastic springs with different level of gaps are employed to calculate the impact between the buildings. Nonlinear Dynamic Time History Analyses (NDTHA) are conducted for seismic evaluation. Also, five different sizes with four different sets of friction coefficients are assumed for base isolators to cover a whole range of base isolation systems with various geometry configurations and fundamental period. The results are investigated in terms of base shear, buildings' drift and top deck acceleration of the superstructure. The results also indicate the profound effect of the stiffness of the adjacent buildings on the value of the impact they impose to the superstructure. Also, in situations of potential pounding, the increment of the fundamental period of the TFPB base isolator could intensify the impact force up to nearly five-fold.

• Earthquakes and Structures
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• v.12 no.5
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• pp.515-527
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• 2017

Recently, Friction dampers become popular due to the desirable performance in the energy dissipation of lateral loads. A lot of research which has been conducted on these dampers results in developing friction dampers with low sensitivity to the number of cycles and temperature increases. Friction dampers impose high residual drifts to the buildings because of low post-yield stiffness of the damper which results from increasing lateral displacement and period of buildings. This issue can be more critical under strong aftershocks which results in increasing of structural damages. In this paper, in addition to the assessment of aftershock on steel buildings equipped with friction dampers, methods for controlling residual drifts and decreasing the costs of retrofitting are investigated. Utilizing rigid connections as a lateral dual system and activating lateral stiffness of gravity columns by adding elastic braces are as an example of effective methods investigated in this research. The results of nonlinear time history analyses on the low to medium rise steel frames equipped with friction dampers illustrate a rise in residual drifts as the result of aftershocks. In addition, the results show that different slip loads of friction damper can affect the residual drifts. Furthermore, elastic stories in comparison to rigid connections can reduce residual drifts of buildings in an effective fashion, when most slip loads of friction dampers are considered.

• International Journal of High-Rise Buildings
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• v.3 no.1
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• pp.81-87
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• 2014

The use of Buckling Restrained Braces (BRB) for enhancing the performance of the buildings is gaining wider acceptance. This paper presents the first application of these devices in a major high-rise building in the Philippines. A 50-storey residential reinforced concrete building tower, with ductile core wall, with BRB system is investigated. The detailed modeling and design procedure of buckling restrained brace system is presented for the optimal design against the two distinct levels of earthquake ground motions; serviceable behavior for frequent earthquakes and very low probability of collapse under extremely rare earthquakes. The stiffness and strength of the buckling restrained brace system are adjusted to optimize the performance of the structural system under different levels of earthquakes. Response spectrum analysis is conducted for Design Basis Earthquake level and Service level, while nonlinear time history analysis is performed for the most credible earthquake. The case study results show the effectiveness of buckling restrained braces.

• Earthquakes and Structures
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• v.15 no.2
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• pp.123-132
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• 2018

In this paper the strain energy density (SED) model is used to analyze the seismic behavior of suspen-domes and a new criterion is established for judging the seismic failure based on a characteristic point in the SED model. Firstly, a nonlinear time-history response analysis was carried out using the finite-element package ANSYS for typical suspen-domes subjected to different ground motions. The seismic responses including nodal displacements, ratios of yielding members, strain energy density and structural maximum deformation energy were extracted corresponding to the increasing peak ground acceleration (A). Secondly, the SED sum ($I_d$) was calculated which revealed that the $I_d-A$ curve exhibited a relatively large change (called a characteristic point) at a certain value of A with a very small load increment after the structures entered the elastic-plastic state. Thirdly, a SED criterion is proposed to judge the seismic failure load based on the characteristic point. Subsequently, the case study verifies the characteristic point and the proposed SED criterion. Finally, this paper describes the unity and application of the SED criterion. The SED method may open a new way for structural appraisal and the SED criterion might give a unified criterion for predicting the failure loads of various structures subjected to dynamic loads.

• Earthquakes and Structures
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• v.17 no.6
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• pp.533-543
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• 2019

This paper presents a study on the behavior of an RC bridge under near-field and far-field ground motions. For this purpose, a dynamic nonlinear finite element time history analysis has been conducted. The near-field and far-field records are chosen pairwise from the same events which are fits to the seismic design of the bridge. In order to perform an accurate seismic evaluation, the model has been analyzed under two vertical and horizontal components of ground motions. Parameters of relative displacement, residual displacement, and maximum plastic strain have been considered and compared in terms of near-field and far-field ground motions. In the following, in order to decrease the undesirable effects of near-field ground motions, a viscous damper is suggested and its effects have been studied. In this case, the results show that the near-field ground motions increase maximum relative and residual displacement respectively up to three and twice times. Significant seismic improvements were achieved by using viscous dampers on the bridge model. Somehow under the considered near-field ground motion, parameters of residual and relative displacement decrease dramatically even less than the model without damper under the far-field record of the same ground motion.

• Computers and Concrete
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• v.25 no.3
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• pp.273-282
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• 2020

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