• Title/Summary/Keyword: Equivalent linearization

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Influence of the Francis Turbine location under vortex rope excitation on the Hydraulic System Stability

  • Alligne, S.;Nicolet, C.;Allenbach, P.;Kawkabani, B.;Simond, J.J.;Avellan, F.
    • International Journal of Fluid Machinery and Systems
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    • v.2 no.4
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    • pp.286-294
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    • 2009
  • Hydroelectric power plants are known for their ability to cover variations of the consumption in electrical power networks. In order to follow this changing demand, hydraulic machines are subject to off-design operation. In that case, the swirling flow leaving the runner of a Francis turbine may act under given conditions as an excitation source for the whole hydraulic system. In high load operating conditions, vortex rope behaves as an internal energy source which leads to the self excitation of the system. The aim of this paper is to identify the influence of the full load excitation source location with respect to the eigenmodes shapes on the system stability. For this, a new eigenanalysis tool, based on eigenvalues and eigenvectors computation of the nonlinear set of differential equations in SIMSEN, has been developed. First the modal analysis method and linearization of the set of the nonlinear differential equations are fully described. Then, nonlinear hydro-acoustic models of hydraulic components based on electrical equivalent schemes are presented and linearized. Finally, a hydro-acoustic SIMSEN model of a simple hydraulic power plant, is used to apply the modal analysis and to show the influence of the turbine location on system stability. Through this case study, it brings out that modeling of the pipe viscoelastic damping is decisive to find out stability limits and unstable eigenfrequencies.

Effect of Energy Loss by a Vertical Slotted Wall (직립 슬릿벽에 의한 에너지 손실효과)

  • Cho, Il-Hyoung
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.27 no.5
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    • pp.295-303
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    • 2015
  • The eigenfunction expansion method is appled for the wave scattering by a vertical slotted, where both the inertial and quadratic drag terms are involved. Quadratic drag term representing the energy loss is linearized by the application of socalled equivalent linearization. The drag coefficient, which was empirically determined by Yoon et al.(2006) and Huang(2007) is used. Analytical results are verified by comparison to the experimental results conducted by Kwon et al.(2014) and Zhu and Chwang(2001). Using the developed design tool, the effect of energy loss by a vertical slotted wall is estimated with various design parameters, such as porosity, submergence depth, shape of slits and wave characteristics. It is found that the maximum value of energy loss across the slotted wall is generated at porosity value less than P = 0.1. The present solutions can provide a good predictive tools to estimate the wave absorbing efficiency by a slotted-wall breakwater.

Evaluation of Seismic Performance of Bearing Wall Structure with Coupling Beam (연결보가 있는 벽식 구조물의 내진성능 평가)

  • Lee, Young-Wook;Tao, Zou
    • Proceedings of the Korea Concrete Institute Conference
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    • 2008.04a
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    • pp.1049-1052
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    • 2008
  • Coupling beams have been used in bearing wall system during last decades. Practically their sectional effects are fully considered in analysis stage to control lateral displacement because they have good contribution to the stiffness of bearing wall system. But the high resultant forces of coupling beam are not fully satisfied in design stage because coupling beams are restricted in sectional size. In this paper the performance of bearing wall system with coupling beam has been evaluated based on improved equivalent linearization procedure of FEMA 440. 15 storied building is selected for analysis. Variables for performance evaluation are natural period, degree of coupling and soil site. To evaluate performance, demand capacity spectrum is calculated based on KBC 2005. As a result, for the most of the cases the life safety limit of chord rotation of coupling beam is less than the performance point of system for soil site $S_D$. That means that the coupling beam can be severly damaged before the system reaches at performance point.

