• Title/Summary/Keyword: matrix stiffness method

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On the Accuracy of Calculation in the Analysis of Natural Transverse Vibrations of a Ship's Hull (선체고유횡진동해석(船體固有橫振動解析)에 있어서의 계산정도(計算精度))

  • K.C.,Kim;H.S.,Lee
    • Bulletin of the Society of Naval Architects of Korea
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    • v.13 no.1
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    • pp.1-9
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    • 1976
  • Using the computer programs for calculation of natural vibrations of ship's hull developed by the authors et al., an investigation into influences of various parameters on the accuracy of calculation was done through example calculations of a 30,000 DWT petroleum products carrier M/S Sweet Brier built by Korea Shipbuilding and Engineering Corporation. The methodical principles employed for the computer program development are as follows; (a) the ship system is reduced to an equivalent discrete elements system conforming to Myklestad-Prohl model, (b) the problem formulation is of transfer matrix method, and (c) to obtain solutions an extended $G\ddot{u}mbel's$ initial value method is introduced. The scope of the investigation is influences of number of discrete elements, choice of significant system parameters such as rotary inertia, bending stiffness and shear stiffness, and simplification of distributions of added mass and stiffness as trapezoidal ones referred to those of midship section on the calculation accuracy. From the investigation the followings are found out; (1) To obtain good results for the modes up to the seven-noded thirty or more divisions of the hull is desirable. For fundamental mode fifteen divisions may give fairly good results. (2) The influence of rotary inertia is negligibly small at least for the modes up to the 5- or 6- noded. (3) In the case of assuming either bending modes or shear modes the calculation results in considerably higher frequencies as compared with those based on Timoshenko beam theory. However, the calculation base on the slender beam theory surprisingly gives frequencies within 10% error for fundamental modes. (4) It is proved that to simplify distributions of added mass and stiffness as trapezoidal ones referred to those of midship section is a promising approach for the prediction of natural frequencies at preliminary design stage; provided good accumulation of data from similar type ships, we may expect to obtain natural frequencies within 5% error.

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Vehicle-Bridge Interaction Analysis of Railway Bridges by Using Conventional Trains (기존선 철도차량을 이용한 철도교의 상호작용해석)

  • Cho, Eun Sang;Kim, Hee Ju;Hwang, Won Sup
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.29 no.1A
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    • pp.31-43
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    • 2009
  • In this study, the numerical method is presented, which can consider the various train types and can solve the equations of motion for a vehicle-bridge interaction analysis by non-iteration procedure through formulating the coupled equations of motion. The coupled equations of motion for the vehicle-bridge interaction are solved by the Newmark ${\beta}$ of a direct integration method, and by composing the effective stiffness matrix and the effective force vector according to a analysis step, those can be solved with the same manner of the solving procedure of equilibrium equations in static analysis. Also, the effective stiffness matrix is reconstructed by the Skyline method for increasing the analysis effectiveness. The Cholesky's matrix decomposition scheme is applied to the analysis procedure for minimizing the numerical errors that can be generated in directly calculating the inverse matrix. The equations of motion for the conventional trains are derived, and the numerical models of the conventional trains are idealized by a set of linear springs and dashpots with 16 degrees of freedom. The bridge models are simplified by the 3 dimensional space frame element which is based on the Euler-Bernoulli theory. The rail irregularities of vertical and lateral directions are generated by the PSD functions of the Federal Railroad Administration (FRA). The results of the vehicle-bridge interaction analysis are verified by the experimental results for the railway plate girder bridges of a span length with 12 m, 18 m, and the experimental and analytical data are applied to the low pass filtering scheme, and the basis frequency of the filtering is a 2 times of the 1st fundamental frequency of a bridge bending.

