• Title/Summary/Keyword: equations of motion

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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.

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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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.

Dynamic Instability and Multi-step Taylor Series Analysis for Space Truss System under Step Excitation (스텝 하중을 받는 공간 트러스 시스템의 멀티스텝 테일러 급수 해석과 동적 불안정)

  • Lee, Seung-Jae;Shon, Su-Deok
    • Journal of Korean Society of Steel Construction
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    • v.24 no.3
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    • pp.289-299
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    • 2012
  • The goal of this paper is to apply the multi-step Taylor method to a space truss, a non-linear discrete dynamic system, and analyze the non-linear dynamic response and unstable behavior of the structures. The accurate solution based on an analytical approach is needed to deal with the inverse problem, or the dynamic instability of a space truss, because the governing equation has geometrical non-linearity. Therefore, the governing motion equations of the space truss were formulated by considering non-linearity, where an accurate analytical solution could be obtained using the Taylor method. To verify the accuracy of the applied method, an SDOF model was adopted, and the analysis using the Taylor method was compared with the result of the 4th order Runge-Kutta method. Moreover, the dynamic instability and buckling characteristics of the adopted model under step excitation was investigated. The result of the comparison between the two methods of analysis was well matched, and the investigation shows that the dynamic response and the attractors in the phase space can also delineate dynamic snapping under step excitation, and damping affects the displacement of the truss. The analysis shows that dynamic buckling occurs at approximately 77% and 83% of the static buckling in the undamped and damped systems, respectively.

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.

A Non-consecutive Cloth Draping Simulation Algorithm using Conjugate Harmonic Functions (켤레조화함수를 이용한 비순차적 의류 주름 모사 알고리즘)

  • Kang Moon Koo
    • Journal of KIISE:Software and Applications
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    • v.32 no.3
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    • pp.181-191
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    • 2005
  • This article describes a simplified mathematical model and the relevant numerical algorithm to simulate the draped cloth on virtual human body. The proposed algorithm incorporates an elliptical, or non-consecutive, method to simulate the cloth wrinkles on moving bodies without resorting to the result of the past time-steps of drape simulation. A global-local analysis technique was employed to decompose the drape of cloths into the global deformation and the local wrinkles that will be superposed linearly The global deformation is determined directly by the rotation and the translation of body parts to generate a wrinkle-free yet globally deformed shape of cloth. The local wrinkles are calculated by solving simple elliptical equations based on the orthogonality between conjugate harmonic functions representing the wrinkle amplitude and the direction of wrinkles. The proposed method requires no interpolative time frames even for discontinuous body postures. Standing away from the incremental approach of time integration in conventional methods, the proposed method yields a remarkable reduction of CPU time and an enhanced stability. Also, the transient motion of cloth could be achieved by interpolating between the deformations corresponding to each static posture.

Free Vibration Analysis of a Degenerated Timoshenko Beam Including the Effect of Shear Deformation and Rotatory Inertia (전단변형(剪斷變形)과 회전관성(回轉慣性)을 고려(考慮)한 Timoshenko 보의 자유진동(自由振動) 해석(解析))

  • Byun, Dong Kyun;Shin, Young Shik;Jang, Jong Tak
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.3 no.4
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    • pp.109-122
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    • 1983
  • An accurate thick beam element (TB4) which includes the effects of the shear deformation and rotatory inertia has been degenerated from the three dimensional continuum by employing the Timoshenko beam assumptions. The proposed TB4 element has four nodes and two degrees of freedom at each node, totally eight degrees of freedom. The transverse deflection W and plane rotation ${\theta}$ with the cubic interpolation functions are selected as nodal variables. The element characteristics are formulated by discretizing the beam equations of motion, using the Galerkin weighted residual method, and are numerically integrated by the reduced shear integration technique, using the three-point Gauss quadrature with the various shear coefficients. Several numerical examples are analyzed to demonstrate the accuracy and the monotonic convergence behavior of the proposed TB4 beam element. The result indicates that the TB4 element shows the more excellent performance and the monotonic convergence behavior than the other existing Timoshenko beam type elements for the whole range of the beam aspect ratios, in both static and free vibration analyses.

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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.

An Analysis on the Sinking Resistance of Purse Seine - 2. In the Case of the Model Purse Seine with Different Netting Material and Sinkers - (旋網의 沈降 抵抗 解析 - 2. 網地材料와 沈子量 다른 模型網의 경우 -)

  • Kim, Suk-Jong
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.40 no.1
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    • pp.29-36
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    • 2004
  • This study deals with an analysis on the sinking resistance for the model purse seine, in the case of different netting material and sinkers. The experiment was carried out using rune simplified model seines of knotless nettings. Dimension of model seines 420cm for corkline and 85cm for seine depth, three groups of models rigged 25, 45 and 60g with the same weighted sinkers in water were used. These were named PP-25, PA-25, PES-25, PP-45, PA-45, PES-45, PP-60, PA-60 and PES-60 seine. The densitie($\rho$) of netting materials were 0.91g/cm$cm^3$, 1.14g/cm$cm^3$ and 1.38g/cm$m^3$. Experiments carried out in the observation channel in a flume tank under still water conditions. Sinking motion was recorded by the one set of TV-camera for VTR, and reading coordinate carried out by the video digitization system. Differential equations were derived from the conservation of momenta of the model purse seines and used to determine the sinking speeds of the depths of leadline and the other portions of the seines. An analysis carried out by simultaneous differential equations for numerical method by sub-routine Runge-Kutta-Gill The results obtained were as follows : 1. Average sinking speed of leadline for the model seines rigged 60g with the same weighted sinkers in water was fastest for 12.2cm/sec of PES seine, followed by 11.4cm/sec of PA and 10.7cm/sec of PP seines. 2. The coefficient of resistance for netting of seine was estimated to be $K_D=0.09(\frac{\rho}{\rho_w})^4$ 3. The coefficient of resistance for netting bundle of seine was estimated to be $C_R=0.91(\frac{\rho}{\rho_w})$ 4. In all seines, the calculated depths of leadline closely agreed with the measured ones, each 25g, 45g, 60g of weighted sinkers were put into formulas meas.=1.04cal., meas.=0.99cal. and meas.=0.98 cal.