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Pavement condition assessment through jointly estimated road roughness and vehicle parameters

  • Shereena, O.A.;Rao, B.N.
    • Structural Monitoring and Maintenance
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    • v.6 no.4
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    • pp.317-346
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    • 2019
  • Performance assessment of pavements proves useful, in terms of handling the ride quality, controlling the travel time of vehicles and adequate maintenance of pavements. Roughness profiles provide a good measure of the deteriorating condition of the pavement. For the accurate estimates of pavement roughness from dynamic vehicle responses, vehicle parameters should be known accurately. Information on vehicle parameters is uncertain, due to the wear and tear over time. Hence, condition monitoring of pavement requires the identification of pavement roughness along with vehicle parameters. The present study proposes a scheme which estimates the roughness profile of the pavement with the use of accurate estimates of vehicle parameters computed in parallel. Pavement model used in this study is a two-layer Euler-Bernoulli beam resting on a nonlinear Pasternak foundation. The asphalt topping of the pavement in the top layer is modeled as viscoelastic, and the base course bottom layer is modeled as elastic. The viscoelastic response of the top layer is modeled with the help of the Burgers model. The vehicle model considered in this study is a half car model, fitted with accelerometers at specified points. The identification of the coupled system of vehicle-pavement interaction employs a coupled scheme of an unbiased minimum variance estimator and an optimization scheme. The partitioning of observed noisy quantities to be used in the two schemes is investigated in detail before the analysis. The unbiased minimum variance estimator (MVE) make use of a linear state-space formulation including roughness, to overcome the linearization difficulties as in conventional nonlinear filters. MVE gives estimates for the unknown input and fed into the optimization scheme to yield estimates of vehicle parameters. The issue of ill-posedness of the problem is dealt with by introducing a regularization equivalent term in the objective function, specifically where a large number of parameters are to be estimated. Effect of different objective functions is also studied. The outcome of this research is an overall measure of pavement condition.

Effect of relative stiffness on seismic response of subway station buried in layered soft soil foundation

  • Min-Zhe Xu;Zhen-Dong Cui;Li Yuan
    • Geomechanics and Engineering
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    • v.36 no.2
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    • pp.167-181
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    • 2024
  • The soil-structure relative stiffness is a key factor affecting the seismic response of underground structures. It is of great significance to study the soil-structure relative stiffness for the soil-structure interaction and the seismic disaster reduction of subway stations. In this paper, the dynamic shear modulus ratio and damping ratio of an inhomogeneous soft soil site under different buried depths which were obtained by a one-dimensional equivalent linearization site response analysis were used as the input parameters in a 2D finite element model. A visco-elasto-plastic constitutive model based on the Mohr-Coulomb shear failure criterion combined with stiffness degradation was used to describe the plastic behavior of soil. The damage plasticity model was used to simulate the plastic behavior of concrete. The horizontal and vertical relative stiffness ratios of soil and structure were defined to study the influence of relative stiffness on the seismic response of subway stations in inhomogeneous soft soil. It is found that the compression damage to the middle columns of a subway station with a higher relative stiffness ratio is more serious while the tensile damage is slighter under the same earthquake motion. The relative stiffness has a significant influence on ground surface deformation, ground acceleration, and station structure deformation. However, the effect of the relative stiffness on the deformation of the bottom slab of the subway station is small. The research results can provide a reference for seismic fortification of subway stations in the soft soil area.

Seismic Soil-Structure Interaction Analyses of LNG Storage Tanks Depending on Foundation Type (기초 형식에 따른 LNG 저장탱크의 지반-구조물 상호작용을 고려한 지진응답 분석)

  • Son, Il-Min;Kim, Jae-Min;Lee, Changho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.32 no.3
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    • pp.155-164
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    • 2019
  • In this study, the soil-structure interaction(SSI) effect on the seismic response of LNG storage tanks was investigated according to the type of foundation. For this purpose, a typical of LNG storage tank with a diameter of 71m, which is constructed on a 30m thick clay layer over bedrock was selected, and nonlinearity of the soil was taken into account by the equivalent linearization method. Four different types of foundations including shallow foundation, piled raft foundation, and pile foundations(surface and floating types) were considered. In addition, the effect of soil compaction in group piles on seismic response of the tank was investigated. The KIESSI-3D, which is a SSI analysis package in the frequency domain, was used for the SSI analysis. Stresses in the outer tank, and base shear and overturning moment in the inner tank were calculated. From the comparisons, the following conclusions could be made: (1) Conventional fixed base seismic responses of outer tank and inner tank can be much larger than those of considering the SSI effect; (2) The influence of SSI on the dynamic response of the inner tank and the outer tank depends on the foundation types; and (3) Change in the seismic response of the structure by soil compaction in the piled raft foundation is about 10% and its effect is not negligible in the seismic design of the structure.