Behavior of Woven-glass/Epoxy Composites after Impact Loading (접촉하중형태에 따른 복합재의 거동변화)

  • 이재준;김병식;황성식;김태우;김찬묵
    • Proceedings of the Korean Society For Composite Materials Conference
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    • 2002.05a
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    • pp.53-56
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    • 2002
  • External low-velocity impact loadings onto the composites cause reduction of stiffness and/or strength. The reductions indicate that internal(external) damages were developed within the composites. These damages could be matrix cracking, fiber/matrix debonding, or delamination between layers. In previous studies, damage evaluation have been done by applying secondary mechanical loading such as buckle-driven compressive, or fatigue, or flexural loadings. An evaluation method by applying indentation loadings on the composites was proposed. The load-displacement curves obtained from the indentation testing provided the extent of damages within the composites due to impact loadings.

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Stability analysis of pump using finite element method (유한요소법에 의한 펌프축계의 안정성해석)

  • 양보석
    • Journal of Advanced Marine Engineering and Technology
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    • v.10 no.4
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    • pp.31-40
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    • 1986
  • With the tendency toward high speed and high pressure in centrifugal pumps, the problem of sub-synchronous vibration has arisen, caused by the hydraulic forces of the working fluid, such as wearring, balance piston, impeller, etc.. These forces can drastically alter the rotor critical speeds and stability characteristics, and can be acted significant destabilizing forces. For preventing such self-excited vibration, the desing of the rotor system needs, which would secure the stability of the machine. In this paper, a procedure is presented for dynamic modeling of rotor-bearing-seal-impeller systems which consist of rigid disks, distributed parameter finite rotor elements and discrete bearings, seals and impellers. A finite element model including the effects of rotatory inertia and gyroscopic moments is developed using the consistent matrix approach. The technique of dynamic matrix reduction is applied to the shaft matrices to reduce them to a set of matrices of dynamic of significantly fewer degrees of freedom. The representation of bearing, seal and impeller elements is in term of linearized stiffness and damping matrices by reasonably small perturbations from equilibrium. The stability behavior of a typical double suction centrifugal pump is presented. Results show the influence of clearance and flow conditions on running speeds and stability characteristics.

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Spectral Element Analysis of the Pipeline Conveying Internal Unsteady Fluid (내부 비정상 유동을 갖는 파이프계의 스펙트럼요소해석)

  • Park, Jong-Hwan;Lee, U-Sik
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.29 no.12 s.243
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    • pp.1574-1585
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    • 2005
  • In this paper, a spectral element model is developed for the uniform straight pipelines conveying internal unsteady fluid. Four coupled pipe-dynamics equations are derived first by using the Hamilton's principle and the principles of fluid mechanics. The transverse displacement, the axial displacement, the fluid pressure and the fluid velocity are all considered as the dependent variables. The coupled pipe-dynamics equations are then linearized about the steady state values of the fluid pressure and velocity. As the final step, the spectral element model represented by the exact dynamic stiffness matrix, which is often called spectral element matrix, is formulated by using the frequency-domain solutions of the linearized pipe-dynamics equations. The FFT-based spectral dynamic analyses are conducted to evaluate the accuracy of the present spectral element model and also to investigate the structural dynamic characteristics and the internal fluid transients of an example pipeline system.

A Study of Natural Frequency of Offshore Wind Turbine JACKET (해상 풍력 발전 JACKET의 고유 진동수에 관한 연구)

  • Lee, Jung-Tak;Son, Choong-Yul;Lee, Kang-Su;Won, Jong-Bum;Kim, Sang-Ho;Kim, Tae-Yong
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2006.11a
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    • pp.434-438
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    • 2006
  • The purpose of this paper is that investigates the Natural Frequency behavior characteristic of Wind Turbine Jacket Type Tower model, and calculated that the stress values of Thrust Load, Wave Load, Wind Load, Current Loda, Gravity Load, etc., environment evaluation analysis during static Operating Wind Turbine Jacket Type Tower model, carried out of Natural Frequency analysis of total load case to stress matrix, Frequency calculated that calculated Add Natural Frequency to stiffness matrix for determinant to stress results. The finite element analysis is performed with commercial F.E.M program (ANSYS) on the basis of the natural frequency and mode shape.

