• Title/Summary/Keyword: linear superposition principle

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Analytical approaches to the charging process of stratified thermal storage tanks with variable inlet temperature (변온유입 성층축열조의 충전과정에 대한 해석적 접근)

  • Yoo, Hoseon
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.9 no.1
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    • pp.43-54
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    • 1997
  • This paper presents an approximate analytical solution to a two-region one-dimensional model for the charging process of stratified thermal storage tanks with variable inlet temperature in the presence of momentum-induced mixing. Based on the superposition principle, an arbitrary-varying inlet temperature is decomposed into inherent discontinuous steps and continuous intervals approximated as a finite number of piecewise linear functions. This approximation allows the temperature of the upper perfectly-mixed layer to be expressed in terms of constant, linear and exponential functions with respect to time. Applying the Laplace transform technique to the model equation for the lower thermocline layer subject to each of three representative interfacial conditions yields compact-form solutions, a linear combination of which constitutes the final temperature profile. A systematic method for deriving solutions to the plug-flow problem having polynomial-type boundary conditions is also established. The effect of adiabatic exit boundary on solution behaviors proves to be negligible under the actual working conditions, which justifies the assumption of semi-infinite domain introduced in the solution procedure. Finally, the approximate solution is validated by comparing it with an exact solution obtained for a specific variation of inlet temperature. Excellent agreements between them suffice to show the necessity and utility of this work.

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A piecewise linear transverse shear transfer model for bolted side-plated beams

  • Li, Ling-Zhi;Jiang, Chang-Jiu;Su, Ray Kai-Leung;Lo, Sai-Huen
    • Structural Engineering and Mechanics
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    • v.62 no.4
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    • pp.443-453
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    • 2017
  • The performance of bolted side-plated (BSP) beams is affected by the degree of transverse partial interaction, which is a result of the interfacial slip caused by transverse shear transfer between the bolted steel plates and the reinforced concrete beams. However, explicit formulae for the transverse shear transfer profile have yet to be derived. In this paper, a simplified piecewise linear shear transfer model was proposed based on force superposition principle and simplification of shear transfer profiles derived from a previous numerical study. The magnitude of shear transfer was determined by force equilibrium and displacement compatibility condition. A set of design formulae for BSP beams under several basic load cases was also derived. Then the model was verified by test results. A worked example was also provided to illustrate the application of the proposed design formulae. This paper sheds some light on the shear force transfer mechanism of anchor bolts in BSP beams, and offers a practical method to evaluate the influence of transverse partial interaction in strengthening design.

A Study on Computational Method for Fatigue Life Prediction of Vehicle Structures (차체 구조물의 피로수명 예측을 위한 컴퓨터 시뮬레이션 방법에 관한 연구)

  • 이상범;박태원;임홍재
    • Journal of KSNVE
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    • v.10 no.4
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    • pp.686-691
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    • 2000
  • In this paper a computer aided analysis method is proposed for durability assessment in the early design stages using dynamic analysis, stress analysis and fatigue life prediction method. From dynamic analysis of a vehicle suspension system, dynamic load time histories of a suspension component are calculated. From the dynamic load time histories and the stress of the suspension component, a dynamic stress time history at the critical location is produced using the superposition principle. Using linear damage law and cycle counting method, fatigue life cycle is calculated. The predicted fatigue life cycle is verified by experimental durability tests.

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A Study on Computational Method for Fatigue Life Prediction of Vehicle Structures (차체 구조물의 피로수명 예측을 위한 컴퓨터 시뮬레이션 방법에 관한 연구)

  • Lee, Sang-Beom;Park, Tae-Won;Park, Jong-Sung;Lee, Sun-Byung;Yim, Hong-Jae
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2000.06a
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    • pp.1883-1888
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    • 2000
  • In this paper a computer aided analysis method is proposed for durability assessment in the early design stages using dynamic analysis, stress analysis and fatigue life prediction method. From dynamic analysis of a vehicle suspension system, dynamic load time histories of a suspension component are calculated. From the dynamic load time histories and the stress of the suspension component, a dynamic stress time history at the critical location is produced using the superposition principle. Using linear damage law and cycle counting method, fatigue life cycle is calculated. The predicted fatigue life cycle is verified by experimental durability tests.

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A Study on the Performance Index of Automatic Steering System of Fishing Boat Using Frequency Response Analysis (주파수 응답해석을 이용한 파랑조건에 따른 어선 자동 조타시스템의 성능평가지수에 관한 연구)

  • 이경우;손경호
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.39 no.1
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    • pp.1-7
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    • 2003
  • When a ship is course-keeping in the open seas, autopilot system is adapted. The design of autopilot system is very important for improvement of ship′s element research. Automatic steering system consists of autopilot device, power unit, steering gear, magnetic or gyro compass and ship dynamics. In order to evaluate automatic steering system of ships 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. In this paper, I provide evaluation method of autopilot navigation system of the fishing ship. Prediction method based on the principle of linear superposition is introduced for irregular disturbance. For the evaluation of automatic steering system of a ship, "performance index" is introduced from the viewpoint of energy saving and calculation method is frequency response analysis. Finally, I carried out calculation of sensitivity of control constants of autopilot with various conditions of ocean environments.

