• Title/Summary/Keyword: Motion equations

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Vibration Analysis of Multi Cracked Nonuniform Nanobeam by using Differential Transformation Method (미분변환법을 이용한 다중 크랙을 갖는 비균일 나노빔의 진동해석)

  • Shin, Young-Jae;Park, Sung-Hyun;Kim, Jin-Hong;Yoo, Yeong-Chan
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.20 no.5
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    • pp.93-101
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    • 2016
  • In this study, the governing equations of motion for multi-cracked nonuniform nanobeam based on nonlocal elasticity theory and embedded in an elastic medium were derived. DTM(differential transformation method) was applied to vibration analysis of multi-cracked nonuniform nanobeam based on nonlocal elasticity theory and embedded in an elastic medium. The non-dimensional natural frequencies of this nanobeam were obtained for eoe, crack stiffness and elastic medium stiffness with various boundary conditions. The results obtained by this method was compared with previous works and showed the close agreement between two methods. The important conclusions obtained by this study are as follows : 1. As the length of nanobeam is shorter, the effect of scale coefficient is greater. 2. The locations of crack change non-dimensional natural frequency, In the case of fixed-fixed ends, the non-dimensional natural frequency is the biggest in the first crack location of 0.6L of nanobeam length, and the smallest in both ends. In the case of fixed-free ends, the closer the location of first crack go tho the free end, the bigger the non-dimensional natural frequency. 3. As the stiffness of crack is greater, the non-dimensional natural frequency is smaller, And the effect of crack stiffness is similar on both fixed-free ends and fixed-fixed ends. 4. The bigger the stiffness of elastic medium, the greater the non - dimensional natural frequency.

A Numerical Simulation of Three- Dimensional Nonlinear Free surface Flows (3차원 비선형 자유표면 유동의 수치해석)

  • Chang-Gu Kang;In-Young Gong
    • Journal of the Society of Naval Architects of Korea
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    • v.28 no.1
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    • pp.38-52
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    • 1991
  • In this paper, a semi-Lagrangian method is used to solve the nonlinear hydrodynamics of a three-dimensional body beneath the free surface in the time domain. The boundary value problem is solved by using the boundary integral method. The geometries of the body and the free surface are represented by the curved panels. The surfaces are discretized into the small surface elements using a bi-cubic B-spline algorithm. The boundary values of $\phi$ and $\frac{\partial{\phi}}{\partial{n}}$ are assumed to be bilinear on the subdivided surface. The singular part proportional to $\frac{1}{R}$ are subtracted off and are integrated analytically in the calculation of the induced potential by singularities. The far field flow away from the body is represented by a dipole at the origin of the coordinate system. The Runge-Kutta 4-th order algorithm is employed in the time stepping scheme. The three-dimensional form of the integral equation and the boundary conditions for the time derivative of the potential Is derived. By using these formulas, the free surface shape and the equations of motion are calculated simultaneously. The free surface shape and fille forces acting on a body oscillating sinusoidally with large amplitude are calculated and compared with published results. Nonlinear effects on a body near the free surface are investigated.

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3-D Kinematic comparison of One Hand Backhand Stroke and Two Hand Backhand Stroke in Tennis (테니스 한손 백핸드 스트로크와 양손 백핸드 스트로크 동작의 3차원 운동학적 비교 분석)

