• Title/Summary/Keyword: equations of motion

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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.

Comparison of Newton's and Euler's Algorithm in a Compound Pendulum (복합진자 모형의 뉴튼.오일러 알고리즘 비교)

  • Hah, Chong-Ku
    • Korean Journal of Applied Biomechanics
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    • v.16 no.3
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    • pp.1-7
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    • 2006
  • The Primary type of swinging motion in human movement is that which is characteristic of a pendulum. The two types of pendulums are identified as simple and compound. A simple pendulum consist of a small body suspended by a relatively long cord. Its total mass is contained within the bob. The cord is not considered to have mass. A compound pendulum, on the other hand, is any pendulum such as the human body swinging by hands from a horizontal bar. Therefore a compound pendulum depicts important motions that are harmonic, periodic, and oscillatory. In this paper one discusses and compares two algorithms of Newton's method(F = m a) and Euler's method (M = $I{\times}{\alpha}$) in compound pendulum. Through exercise model such as human body with weight(m = 50 kg), body length(L = 1.5m), and center of gravity ($L_c$ = 0.4119L) from proximal end swinging by hands from a horizontal bar, one finds kinematic variables(angle displacement / velocity / acceleration), and simulates kinematic variables by changing body lengths and body mass. BSP by Clauser et al.(1969) & Chandler et al.(1975) is used to find moment of inertia of the compound pendulum. The radius of gyration about center of gravity (CoG) is $k_c\;=\;K_c{\times}L$ (단, k= radius of gyration, K= radius of gyration /segment length), and then moment of inertia about center of gravity(CoG) becomes $I_c\;=\;m\;k_c^2$. Finally, moment of inertia about Z-axis by parallel theorem becomes $I_o\;=\;I_c\;+\;m\;k^2$. The two-order ordinary differential equations of models are solved by ND function of numeric analysis method in Mathematica5.1. The results are as follows; First, The complexity of Newton's method is much more complex than that of Euler's method Second, one could be find kinematic variables according to changing body lengths(L = 1.3 / 1.7 m) and periods are increased by body length increment(L = 1.3 / 1.5 / 1.7 m). Third, one could be find that periods are not changing by means of changing mass(m = 50 / 55 / 60 kg). Conclusively, one is intended to meditate the possibility of applying a compound pendulum to sports(balling, golf, gymnastics and so on) necessary swinging motions. Further improvements to the study could be to apply Euler's method to real motions and one would be able to develop the simulator.

Design Optimization for Kinematic Characteristics of Automotive Suspension considering Constraints (구속조건을 고려한 자동차 현가장치 기구특성의 최적설계)

  • Lee, Chang-Ro;Kim, Hyo-Jun
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.18 no.3
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    • pp.306-311
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    • 2017
  • This paper deals with the design optimization of the kinematic characteristics of an automotive suspension system. The kinematic characteristics of the suspension determine the attitude of the wheels, such as the toe and camber, which not only relates to tire wear during driving, but also greatly affects the control of the vehicle and its stability, which corresponds to the motion performance of the vehicle. Therefore, it is very important to determine the characteristics of the suspension mechanism at the initial stage of the design. In this study, a displacement analysis is performed to determine the kinematic properties of the suspension for the McPherson strut suspension. For this purpose, a set of constraint equations for the joints constituting the suspension mechanism was established and a program was developed to solve them. We also used ADS, a design optimization program, to obtain the desired kinematic characteristics of the suspension. As the design variables for optimization, we used the coordinates of the hard points, which are the points of attachment of the suspension to the vehicle body, and are defined as the summation of the toe-in for the up and down movement of the wheel as the objective function. As the constraint functions, the maximum camber angle and minimum roll center height, which are design requirements, are considered. As a result of this study, it was possible to determine the optimal locations of the hard points that satisfy both constraint functions and minimize the change of the toe-in.

An Analysis of Sinking Resistance for Purse Seine - In the Case of the Model Seine with Different d/l - (선망의 침강 저항 해석 - d/l이 다른 모형망의 경우 -)

  • Kim, Suk-Jong;Park, Jeong-Sik
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.34 no.3
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    • pp.274-282
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    • 1998
  • This study deals with sinking resistance for purse seine, in the case of different d/l, ratio of twine diameter and leg length. Experiments carried out on the six types simplified reduced model seines which were made of knotless netting. The nettings were woven in different leg length 4.3, 5.0, 5.5, 6.0, 6.6 and 7.7mm of polyester 28 tex two threads two -ply twine, and each of the seines were named I, II, III, IV, V and Ⅵ seine. Dimension of seine models were 450cm for corkline and 85cm for seine depth, each seines rigged up 160g of float for a floatline and 50g (underwater weight) of lead for a leadline. Experiments were measured in the observation channel of a flume tank at the static conditions Sinking motion was recorded by the two sets TV-camera for VTR which were placed in top and side of the model seine, and reading coordinate carried out by the video digitization system. An analysis were calculated out by simultaneous differential equations for numerical method by Runge - Kutta - Gill sub - routine. The results obtained were as follows: 1. Average sinking speed of seine of seine margin was fastest for Ⅵ seine followed by V, IV, III, II and I seines. 2. The coefficient of resistance for a seine wall was depended upon the ratio of d/l : KD =0.081 (d/l )-0.5 3. The coefficient of resistance for netting bundle was not depended upon the ratio of d/l :CR = 0.91 (), d : Twine diameter, l : Leg length, : Density of netting materals, $\omega$ : Density of water

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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.