Life Time Prediction Using Accelerated Ageing Test for a CR/CB Rubber Composite

  • Ahn, WonSool;Lee, Hyung Seok
    • Elastomers and Composites
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    • v.52 no.4
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    • pp.237-241
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    • 2017
  • The tensile strength (TS) and elongation-at-break (EB) loss of a CR/CB rubber composite sample prepared for the automotive parts were measured after accelerated thermal ageing at temperatures of 100, 120, 140, and $150^{\circ}C$. The change in TS was observed to be linear from the master curve prepared using the time-temperature superposition-principle (TTSP). An Arrhenius type of shift factor, $a_T$ was used to predict the life time of the sample, and a plot of ln $a_T$ vs. 1/T was also shown to be linear. The activation energy ($E_a$) of the sample was calculated as 70.30 kJ/mole from the Arrhenius plot. The expected life time of the sample was predicted at the given operating conditions by applying Arrhenius analysis. Assuming the $E_a$ value was constant at lower operating condition, life time of the sample was calculated as 2.3 years when the life limit was set as time to reach the 20% decrease of the initial TS value at operating temperature of $40^{\circ}C$.

Life-time Prediction of a FKM O-ring using Intermittent Compression Stress Relaxation (CSR) and Time-temperature Superposition (TTS) Principle (간헐 압축응력 완화와 시간-온도 중첩 원리를 이용한 FKM 오링의 수명 예측 연구)

  • Lee, Jin-Hyok;Bae, Jong-Woo;Kim, Jung-Su;Hwang, Tae-Jun;Park, Sung-Doo;Park, Sung-Han;Min, Yeo-Tae;Kim, Won-Ho;Jo, Nam-Ju
    • Elastomers and Composites
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    • v.45 no.4
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    • pp.263-271
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    • 2010
  • Intermittent CSR testing was used to investigate the degradation of an FKM O-ring, also the prediction of its life-time. An intermittent CSR jig was designed taking into consideration the O-ring's environment under use. The testing allowed observation of the effects of friction, heat loss, and stress relaxation by the Mullins effect. Degradation of O-rings by thermal aging was observed between 60 and $160^{\circ}C$. In the high temperature of range ($100-160^{\circ}C$) O-rings showed linear degradation behavior and satisfied the Arrhenius relationship. The activation energy was about 60.2 kJ/mol. From Arrhenius plots, predicted life-times were 43.3 years and 69.9 years for 50% and 40% failure conditions, respectively. Based on TTS (time-temperature superposition) principle, degradation was observed at $60^{\circ}C$, and could save testing time. Between 60 and $100^{\circ}C$ the activation energy decreased to 48.3 kJ/mol. WLF(William-Landel-Ferry) plot confirmed that O-rings show non-linear degradation behavior under $80^{\circ}C$. The life-time of O-rings predicted by TTS principle was 19.1 years and 25.2 years for each failure condition. The life-time predicted by TTS principle is more conservative than that from the Arrhenius relationship.

Viscoelastic Property Evaluation of Asphalt Cement by Ultrasonic Measurement (초음파 측정법에 의한 아스팔트 세멘트의 점탄성 특성 평가)

  • Lee, Jai-Hak
    • Journal of the Korean Society for Nondestructive Testing
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    • v.20 no.5
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    • pp.402-411
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    • 2000
  • This study investigates the method to measure the viscoelastic properties of asphalt cement, one of the viscoelastic materials, using the ultrasound. The wave speed and attenuation were measured from $-20^{\circ}C$ to $60^{\circ}C$ at the frequency of 2.25MHz. Then, the storage and loss longitudinal moduli, loss tangent storage and loss longitudinal compliances were found depending on the temperatures based on the linear viscoelastic theory. Stress relaxation, creep, and viscosity were predicted using Maxwell and Voigt-Kelvin viscoelastic models. The validity of superposition principle and shift factor were verified by comparing the present results to the data reported in the literatures.