  • Choi, Ji-Young;Shin, Je-Min
    • Korean Journal of Applied Biomechanics
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    • v.15 no.4
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    • pp.85-95
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    • 2005
  • The purpose of this study was to investigate the relations between the segments of the body, the three dimensional anatomical angle during One Hand Backhand Stroke and Two Hand Backhand in tennis. For the movement analysis three dimensional cinematographical method(APAS) was used and for the calculation of the kinematic variables a self developed program was used with the LabVIEW 6.1 graphical programming(Johnson, 1999) program. By using Eular's equations the three dimensional anatomical Cardan angles of the joint and racket head direction were defined. 1. In three dimensional maximum linear velocity of racket head the X axis and Y axis(horizontal direction) showed $-11.04{\pm}2.69m/sec$, $-9.31{\pm}0.49m/sec$ before impact, the z axis(vertical direction) maximum linear velocity of racket head did not show at impact but after impact this will resulted influence upon hitting ball. It could be suggest that Y axis velocity of racket head influence on ball direction and z axis velocity influence on ball spin after impact. The stance distance between right foot and left foot was mean $75.4{\pm}5.86cm$ during one hand backhand stroke and $72.6{\pm}4.67cm$ during two hand backhand stroke. 2. The three dimensional anatomical angular displacement of trunk in interna rotation-external rotation showed most important role in backhand stroke. and is follwed by flexion-extension. the three dimensional anatomical angular displacement of trunk did not show significant difference between one hand backhand stroke and two hand backhand stroke but the three dimensional anatomical angular displacement of trunk was bigger than one hand backhand stroke. 3. while backhand stroke, the flexion-extension and adduction-abduction of right shoulder joint showed significant different between one hand backhand stroke and two hand backhand stroke. the three dimensional anatomical angular displacement of right shoulder joint showed more flex and abduct in one hand backhand stroke. 4. The three dimensional anatomical angular displacement of left shoulder showed flexion, adduction, and external rotation at impact. after impact, The angular displacement as adduction-abduction of left shoulder changed motion direction as abduction. angular displacement of left shoulder as flexion-extension showed bigger than the right shoulder.

Dynamic Modeling and Simulation of a Towing Rope using Multiple Finite Element Method (다물체 요소이론을 이용한 예인줄 동역학의 모델링 및 시뮬레이션)

  • Yoon, Hyeon-Kyu;Lee, Hong-Seok;Park, Jong-Kyu;Kim, Yeon-Gyu
    • Journal of Navigation and Port Research
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    • v.36 no.5
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    • pp.339-347
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    • 2012
  • After towing rope connecting a barge to a tug was subdivided into multiple finite elements, then those dynamic models was established using Newton's second law and considering the external force and moment such as tension, drag, Coriolis force, gravity, buoyancy, and impact due to free surface acting on each element. While the previous research on the model of towing rope considered only translation, five-degree-of-freedom equations of motion except roll based on the body-fixed frame were established in this paper. All elements are connected by a spring and a damper, and the stiffness of the spring was set as the equivalent value of the real rope. In order to confirm the established multiple finite element model, various scenarios such as freely falling of towing rope in the air and above the free surface, accelerating of a tug which tows a barge connected by towing rope, and sinusoidal moving of a tug were set up and simulated. As the results, the trajectories of the tug, the barge, and the towing rope showed good tendencies to the ones of real expected situations.

Seismic Performance Evaluation of a Cone-type Friction Pendulum Bearing System (원추형 마찰진자베어링의 내진성능평가)

  • Jeon, Bub-Gyu;Chang, Sung-Jin;Park, Kyung-Rock;Kim, Nam-Sik;Jung, Duk-Young
    • Journal of the Earthquake Engineering Society of Korea
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    • v.15 no.2
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    • pp.23-33
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    • 2011
  • In this study, a CFPBS (Cone-type Friction Pendulum Bearing System) was developed which controls the acceleration delivered to the structure to prevent damage and degradation of the critical communication equipment in case of an earthquake. The isolation performance of the CFPBS was evaluated by numerical analysis. The CFPBS was manufactured in the shape of a cone differenced from the existing FPS (Friction Pendulum System), and a pattern was engraved on the friction surface. The natural frequencies of the CFPBS were evaluated from a free-vibration test with the seismic isolator system consisting of four CFPBSs. In order to verify its earthquake-resistant performance, a numerical analysis program was created from the equation of the CFPBS induced from the equations of motion. A simplified theoretical equation of the CFPBS was proposed to manufacture the equipment which could demonstrate the necessary performance. Artificial seismic waves satisfying the maximum earthquake scale of the Korean Building Code-Structural (KBC-2005) were created and verified to review the earthquake-resistant performance of the CFPBS by numerical analysis. The superstructural mass of the CFPBS and skew angle of the friction surface were considered for numerical analysis with El Centro NS (1940), Kobe NS (1995) and artificial seismic waves. The CFPBS isolation performance evaluation was based on the results of numerical analysis and the executed comparative analysis between the results from numerical analysis and the simplified theoretical equation under the same conditions.

