• Title/Summary/Keyword: Linear spring model

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Nonlinear rheology of linear polymer melts: Modeling chain stretch by interchain tube pressure and Rouse time

  • Wagner, Manfred H.;Rolon-Garrido, Victor H.
    • Korea-Australia Rheology Journal
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    • v.21 no.4
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    • pp.203-211
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    • 2009
  • In flows with deformation rates larger than the inverse Rouse time of the polymer chain, chains are stretched and their confining tubes become increasingly anisotropic. The pressures exerted by a polymer chain on the walls of an anisotropic confinement are anisotropic and limit chain stretch. In the Molecular Stress Function (MSF) model, chain stretch is balanced by an interchain pressure term, which is inverse proportional to the $3^{rd}$ power of the tube diameter and is characterized by a tube diameter relaxation time. We show that the tube diameter relaxation time is equal to 3 times the Rouse time in the limit of small chain stretch. At larger deformations, we argue that chain stretch is balanced by two restoring tensions with weights of 1/3 in the longitudinal direction of the tube (due to a linear spring force) and 2/3 in the lateral direction (due to the nonlinear interchain pressure), both of which are characterized by the Rouse time. This approach is shown to be in quantitative agreement with transient and steady-state elongational viscosity data of two monodisperse polystyrene melts without using any nonlinear parameter, i.e. solely based on the linear-viscoelastic characterization of the melts. The same approach is extended to model experimental data of four styrene-butadiene random copolymer melts in shear flow. Thus for monodisperse linear polymer melts, for the first time a constitutive equation is presented which allows quantitative modeling of nonlinear extension and shear rheology on the basis of linear-viscoelastic data alone.

linear Viscoelastic Properties and Relaxation Time Spectrum of Dilute Polymer Solutions (묽은 고분자 용액의선형 점탄성과 완화 시간 스펙트럼)

  • 안경현
    • The Korean Journal of Rheology
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    • v.7 no.3
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    • pp.211-224
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    • 1995
  • 묽은 고분자 용액의선형 점탄성과 완화시간 스펙트럼에 대하여 비드수, 유체역학적 상호작용, 배제 부피와 비선형 스프링들의 영향을 비드-스프링 모델을 통하여 연구하였다. Fixman의 모델을 개량하였고, 비선형 스프링개념을 도입한후 선형점탄성에 관한 식들을 유 도하였다. 그중에서 주로 복고 점도의 크기와 위상차에 대한 BSM 파라미터들의 영향을 살 펴보았다. 실험데이터에서 진동수에 따른 위상차의 평평한 부분의 길이로부터 비드수를 Mark-Houwink 식의 지수 값으로부터 유체역학적 상호작용 파라미터를 그리고 fitting 파라 미터로써 배제 부피 파라미터와 비선형 스프링 파라미터의 함수형태로 표현되는 동적 확장 파라미터를 결정할수 있었다. 또한 광산란 실험등으로부터 배제 부피 파라미터를 결정하게 된다면 이로부터 비선형 스프링 파라미터도 결정할수 있음을 알수 있었다. 한편 불연속적인 현태인 BSM의 완화시간 스펙트럼에 미치는 BSM 파라미터들의 영향을 분석함으로써 각 파람터의 효과와 차이점을 분명히 알수 있었다. 본논문에서는 BSM에 비드수, 유체역학적 상호작용 배제 부피 그리고 비선형 스프링 효과를 동시에 적용하는 방법을 제시하였으며 이 방법을 통하여 묽은 고분자 용액의 선형 점탄성 실험 데이터를 정량적으로 설명할 수 있었다.

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Evaluating the accuracy of a new nonlinear reinforced concrete beam-column element comprising joint flexibility

  • Izadpanah, Mehdi;Habibi, AliReza
    • Earthquakes and Structures
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    • v.14 no.6
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    • pp.525-535
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    • 2018
  • This study presents a new beam-column model comprising material nonlinearity and joint flexibility to predict the nonlinear response of reinforced concrete structures. The nonlinear behavior of connections has an outstanding role on the nonlinear response of reinforced concrete structures. In presented research, the joint flexibility is considered applying a rotational spring at each end of the member. To derive the moment-rotation behavior of beam-column connections, the relative rotations produced by the relative slip of flexural reinforcement in the joint and the flexural cracking of the beam end are taken into consideration. Furthermore, the considered spread plasticity model, unlike the previous models that have been developed based on the linear moment distribution subjected to lateral loads includes both lateral and gravity load effects, simultaneously. To confirm the accuracy of the proposed methodology, a simply-supported test beam and three reinforced concrete frames are considered. Pushover and nonlinear dynamic analysis of three numerical examples are performed. In these examples the nonlinear behavior of connections and the material nonlinearity using the proposed methodology and also linear flexibility model with different number of elements for each member and fiber based distributed plasticity model with different number of integration points are simulated. Comparing the results of the proposed methodology with those of the aforementioned models describes that suggested model that only uses one element for each member can appropriately estimate the nonlinear behavior of reinforced concrete structures.