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Development of the Predicted Model for the HMA Dynamic Modulus by using the Impact Resonance Testing and Universal Testing Machine (충격공진실험과 만능재료시험기에 의한 아스팔트 공시체의 동탄성계수 예측 모델 개발)

  • Kim, Do Wan;Kim, Dong-Ho;Mun, Sungho
    • International Journal of Highway Engineering
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    • v.16 no.3
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    • pp.43-50
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    • 2014
  • PURPOSES : The dynamic modulus can be determined by applying the various theories from the Impact Resonance Testing(IRT) Method. The objective of this paper is to determine the best theory to produce the dynamic modulus that has the lowest error as the dynamic modulus data obtained from these theories(Complex Wave equation Resonance Method related to either the transmissibility loss or not, Dynamic Stiffness Resonance Method) compared to the results for dynamic modulus determined by using the Universal Testing Machine. The ultimate object is to develop the predictive model for the dynamic modulus of a Linear Visco-Elastic specimen by using the Complex Wave equation Resonance Method(CWRM) came up for an existing study(S. O. Oyadiji; 1985) and the Optimization. METHODS : At the destructive test which uses the Universal Testing Machine, the dynamic modulus results along with the frequency can be used for determining the sigmoidal master curve function related to the reduced frequency by applying Time-Temperature Superposition Principle. RESULTS : The constant to be solved from Eq. (11) is a value of 14.13. The reduced dynamic modulus obtained from the IRT considering the loss factor related to the impact transmissibility has RMSE of 367.7MPa, MPE of 3.7%. When the predictive dynamic modulus model was applied to determine the master curve, the predictive model has RMSE of 583.5MPa, MPE of 3.5% compared to the destructive test results for the dynamic modulus. CONCLUSIONS : Because we considered that the results obtained from the destructive test had the most highest source credibility in this study, the dynamic modulus data obtained respectively from DSRM, CWRM were compared to the results obtained from the destructive test by using th IRT. At the result, the reduced dynamic modulus derived from DSRM has the most lowest error.

Motions of Semi-submersible Drilling Rigs in Deep Water (Semi-submersible 석유시추선(石油試錐船)(부체해양구조물(浮體海洋構造物))의 운동(運動) -계산방법(計算方法), 해석(解析) 및 응용(應用))

  • Jin-S.,Chung
    • Bulletin of the Society of Naval Architects of Korea
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    • v.11 no.2
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    • pp.23-40
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    • 1974
  • Semisubmersible 해양석유시추선의 기본설계에 필요한 파랑중(波浪中)에서 운동(運動)을 계산(計算)하는 이론적방법(理論的方法)을 제시하고 "MOHOLE"과 "SEDCO 1350-F" 석유시추선들의 운동(運動)을 해석하였다. 이 규칙파에서 운동계산을 불규칙해양파(波)에 적용하는 응용해석을 보여주었다. 현재 이론적 방법으로는 6자유도(自由度)의 운동을 해양파의 어떤 방향에 대해서도 정확히 계산할 수 있으며 계산의 정확성은 수조(水槽)에서의 모형선의 운동측정치와 실선(實船)의 운동측정치와 비교하여 증명되었다. 또 현재의 방법은 종전에 개발된 방법보다 더 일반적(一般的)인 경우를 다룰 수 있으며 결과치도 더 정확하다. 극소운동특성을 갖는 해양석유시추선과 부체(浮體)해양구조물의 설계는 경비가 비싸고 시간이 많이 드는 모형실험보다는 유체역학적(流體力學的) Parameters를 신속 정확히 자주 변경 검토해야 하는 기본설계단계에서는 정확한 이론적인 전자계산기에 의한 계산방법이 절실히 필요하다. 예상(豫想)과 같은 부가질량(附加質量)과 감쇠력(減衰力)은 Resonance 운동주기에서만 운동에 영향을 준다. 해양구조물에 작용하는 파력(波力)은 Froude-Krilov force, 부가질량(附加質量) 및 감쇠력(減衰力)과 Restoring force로 구성했으며 규칙파(規則波)에서의 6자유도(自由度) 운동방정식은 본 논문에 제시된 실험측정치(値)와 실험으로 정확도가 증명된 이론치(値)의 부가질량과 감쇠력 계수(係數)를 써서 풀었다. 규칙파(規則波)에서의 계산된 운동을 Pierson Moskowitz 해양파(海洋波) 스펙트럼과 linear superposition principle에 의해 불규칙해양파(不規則海洋波)에서의 운동을 계산하는데 사용했다. 불규칙파(不規則波)에서의 운동은 운동스펙트럼과 통계적 운동치로 나타냈다. 현재의 계산방법은 실제 기본설게에 사용되어 왔으며, 다른 응용분야는 파랑중(波浪中)에서의 파면(波面)과 Deck간(間)의 Clearance, 계류선(係留線)의 동장력(動張力)계산의 기본 Data 및 기본설계의 Draft 등 Parameters를 통(通)한 Optimum Design 등(等)이다. 파(波)의 한 방향(方向)에 대(對)한 전자계산기(電子計算機)(IBM 370 또는 CDC 6400)에 의한 운동계산은 10초(秒)미만밖에 안걸린다. 또 현재의 계산방법은 해양석유시추선뿐 아니라 이와 비슷한 부체(浮體)해양구조물과 Pipe-laying선(船) 또 Supply Boat설계(設計)에도 쓰여지고 있다.

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