Comparison of Methods Predicting VS30 from Shallow VS Profiles and Suggestion of Optimized Coefficients (얕은 심도 VS주상도를 활용한 VS30 예측 방법론 비교 및 최적 계수 제시)

  • Choi, Inhyeok;Kwak, Dongyoup
    • Journal of the Korean Geotechnical Society
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    • v.36 no.3
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    • pp.15-23
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    • 2020
  • Ground motion models predicting intensity measures on surface use a time-averaged shear wave velocity, VS30, as a key variable simulating site effect. The VS30 can be directly estimated from VS profiles if the profile depth (z) is greater than or equal to 30 m. However, some sites have VS profiles with z < 30 m. In this case VS30 can be predicted using extension models. This study proposes new coefficient sets for existing prediction equations using 297 Korea VS profiles. We have collected VS profiles from KMA and Geoinfo database. Fitting six existing methods to data, we suggest new coefficients for each method and evaluate their performance. It turns out that if z ≥ 15 m, the standard deviation (σ) of residual in log10 is 0.061, which indicates that the estimated VS30 is nearly accurate. If z < 15 m, the σ keeps increasing up to 0.1 for z = 5 m, so we caution the use of models at very low z. Nonetheless, we recommend investigating up to 30 m depth for VS30 calculation if possible.

The Earth-Moon Transfer Trajectory Design and Analysis using Intermediate Loop Orbits (중개궤도를 이용한 지구-달 천이궤적의 설계 및 분석)

  • Song, Young-Joo;Woo, Jin;Park, Sang-Young;Choi, Kyu-Hong;Sim, Eun-Sup
    • Journal of Astronomy and Space Sciences
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    • v.26 no.2
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    • pp.171-186
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    • 2009
  • Various Earth-Moon transfer trajectories are designed and analyzed to prepare the future Korea's Lunar missions. Minimum fuel trajectory solutions are obtained for the departure year of 2017, 2020, 2022, and every required mission phases are analyzed from Earth departure to the final lunar mission orbit. N-body equations of motion are formulated which include the gravitational effect of the Sun, Earth and Moon. In addition, accelerations due to geopotential harmonics, Lunar J2 and solar radiation pressures are considered. Impulsive high thrust is assumed as the main thrusting method of spacecraft with launcher capability of KSLV-2 which is planned to be developed. For the method of injecting a spacecraft into a trans Lunar trajectory, both direct shooting from circular parking orbit and shooting from the multiple elliptical intermediate orbits are adapted, and their design results are compared and analyzed. In addition, spacecraft's visibility from Deajeon ground station are constrained to see how they affect the magnitude of TLI(Trans Lunar Injection) maneuver. The results presented in this paper includes launch opportunities, required optimal maneuver characteristics for each mission phase as well as the trajectory characteristics and numerous related parameters. It is confirmed that the final mass of Korean lunar explorer strongly depends onto the initial parking orbit's altitude and launcher's capability, rather than mission start time.

3-D Kinematic Analysis According to Open Stance Patterns During Forehand Stroke in Tennis (테니스 포핸드 스트로크 동안 오픈스탠스 조건에 따른 3차원 운동학적 분석)

