• Title/Summary/Keyword: moment equations

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Nonlinear Response Phenomena of a Randomly Excited Vibration Absorber System (불규칙적으로 가진되는 동흡진기계의 비선형응답현상)

  • Cho, Duk-Sang
    • Journal of the Korean Society of Industry Convergence
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    • v.3 no.2
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    • pp.141-147
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    • 2000
  • The nonlinear response statistics of an autoparameteric system under broad-band random excitation is investigated. The specific system examined is a vibration absorber system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. The Fokker-Planck equations is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian closure method the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The jump phenomenon was found by Gaussian closure method under random excitation.

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Numerical Analysis of Tapered Circular Arch with Fixed Ends (양단고정 변단면 도호아-치의 수치해석에 관한 연구)

  • 박문호;이병구
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.19 no.3
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    • pp.4462-4471
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    • 1977
  • The governing differential equations for the tapered circular arch with fixed ends have been derived, and a numerical procedure for the solution of these equations have been developed. The governing differential equations were solved numerically by an initial value integration procedure and Shooting Methods for boundary value problems. The Rungekutta fourth order integration technique was used. The methods was programmed for a Cyber 73-18 computer System, and all esults were obtained on this computer. A detailed study has been made for a fixed arch with an angle of opening equal to 0.7 radian, and the results are presented in detail in tables and curves. It is hoped that the results presented herein is applied to the deformations of gives point from the tri-axial direction of tapered circular arch with fixed ends, bending moment, and torsional moment, and that at the same time results to be used for archwise structures in steel structure.

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Inelastic lateral-torsional buckling strengths of stepped I-beams subjected to general loading condition

  • Park, Jong Sup;Park, Yi Seul
    • Structural Engineering and Mechanics
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    • v.48 no.2
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    • pp.275-289
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    • 2013
  • The cross sections of multi-span beams are sometimes suddenly increased at the interior support of continuous beams to resist high negative moment. An earlier study on elastic lateral torsional buckling of stepped beams was conducted to propose new design equations. This research aims to continue the earlier study by considering the effect of inelastic buckling of stepped beams subjected to pure bending and general loading condition. A three-dimensional finite element-program ABAQUS and a statistical program MINITAB were used in the development of new design equations. The inelastic lateral torsional buckling strengths of 36 and 27 models for singly and doubly stepped beams, respectively, were investigated. The general loading condition consists of 15 loading cases based on the number of inflection point within the unbraced length of the stepped beams. The combined effects of residual stresses and geometrical imperfection were also considered to evaluate the inelastic buckling strengths. The proposed equations in this study will definitely improve current design methods for the inelastic lateral-torsional buckling of stepped beams and will increase efficiency in building and bridge design.

Comparison Between Two Analytical Solutions for Random Vibration Responses of a Spring-Pendulum System with Internal Resonance (내부공진을 가진 탄성진자계의 불규칙 진동응답을 위한 두 해석해의 비교)

  • 조덕상;이원경
    • Journal of KSNVE
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    • v.8 no.4
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    • pp.715-722
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    • 1998
  • An investigation into the stochastic bifurcation and response statistics of an autoparameteric system under broad-band random excitation is made. The specific system examined is a spring-pendulum system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. The Fokker-Planck equations is used to genrage a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian and non-Gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinanary differential equations. In view of equilibrium solutions of this system and their stability we examine the stochastic bifurcation and response statistics. The analytical results are compared with results obtained by Monte Carlo simulation.

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Dynamic Walking Planning and Inverse Dynamic Analysis of Biped Robot (이족로봇의 동적 보행계획과 역동역학 해석)

  • Park, In-Gyu;Kim, Jin-Geol
    • Journal of the Korean Society for Precision Engineering
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    • v.17 no.9
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    • pp.133-144
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    • 2000
  • The dynamic walking planning and the inverse dynamics of the biped robot is investigated in this paper. The biped robot is modeled with 14 degrees of freedom rigid bodies considering the walking pattern and kinematic construction of humanoid. The method of the computer aided multibody dynamics is applied to the dynamic analysis. The equations of motion of biped are initially represented as terms of the Cartesian corrdinates then they are converted to the minimum number of equations of motion in terms of the joint coordinates using the velocity transformation matrix. For the consideration of the relationships between the ground and foot the holonomic constraints are added or deleted on the equations of motion. the number of these constraints can be changed by types of walking patterns with three modes. In order for the dynamic walking to be stabilizable optimized trunk positions are iteratively determined by satisfying the system ZMP(Zero Moment Point) and ground conditions.

