• 제목/요약/키워드: linear superposition principle

검색결과 21건 처리시간 0.02초

진동전단유동장에서 점탄성 반고형 연고기제(바셀린)의 레올로지 거동 (Rheological Behavior of Viscoelastic Semi-Solid Ointment Base (Vaseline) in Oscillatory Shear Flow Fields)

  • 송기원;장갑식
    • Journal of Pharmaceutical Investigation
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    • 제36권1호
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    • pp.31-38
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    • 2006
  • Using a Rheometries Dynamic Analyzer (RDA II), the dynamic viscoelastic properties of a semi-solid ointment base (vaseline) in large amplitude oscillatory shear flow fields were measured over a temperature range of $25{\sim}45^{\circ}C$ and the linear viscoelastic behavior in small amplitude oscillatory shear flow fields was investigated over a wide range of angular frequencies. In this article, the nonlinear viscoelastic behavior was reported from the experimentally obtained data and the effect of temperature on this behavior was discussed in detail. In addition, the angular frequency and temperature dependencies of a linear viscoelastic behavior were explained. Finally, the applicability of a time-temperature superposition principle originally developed for polymeric materials was examined using a shift factor. Main results obtained from this study can be summarized as follows : (1) At very small strain amplitude region, vaseline shows a linear viscoelastic behavior independent of the imposed deformation magnitudes. Above a critical strain amplitude $({\gamma}_{0}=0.1{\sim}0.2%)$, however, vaseline exhibits a nonlinear viscoelastic behavior ; indicating that both the storage modulus and dynamic viscosity are sharply decreased with increasing deformation magnitude. (2) In large amplitude oscillatory shear flow fields, an elastic behavior (storage modulus) has a stronger strain amplitude dependence and begins to show a nonlinear behavior at a smaller strain amplitude region than does a viscous behavior (dynamic viscosity). (3) In small amplitude oscillatory shear flow fields, the storage modulus as well as the loss modulus are continuously increased as an increase in angular frequency and an elastic nature is always superior to a viscous behavior over a wide range of angular frequencies. (4) A time-temperature superposition principle can successfully be applicable to vaseline. This finding allows us to estimate the dynamic viscoelastic behavior of vaseline over an extraordinarily extended range (11 decades) of angular frequencies inaccessible from the experimentally measured range (4 decades).

점탄성 거동을 하는 복합재료 판의 대변위 진동해석 (Nonlinear vibration analysis of viscoelastic laminated plates undergoing large deflection)

  • 김태우;김지환
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2000년도 추계학술대회논문집
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    • pp.546-552
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    • 2000
  • Dynamic behavior of laminated composite plates undergoing moderately large deflection is investigated taking into account the viscoelastic behavior of material properties. Based on von Karman's non-linear deformation theory and Boltzmann's superposition principle, non-linear and hereditary type governing equations are derived. Finite element analysis and the method of multiple scales is applied to examine the effect of large amplitude on the dissipative nature of viscoelastic laminated plates.

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폴리스티렌의 점탄성 계수에 관한 실험적 연구 (An Experimental study on the Viscoelastic Coefficient of Polystyrene)

  • 윤경환;유봉근
    • 대한기계학회:학술대회논문집
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    • 대한기계학회 2000년도 춘계학술대회논문집A
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    • pp.751-754
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    • 2000
  • Stress relaxation experiments were performed to obtain the material properties to be used in the linear viscoelastic study. Master curve of the modulus of polystyrene were obtained by using the time-temperature superposition principle. Because Shyu and Tobolsky's tensile relaxation modulus master curve or Polystyrene material showed very large difference, in-house data were required to calculate the residual stresses in injection-molded products more accurately. Our own experimental data showed that the master curve Shyu's data should be shifted about two orders in material time coordinate.