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

  • Oh, Seunghoon;Jung, Dongho;Jung, Jae-Hwan;Hwang, Sung-Chul;Cho, Seok-kyu;Sung, Hong Gun
    • Proceedings of the Korean Institute of Navigation and Port Research Conference
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    • 2019.05a
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    • pp.185-188
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    • 2019
  • In this paper, the towing stability of the LNG bunker barge is estimated. Currently, LNG bunkering barge is being developed as an infrastructure for the bunkering of LNG (Liquefied Natural Gas), an eco-friendly energy source. Since the LNG bunker barge are in the form of towed ship connected to the tow line, the towing stability of the LNG bunker barge is very important for the safety of not only the LNG bunker barge but also the surrounding sailing vessels. The numerical code for towing simulation was developed to estimate the towing stability of the LNG bunker barge at the initial design stage. The MMG(Manoeuvring Mathematical Group) model was applied to the equations of motion and the empirical formula was applied to the maneuvering coefficients so that they could be used in the initial design stage. To validity of the developed numerical code, it was compared with published calculation and model test results. Towing simulations were carried out according to with and without stern skeg of the LNG bunker barge using the developed numerical code. Through the results of the simulations, the appropriateness of the stern skeg area designed was confirmed.

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Study on the Applicability of a New Multi-body Dynamics Program Through the Application to the Heave Compensation System (상하동요 감쇠장치 적용을 통한 새로운 다물체동역학 프로그램의 적용성 검토)

  • Ku, Nam-Kug;Ha, Sol;Roh, Myung-Il
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.26 no.4
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    • pp.247-254
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    • 2013
  • In this paper, dynamic response analysis of a heave compensation system is performed for offshore drilling operations based on multibody dynamics. With this simulation, the efficiency of the heave compensation system can be virtually confirmed before it is applied to drilling operations. The heave compensation system installed on a semi-submersible platform consists of a passive and an active heave compensator. The passive and active heave compensator are composed of several bodies that are connected to each other with various types of joints. Therefore, to carry out the dynamic response analysis, the dynamics kernel was developed based on mutibody dynamics. To construct the equations of motion of the multibody system and to determine the unknown accelerations and constraint forces, the recursive Newton-Euler formulation was adapted. Functions of the developed dynamics kernel were verified by comparing them with other commercial dynamics kernels. The hydrostatic force with nonlinear effects, the linearized hydrodynamic force, and the pneumatic and hydraulic control forces were considered as the external forces that act on the platform of the semi-submersible rig and the heave compensation system. The dynamic simulation of the heave compensation system of the semi-submersible rig, which is available for drilling operations with a 3,600m water depth, was carried out. From the results of the simulation, the efficiency of the heave compensation system were evaluated before they were applied to the offshore drilling operations. Moreover, the calculated constraint forces could serve as reference data for the design of the mechanical system.

A Study on a Sliding Mode Control Algorithm for Dynamic Positioning System of a Vessel (선박의 동적위치유지 시스템을 위한 Sliding Mode 제어 연구)

  • Young-Shik Kim;Jang-Pyo Hong
    • Journal of Navigation and Port Research
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    • v.47 no.4
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    • pp.256-270
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    • 2023
  • In this study, a sliding mode (SM) controller for dynamic positioning (DP) was specifically designed for a turret connection operation of a ship or an offshore structure in which an arbitrary point on the structure could be controlled as the motion center instead of the center of mass. The SM controller allows control of the arbitrary point and provides capability to manage uncertainties in the dynamics of ships and offshore structures, external forces caused by unknown changing marine environments, and transient performance of DP systems. The Jacobian matrix included in kinematic equations of the controlled object was modified to design the SM controller to control based on an arbitrary point of ships or offshore structures. To ensure robustness of the controller, the Lyapunov stability theory was applied in the design of the SM controller. In general, for robustness in DP control, gain scheduling based on a proportional-derivative (PD) control algorithm is employed. However, finding appropriate gains for gain scheduling complicates the application of DP systems. Therefore, in this study, the SM control algorithm was considered to mitigate the complexity of the DP controller for ships and offshore structures. To validate the proposed SM control algorithm, time-domain simulations were conducted and utilized to evaluate the performance of the control algorithm. The effectiveness of the proposed SM controller was assessed by comparing simulation results with results of a conventional PD control algorithm applied in DP control.

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.

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.