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A Study on the Axial and Torsional Coupled Vibration of Marine propeller shafts (선박 추진축의 종 비틂 연성진동에 관한 연구)

  • 김용철;정태영;전윤호
    • Journal of Ocean Engineering and Technology
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    • v.8 no.1
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    • pp.71-83
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    • 1994
  • The axial and torsional coupled vibration of marine propeller shafts can be mainly caused by actual shape of the crank shaft and hydrodynamic forces and moments due to propellers : the former leads to stiffness matrix coupling and the latter leads to inertia and damping matrix coupling. In the present paper the characteristics of the coupled vibration of marine propeller shafts due to hydrodynamic coupling is investigated in details. First, the modelling procedure of the system and analysis technique are also developed. To verify the present method the numerical calculations were also performed. Finally, the results were compared with existing data in the literature and it was found to be in good agreement.

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Nano research for investigating the effect of SWCNTs dimensions on the properties of the simulated nanocomposites: a molecular dynamics simulation

  • Farazin, Ashkan;Mohammadimehr, Mehdi
    • Advances in nano research
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    • v.9 no.2
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    • pp.83-90
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    • 2020
  • This research investigates the effect of single walled carbon nanotubes (SWCNTs) dimensions in terms of diameter on the mechanical properties (longitudinal and transverse Young's modulus) of the simulated nanocomposites by molecular dynamics (MDs) method. MDs utilized to create nanocomposite models consisting of five case studies of SWCNTs with different chiralities (5, 0), (10, 0), (15, 0), (20, 0) and (25, 0) as the reinforcement and using polymethyl methacrylate (PMMA) as the common matrix. The results show that with increasing of SWCNTs diameter, the mechanical and physical properties increase. It is important that with the increasing of SWCNTs diameter, density, longitudinal and transverse Young's modulus, shear modulus, poisson's ratio, and bulk modulus of simulated nanocomposite from (5, 0) to (25, 0) approximately becomes 1.54, 3, 2, 1.43, 1.11 and 1.75 times more than (5, 0), respectively. Then to validate the results, the stiffness matrix is obtained by Materials studio software.

Mechanical Behavior and Fracture Resistance of $SCS6/Si_3N_4$ CFCCs ($SCS6/Si_3N_4$ 연속섬유강화 세라믹 복합재료의 기계적 거동 및 파괴저항평가)

  • Yoon, Yu-Sung;Kwon, Oh-Heon;Jenkins, Michael G.
    • Proceedings of the KSME Conference
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    • 2001.06a
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    • pp.658-662
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    • 2001
  • Continuous fiber ceramic composites(CPCCs) having the advantages of ceramics resistance to heat, eroson can be applied in chemical reactors and engine. CFCCs has relatively high stiffness in spite of low weight. In particular, it exhibits greatly increased toughness, which serves to decrease its inherent damage characteristics of the brittle nature of monolithic ceramics. In this wort, tensile and flexural test for SCS6 fiber/ $Si_3N_4$ matrix composites were studied. An objective of this study is to obtain the basic quantities of mechanical properties for tension and flexural test and link these to the fracture resistance behavior. Then, we showed that wok of fracture concept was useful as a method for describing fracture restance behavior of CFCCs.

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A Study of Natural Frequency of Offshore Wind Turbine JACKET (해상 풍력 발전 JACKET의 고유진동수에 관한 연구)

  • Lee, Kang-Su;Lee, Jung-Tak;Son, Choong-Yul
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.17 no.2 s.119
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    • pp.130-135
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    • 2007
  • The purpose of this paper is that investigates the Natural Frequency behavior characteristic of wind turbine jacket type tower model, and calculated that the stress values of thrust load, wave load, wind load, current loda, gravity load, etc., environment evaluation analysis during static operating wind turbine jacket type tower model, carried out of natural frequency analysis of total load case to stress matrix, frequency calculated that calculated add natural frequency to stiffness matrix for determinant to stress results. The finite element analysis is performed with commercial F.E.M program (ANSYS) on the basis of the natural frequency and mode shape.