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분포하중(分布荷重)을 받는 구형판(矩形板)의 탄성해석(彈性解析) (Analysis of Rectangular Plates under Distributed Loads of Various Intensity with Interior Supports at Arbitrary Positions)

  • 장석윤
    • 대한조선학회지
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    • 제13권1호
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    • pp.17-23
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    • 1976
  • Some methods of analysis of rectangular plates under distributed load of various intensity with interior supports are presented herein. Analysis of many structures such as bottom, side shell, and deck plate of ship hull and flat slab, with or without internal supports, Floor systems of bridges, included crthotropic bridges is a problem of plate with elastic supports or continuous edges. When the four edges of rectangular plate is simply supported, the double Fourier series solution developed by Navier can represent an exact result of this problem. If two opposite edges are simply supported, Levy's method is available to give an "exact" solution. When the loading condition and supporting condition of a plate does not fall into these cases, no simple analytic method seems to be feasible. Analysis of a simply supported rectangular plate under irregularly distributed loads of various intensity with internal supports is carried out by applying Navier solution well as the "Principle of Superposition." Finite difference technique is used to solve plates under irregularly distributed loads of various intensity with internal supports and with various boundary conditions. When finite difference technique is applied to the Lagrange's plate bending equation, any of fourth order derivative term in this equation produces at least five pivotal points leading to some troubles when the resulting linear algebraic equations are to be solved. This problem was solved by reducing the order of the derivatives to two: the fourth order partial differential equation with one dependent variable, namely deflection, is changed to an equivalent pair of second order partial differential equations with two dependent variables. Finite difference technique is then applied to transform these equations to a set of simultaneous linear algebraic equations. Principle of Superposition is then applied to handle the problems caused by concentrated loads and interior supports. This method can be used for the cases of plates under irregularly distributed loads of various intensity with arbitrary conditions such as elastic supports, or continuous edges with or without interior supports, and this method can also be solve the influence values of deflection, moment and etc. at arbitrary position of plates under the live load.

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Elastic solutions for shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface

  • Wang, Ling;Zou, Jin-Feng;Yang, Tao;Wang, Feng
    • Geomechanics and Engineering
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    • 제19권3호
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    • pp.201-215
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    • 2019
  • A new approach of analyzing the displacements and stress of the surrounding rock for shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface is investigated in this study. In the proposed approach, by using a virtual image technique, the shear stress of the vertical ground surface is revised to be zero, and elastic solutions of the surrounding rock are obtained before stress revision. To revise the vertical normal stress and shear stress of horizontal ground surface generated by the combined action of the actual and image sinks, the harmonic functions and corresponding stress function solutions were adopted. Based on the Boussinesq's solutions and integral method, the horizontal normal stress of the vertical ground surface is revised to be zero. Based on the linear superposition principle, the final solution of the displacements and stress were proposed by superimposing the solutions obtained by the virtual image technique and the stress revision on the horizontal and vertical ground surfaces. Furthermore, the ground settlements and lateral displacements of the horizontal and vertical ground surfaces are derived by the proposed approach. The proposed approach was well verified by comparing with the numerical method. The discussion based on the proposed approach in the manuscript shows that smaller horizontal ground settlements will be induced by lower tunnel buried depths and smaller limb distances. The proposed approach for the displacement and stress of the surrounding rocks can provide some practical information about the surrounding rock stability analysis of shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface.

다방향파중에서의 선박 자동조타 시스템의 평가 기법에 관한 연구 (A Study on the Estimation of Automatic Steering of Ships in Multi-directional Waves)

  • 이경우;손경호;윤순동
    • 한국항해학회지
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    • 제22권1호
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    • pp.79-89
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    • 1998
  • When an automatic course-keeping is concerned , as is quite popular in modern navigation, the closed-loop steering system consists of autopilot device, power unit(or telemotor unit), steering gear, magnetic or gyro compass and ship dynamics. In order to estimate steering system of ship in open seas, we need to know the characteristics of each component of the system and also to know the characteristics of disturbance to ship dynamics. Calculation methods of irrgular disturbances are based on the linear superposition principle. In this paper, for the purpose of evaluation of automatic steering of ships , the influences of linear control constants of autopilot on propulsive energy loss are investigated bya performance index is introduced from the viewpoint of energy saving. Numberical calculations are carried out for an are carrier and for a fishing boat in multi-directional waves.

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추사파중을 항행하는 선박의 자동조타 시스템 평가에 관한 연구 (A Study on the Evaluation of Automatic Steering System of Ships in Folowing Seas)

  • 이경우;손경호
    • 한국항해학회지
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    • 제25권4호
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    • pp.407-415
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    • 2001
  • In the present study, irregular disturbances to ship dynamics is proposed, where irregular disturbances implying irregular wave and the fluctuating component of wind for the evaluation of automatic steering system of ship in following seas. Prediction method based on the principle of linear superposition. Irregular wave disturbances in following seas is calculated by frequency variation method. The mathematical model of each element of an automatic steering system is derived, which takes account of a few non-linear mechanisms. PD(Proportional-Derivative) controller and low-pass filter with a weather adjustment are adopted to modelling the characteristics of an autopilot. Performance index is introduced from the viewpoint of energy saving, which derived from the concept of energy loss on ship propulsion. Finally, the present methods are applied to two typical types of ship ; an ore carrier and a fishing boat. The various effects of control constants of autopilot on propulsive energy loss are investigated