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Dynamic Walking and Inverse Dynamic Analysis of Biped Walking Robot (이족보행로봇의 동적보행과 역동역학 해석)

  • Park, In-Gyu;Kim, Jin-Geol
    • Proceedings of the KSME Conference
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    • 2000.04a
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    • pp.548-555
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    • 2000
  • The dynamic walking and the inverse dynamics of the biped walking robot is investigated in this paper. The biped robot is modeled with 14 degrees of freedom rigid bodies considering the walking pattern and kinematic construction of humanoid. The method of the computer aided multibody dynamics is applied to the dynamic analysis. The equations of motion of biped are initially represented as terms of the Cartesian coordinates, then they are converted to the minimum number of equations of motion in terms of the joint coordinates using the velocity transformation matrix. For the consideration of the relationships between the ground and foot, the holonomic constraints are added or deleted on the equations of motion. The number of these constraints can be changed by types of walking pattern with three modes. In order for the dynamic walking to be stabilizable, optimized trunk positions are iteratively determined by satisfying the system ZMP(Zero Moment Point) and ground conditions.

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A Study on Lateral Torsional Budding of Arch Subjected to Pure Bending Moment (순수 휨모멘트를 받는 아치의 횡좌굴에 관한 연구)

  • Kim, Saeng Bin;Yoo, Chai Hong;Lee, Sung Chul
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.9 no.3
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    • pp.13-19
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    • 1989
  • A system of coupled differential equations governing the lateral-torsional buckling of thin-walled arches subjected to pure bending moment is presented. The governing differential equations are derived using incremental form of principle of virtual displacement based on updated Lagrangian procedure. The differential equations are solved for the critical end moments of arches with I section, and then comparative studies are made with existing solutions.

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Determination of Natural Frequencies of an Engine Crankshaft Using Finite Elements

  • Park, Myung-Jin
    • The Journal of the Acoustical Society of Korea
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    • v.18 no.4E
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    • pp.20-25
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    • 1999
  • To get accurate natural frequencies of an engine crankshafts, finite element equations of motion are developed, taking real geometries of the shaft into account. For the crankshaft with wide crank webs, a specialized rotating web element is developed. This includes the effects of rotary inertia, gyroscopic moment, and shear. After the finite element equations are constructed, eigenvalues are extracted from the system equations to get natural frequencies, based on the Sturm sequence method which exploits the banded forms of the system matrices to reduce computations. The scheme developed can be used for the free vibration analysis of any type of spinning structures which include skew symmetric gyroscopic moment matrix in the system matrices. The results are compared with experimental data in order to confirm the study.

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Stochastic Responses of a Spring-Pendulum System under Narrow Band Random Excitation (협대역 불규칙가진력을 받는 탄성진자계의 확률적 응답특성)

  • Cho, Duk-Sang
    • Journal of the Korean Society of Industry Convergence
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    • v.4 no.2
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    • pp.133-139
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    • 2001
  • The nonlinear response statistics of an spring-pendulum system with internal resonance under narrow band random excitation is investigated analytically- The center frequency of the filtered excitation is selected to be close to natural frequency of directly excited spring mode. The Fokker-Planck equations is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian closure method the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The nonlinear phenomena, such as jump and multiple solutions, under narrow band random excitation were found by Gaussian closure method.

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A Case Study on the Structural Design Improvement of a Mold M/C's Head Slides for Smooth Motion Regarding to Inertia and Moment Impact (금형가공센터 고속 이송체의 성능 안정화를 위한 설계개선 사례)

  • 최영휴;홍진현;최응영;이재윤;김태형;최원선
    • Proceedings of the Korean Society of Machine Tool Engineers Conference
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    • 2004.04a
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    • pp.410-415
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    • 2004
  • Heavy-weight head slides may cause excessive inertia impact & moment on the machine tool structure when they move or stop abruptly during operation. Consequently these inertia impact and unbalanced moment bring transient vibrations and rough sliding motions on the machine structure. Machine tool engineers have tried many kind of feed-slide designs in order to solve this problem; for example, the design optimization of the moving structure for minimum weight and maximum stiffness, box-in-box type slide design, and so on. In this article, force and moment equilibrium equations regarding to the inertia force & moment were derived for each one of a mold M/C's head slides. Furthermore, five different design configurations of head slide assembly were reviewed for its design improvement regarding to force & moment calculations and finite element structural analysis results.

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