Steady-state response and free vibration of an embedded imperfect smart functionally graded hollow cylinder filled with compressible fluid

  • Bian, Z.G.;Chen, W.Q.;Zhao, J.
    • Structural Engineering and Mechanics
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    • v.34 no.4
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    • pp.449-474
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    • 2010
  • A smart hollow cylinder consisting of a host functionally graded elastic core layer and two surface homogeneous piezoelectric layers is presented in this paper. The bonding between the layers can be perfect or imperfect, depending on the parameters taken in the general linear spring-layer interface model. The effect of such weak interfaces on free vibration and steady-state response is then investigated. Piezoelectric layers at inner and outer surfaces are polarized axially or radially and act as a sensor and an actuator respectively. For a simply supported condition, the state equations with non-constant coefficients are obtained directly from the formulations of elasticity/piezoelasticity. An approximate laminated model is then introduced for the sake of solving the state equations conveniently. It is further assumed that the hollow cylinder is embedded in an elastic medium and is simultaneously filled with compressible fluid. The interaction between the structure and its surrounding media is taken into account. Numerical examples are finally given with discussions on the effect of some related parameters.

Natural frequencies and response amplitude operators of scale model of spar-type floating offshore wind turbine

  • Hong, Sin-Pyo;Cho, Jin-Rae
    • Structural Engineering and Mechanics
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    • v.61 no.6
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    • pp.785-794
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    • 2017
  • This paper is concerned with the comparative numerical and experimental study on the natural behavior and the motion responses of a 1/75 moored scale model of a 2.5 MW spar-type floating offshore wind turbine subject to 1-D regular wave. Heave, pitch and surge motions and the mooring tensions are investigated and compared by numerical and experimental methods. The upper part of wind turbine which is composed of three rotor blades, hub and nacelle is modeled as a lumped mass and three mooring lines are pre-tensioned by means of linear springs. The numerical simulations are carried out by a coupled FEM-cable dynamics code, while the experiments are performed in a wave tank equipped with the specially-designed vision and data acquisition system. Using the both methods, the natural behavior and the motion responses in RAOs are compared and parametrically investigated to the fairlead position, the spring constant and the location of mass center of platform. It is confirmed, from the comparison, that both methods show a good agreement for all the test cases. And, it is observed that the mooring tension is influenced by all three parameters but the platform motion is dominated by the location of mass center. In addition, from the sensitivity analysis of RAOs, the coupling characteristic of platform motions and the sensitivities to the mooring parameters are investigated.

Vertical Z-vibration prediction model of ground building induced by subway operation

  • Zhou, Binghua;Xue, Yiguo;Zhang, Jun;Zhang, Dunfu;Huang, Jian;Qiu, Daohong;Yang, Lin;Zhang, Kai;Cui, Jiuhua
    • Geomechanics and Engineering
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    • v.30 no.3
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    • pp.273-280
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    • 2022
  • A certain amount of random vibration excitation to subway track is caused by subway operation. This excitation is transmitted through track foundation, tunnel, soil medium, and ground building to the ground and ground structure, causing vibration. The vibration affects ground building. In this study, the results of ANSYS numerical simulation was used to establish back-propagation (BP) neural network model. Moreover, a back-propagation neural network model consisting of five input neurons, one hidden layer, 11 hidden-layer neurons, and three output neurons was used to analyze and calculate the vertical Z-vibration level of New Capital's ground buildings of Qingdao Metro phase I Project (Line M3). The Z-vibration level under different working conditions was calculated from monolithic roadbed, steel-spring floating slab roadbed, and rubber-pad floating slab roadbed under the working condition of center point of 0-100 m. The steel-spring floating slab roadbed was used in the New Capital area to monitor the subway operation vibration in this area. Comparing the monitoring and prediction results, it was found that the prediction results have a good linear relationship with lower error. The research results have good reference and guiding significance for predicting vibration caused by subway operation.