  • Choi, Ji-Young;Kim, Ro-Bin
    • Korean Journal of Applied Biomechanics
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    • v.15 no.3
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    • pp.161-173
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    • 2005
  • Recently among several tennis techniques forehand stroke has been greatly changed in the aspect of spin, grip and stance. The most fundamental factor among the three factors is the stance which consists of open, square and closed stance. The purpose of this study was to investigate the relations between the segments of the body, the three dimensional anatomical angle according to open stance patterns during forehand stroke in tennis. For the movement analysis three dimensional cinematographical method(APAS) was used and for the calculation of the kinematic variables a self developed program was used with the LabVlEW 6.1 graphical programming(Johnson, 1999) program. By using Eular's equations the three dimensional anatomical Cardan angles of the joint and racket head angle were defined 1. In three dimensional maximum linear velocity of racket head the X axis showed $11.41{\pm}5.27m/s$ at impact, not the Y axis(horizontal direction) and the z axis(vertical direction) maximum linear velocity of racket head did not show at impact but after impact this will resulted influence upon hitting ball It could be suggest that Y axis velocity of racket head influence on ball direction and z axis velocity influence on ball spin after impact. the stance distance between right foot and left foot was mean $74.2{\pm}11.2m$. 2. The three dimensional anatomical angular displacement of shoulder joint showed most important role in forehand stroke. and is followed by wrist joints, in addition the movement of elbow joints showed least to the stroke. The three dimensional anatomical angular displacement of racket increased flexion/abduction angle until the impact. after impact, The angular displacement of racket changed motion direction as extension/adduction. 3. The three dimensional anatomical angular displacement of trunk in flexion-extension showed extension all around the forehand stroke. The angular displacement of trunk in adduction-abduction showed abduction at the backswing top and adduction around impact. while there is no significant internal-external rotation 4. The three dimensional anatomical angular displacement of hip joint and knee joint increased extension angle after minimum of knee joint angle in the forehand stroke, The three dimensional anatomical angular displacement of ankle joint showed plantar flexion, internal rotation and eversion in forehand stroke. it could be suggest that the plantar pressure of open stance during forehand stroke would be distributed more largely to the fore foot. and lateral side.

Seismic Response Analysis of a Two-Mass Rack System Considering Frictional Behavior (마찰거동을 고려한 이중질량시스템의 지진응답해석)

  • Park, Kwan-Soon;Ok, Seung-Yong;Lee, Jeeho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.31 no.6
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    • pp.347-352
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    • 2018
  • This study proposes seismic response analysis technique of a two-mass rack system which sustains heavy loads with frictional behavioral characteristics. In order to deal with the nonlinear frictional characteristics of the mass on the rack system, the equations of motion of the system has been derived and the appropriate numerical simulation technique has been developed. In order to examine the seismic performance of the proposed system, we consider two parameters that are expected to have great influence on the seismic performance of the system. One is the ratio of the two masses of the load and the rack structure, and the other is the friction coefficient between rack and loaded mass. A number of numerical simulations of the seismic response of structures with various natural frequencies for both parameters have been performed in order to investigate the seismic safety of the rack structures. From the simulated results. it is observed that the maximum displacement of the rack system tends to decrease drastically as the natural frequency of the structure increases regardless of the two parameters of mass ratio and friction coefficient. The proposed study provides important reference data to guarantee the seismic safety of the rack system by considering nonlinear frictional behavior of the loaded mass.

Numerical Study on Towing Stability of LNG Bunkering Barge in Calm Water (LNG 벙커링 바지의 정수 중 예인안정성에 관한 수치연구)

  • Oh, Seung-Hoon;Jung, Dong-Ho;Jung, Jae-Hwan;Hwang, Sung-Chul;Cho, Seok-Kyu;Sung, Hong-Gun
    • Journal of Navigation and Port Research
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    • v.43 no.3
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    • pp.143-152
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    • 2019
  • In this paper, the towing stability of the LNG bunker barge was estimated. Currently, LNG bunkering barge is being developed for the bunkering of LNG (Liquefied Natural Gas), an eco-friendly energy source. Since the LNG bunkering barge assumes the form of a towed ship connected to the tow line, the towing stability of the LNG bunker barge is crucial f not only for the safety of the LNG bunker barge but also the neighboring sailing vessels. In the initial stages, a numerical code for towing simulation was developed to estimate the towing stability of the LNG bunkering barge. The MMG (Maneuvering Mathematical modeling Group) model was applied to the equations of motion while the empirical formula was applied to the maneuvering coefficients for use in the initial design stage. To validate the developed numerical code, it was compared with published calculation and model test results. Towing simulations were done based on the changing skeg area and the towing position of the LNG bunkering barge using the developed numerical codes. As a result, the suitability of the designed stern skeg area was confirmed.