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A Simplified Carrier-Based Pulse-Width Modulation Strategy for Two-level Voltage Source Inverters in the Over-modulation Region

  • Jing, Feng;He, Feng-You
    • Journal of Power Electronics
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    • 제17권6호
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    • pp.1480-1489
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    • 2017
  • In this study, a carrier-based pulse-width modulation (PWM) method for two-level voltage source inverters in the over-modulation region is proposed. Based on the superposition principle, the reference voltage vectors outside the linear modulation boundary are adjusted to relocate to the vector hexagon, while their fundamental magnitudes are retained. In accordance with the adjusted reference vector, the corresponding modulated waves are respectively deduced in over-modulation mode I and II to generate the gate signals of the power switches, guaranteeing the linearity of the fundamental output phase voltage in the over-modulation region. Moreover, due to the linear relationship between the voltage vector and the duty ratios, the complicated sector identification and holding angle calculation found in previous methods are avoided in the modulated wave synthesis, which provides great simplicity for the proposed carrier-based over-modulation strategy. Experimental results demonstrate the effectiveness and validity of the proposed method.

2극법 전기비저항 탐사 자료의 효율적인 해석방법 (Pole-pole array electrical resistivity survey and an effective interpretational scheme of its data)

  • 조동행;이창열;지상근
    • 한국지구물리탐사학회:학술대회논문집
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    • 한국지구물리탐사학회 2000년도 정기총회 및 특별심포지움
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    • pp.112-131
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    • 2000
  • 2극법 전기비저항 탐사는 많은 장점이 있음에도 불구하고 물리검층과 아주 천부의 고고학적 조사를 제외하면 그다지 이용되지 않고 있다. 이는 2극법 전기비저항 탐사에 의한 측정치의 분해능이 다른 전극배열에 비해서, 특히 쌍극자 쌍극자법, 쌍극자 단극자법, 단극자${\cdot}$쌍극자법에 비해서 뒤떨어진다는 사실에 기인한다. 그러나 필자의 경험과 검토에 의하면 상기한 단점은 다음과 같이 보완될 수 있다. 잘 알려진 바와 같이, 여러 전극배열의 전기비저항 탐사에서 각각의 응답은 2극법 응답의 1 차 결합이므로, 여타 전극배열법의 응답은 2극법 응답의 단순한 조합에 의해서 도출할 수 있다. 잡음 때문에 이러한 사실을 실제 적용하기는 어렵다고 보고된 예가 있지만, 필자가 실제의 천부 탐사 자료를 검토해 보았을 때, 반드시 그렇지는 않다고 확신하게 되었다 즉 최종의 지질학적 해석을 내리기 전에, 2극법 자료에서 분해능이 향상된 자료를 도출하는 과정이 필요하고 유용하다는 의미가 된다. 이는 마치 자력탐사 또는 중력탐사에서 2 차 미분도에 의한 분해능 향상과 유사하다.

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간헐 압축응력완화 시험법과 시간-온도 중첩 이론을 이용한 NBR 오링의 노화 거동 분석 연구 (Study on the Degradaion Behavior of Acrylonitrile Rubber(NBR) O-ring by Intermittent CSR and Time-Temperature Superposition Principle)

  • 이진혁;배종우;최명찬;윤유미;김원호;박성한;조남주
    • 한국추진공학회지
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    • 제23권1호
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    • pp.46-51
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    • 2019
  • Intermittent CSR 측정법을 이용하여 NBR 오링의 노화 거동과 수명 예측에 관하여 연구하였다. Intermittent CSR jig는 오링의 실제 사용 환경을 고려하여 설계 제작하였다. 오링의 노화 거동은 $40{\sim}120^{\circ}C$에서의 가속 노화 연구를 통하여 관찰하였다. 오링은 $80^{\circ}C$ 이하에서 비선형 노화 거동을 나타내었다. 오링의 수명은 고장 조건 20%에 대하여 Arrhenius plot으로부터 32.5년, WLF plot으로 부터 22.6년으로 나타났다.