An Experimental Approach to the Linear Actuator with a Finite Difference Equation on the Temperature Domain (온도 영역에 대한 선형 액추에이터의 실험적 고찰과 유한차분 방정식)

  • 김양호;손웅태;황석영
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.18 no.4
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    • pp.68-72
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    • 2004
  • In this paper, the energy conversion theory of the linear actuator deals with the temperature characteristic analysis with verifying temperature of linear Actuator system This model of linear actuator has winding part and mechanical spring, and a plunger. This paper proposed and experimented the linear Actuator(LA) by using finite difference equation(FDE). The experimental result represented the temperature T1 and T2 which remarks Tl is a center of magnetic road inside of actuator winding part, and T2 is a surface of actuator winding part. And the temperature characteristic of the actuator winding part are experimented by the digital temperature meter TECPEL 322.

Comparison of Behaviors of Jointless Bridge according to Depth of Abutment Among Numerical Models (수치해석 모델에 따른 무조인트 교량의 교대 깊이별 거동 비교)

  • Kim, Seung-Won;Lee, Hwan-Woo
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.35 no.3
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    • pp.167-174
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    • 2022
  • This study investigates the behavior of a jointless bridge that integrates superstructure and abutment without an expansion joint. Based on the sensitivity analyses conducted in previous studies, a shell-based model was determined to be the most suitable numerical analysis model for jointless bridges due to the similarity of the model's results compared with the obtained displacement shape, which was influenced by relative errors, precision, and practical aspects. Accordingly, the behavior of a jointless bridge was analyzed at various wall depths using shell element-based and solid element models. In addition, the results of MIDAS Civil and ABAQUS analysis programs were compared. In the case of semi-integrated bridges (A and B), the displacement decreased as the wall depth increased due to the ground reaction force in Case 1 under a linear spring condition and +30℃. In the case where temperature was -30℃, the change in displacement was small because the ground reaction did not occur. As for bridge C (a fully integrated alternating bridge) and bridge D (an integrated chest wall alternating bridge), the displacement decreased as the wall depth increased at both +30 and -30℃ due to pile resistance. As for the comparison between the analysis programs used, the relative error in Case 1 was small, whereas a significant difference in Case 2 was observed. The foregoing variation is possibly due to the difference in the application of the nonlinear spring in the programs.

The Design and Performance Evaluation of a Parallelogram Type Magnetic Spring Suspension for Commercial Vehicle Seat (상용차 시트용 평행사변형구조 마그네틱 현가기구의 설계 및 성능평가)

  • Kwac, Lee Ku;Kim, Hong Gun;Shin, Hee Jae;Jung, Young Bae;Song, Jung Sang
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.39 no.4
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    • pp.353-360
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    • 2015
  • Commercial drivers feel tired more than the general public, because their driving times are long and they experience more idle vibration. In this study, we developed a nonlinear model of a magnetic, linear spring seat suspension to determine the optimal design to improve ride comfort. The resonant frequency for the optimal design of the suspension was found to be 3.5 Hz, and the stiffness was analyzed through displacement-load experiments. Additionally, the vibration transmissibility was analyzed by the suspension stiffness, and the existing coil spring type vibration transmissibility was found to be 0.99. A parallelogram type magnetic spring was determined to result in a better performance than the existing spring with a vibration transmissibility of 0.823.

Design of a new 4-DOF soft finger mechanism (4자유도 새로운 소프트 핑거 설계)

  • Cha, Hyo-Jung;Yi, Byung-Ju
    • The Journal of Korea Robotics Society
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    • v.3 no.4
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    • pp.315-322
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    • 2008
  • A new soft finger mechanism using a spring as a backbone is proposed in this work. It is a 4 DOF mechanism that consists of a spring and 3 cylinders, which behave like joints with 3 up-and-down rotations and 1 left-and-right rotation. To control each joint, cylinders have small holes in their cross-sectional areas, and wires of different length are penetrated into these holes. We can control each joint by pulling the corresponding wire. The forward kinematics is solved by using the geometry of mechanism. And the relationship (Jacobian) between the linear velocity of the wires and the joint angular rate is obtained. A virtual simulator is developed to test the validity of the kinematic model. In the experiment, first, the position control is conducted by tracking a given trajectory. Second, to verify the flexibility and safety, we show that the soft finger deflects in a safe manner, in spite of the collision with environment.

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