• Proceedings of the KSME Conference
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• 2000.11a
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• pp.529-534
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• 2000

A finite element analysis for a rotating cantilever beam is presented in this study. Based on a dynamic modelling method using the stretch deformation instead of the conventional axial deformation, three linear partial differential equations are derived from Hamilton's principle. Two of the linear differential equations show the coupling effect between stretch and chordwise deformations. The other equation is an uncoupled one for the flapwise deformation. From these partial differential equations and the associated boundary conditions, are derived two weak forms: one is for the chordwise motion and the other is for the flapwise motion. The weak forms are spatially discretized with newly defined two-node beam elements. With the discretized equations or the matrix-vector equations, the behaviours of the natural frequencies are investigated for the variation of the rotating speed.

• Journal of Mechanical Science and Technology
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• v.17 no.12
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• pp.1977-1985
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• 2003

In the present study, the dynamic modelling of planar mechanisms that consist of a system of rigid bodies is carried out using point coordiantes. The system of rigid bodies is replaced by a dynamically equivalent constrained system of particles. Then for the resulting equivalent system of particles, the concepts of linear and angular momentums are used to generate the equations of motion without either introducing any rotational coordinates or distributing the external forces and force couples over the particles. For the open loop case, the equations of motion are generated recursively along the open chains. For the closed loop case, the system is transformed to open loops by cutting suitable kinematic joints with the addition of cut-joints kinematic constraints. An example of a multi-branch closed-loop system is chosen to demonstrate the generality and simplicity of the proposed method.

• 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.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.12
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• pp.1433-1441
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• 2009

In multibody dynamic analysis, one of the most important problems is to reduce computation times for real-time simulation. This paper presents the derivation procedure of equations of motion of a 6${\times}$6 autonomous vehicle in terms of chassis local coordinates which do not require coordinates transformation matrix to enhance efficiency for real-time dynamic analysis. Also, equations of motion are derived using the VT(velocity transformation) technique and symbolic computation method coded by MATLAB. The Jacobian matrix of the equations of motion of a system is derived from symbolic operations to apply the implicit integration method. The analysis results were compared with ADAMS results to verify the accuracy and approve the feasibility of real time analysis.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.2
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• pp.200-207
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• 2009

Complex systems are made of many subsystems, those are developed and manufactured by many part companies. Even though the information for a part is necessary to analyze the performance of the other part, it is not so easy to get the information for that part from other companies due to many reasons like security or compatibilities. If the modal parameters of a system between the connecting points are available, we can reconstruct a reduced model for that system in a physical coordinate not in a generalized coordinate. The assemble of the equations of motion for the main system and the reduced equations of motion for the connected system can give a response of the main system considering the effects of connected systems. The results show that the proposed method can give the response of a system accurately. The rule for the selection of modes is to use the fundamental modes whose natural frequencies are low.

• Structural Engineering and Mechanics
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• v.55 no.2
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• pp.281-298
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• 2015

In this study, nonlinear transverse vibrations of tensioned Euler-Bernoulli nanobeams are studied. The nonlinear equations of motion including stretching of the neutral axis and axial tension are derived using nonlocal beam theory. Forcing and damping effects are included in the equations. Equation of motion is made dimensionless via dimensionless parameters. A perturbation technique, the multiple scale methods is employed for solving the nonlinear problem. Approximate solutions are applied for the equations of motion. Natural frequencies of the nanobeams for the linear problem are found from the first equation of the perturbation series. From nonlinear term of the perturbation series appear as corrections to the linear problem. The effects of the various axial tension parameters and different nonlocal parameters as well as effects of different boundary conditions on the vibrations are determined. Nonlinear frequencies are estimated; amplitude-phase modulation figures are presented for simple-simple and clamped-clamped cases.

• Structural Engineering and Mechanics
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• v.54 no.3
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• pp.597-605
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• 2015

In this study, linear vibrations of an axially moving beam under non-ideal support conditions have been investigated. The main difference of this study from the other studies; the non-ideal clamped support allow minimal rotations and non-ideal simple support carry moment in minimal orders. Axially moving Euler-Bernoulli beam has simple and clamped support conditions that are discussed as combination of ideal and non-ideal boundary with weighting factor (k). Equations of the motion and boundary conditions have been obtained using Hamilton's Principle. Method of Multiple Scales, a perturbation technique, has been employed for solving the linear equations of motion. Linear equations of motion are solved and effects of different parameters on natural frequencies are investigated.

• Earthquakes and Structures
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• v.22 no.4
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• pp.431-437
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• 2022

One of the best choice for transportation of oil and gas at the end of rivers or seas is concrete pipelines. In this article, a concrete pipe at the end of river is assumed under the earthquake load. The Classic shell theory is applied for the modelling and the corresponding motion equations are derived by energy method. An external force induced by fluid around the pipe is asssumed in the final motion equations. For the solution of motion equations, the differential quadrature method (DQM) and Newmark method are applied for deriving the dynamic deflection of the pipe. The effects of various parameters including boundary conditions, fluid and length to thickness ratio are presented on the seismic response of the concrete pipe. The outcomes show that the clamped pipe has lower dynamic deflection with respect to simply pipe. In addition, with the effect of fluid, the dynamic defelction is increased significantly.

• Earthquakes and Structures
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• v.22 no.5
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• pp.439-445
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• 2022

One of the best choice for transportation of oil and gas at the end of rivers or seas is concrete pipelines. In this article, a concrete pipe at the end of river is assumed under the earthquake load. The Classic shell theory is applied for the modelling and the corresponding motion equations are derived by energy method. An external force induced by fluid around the pipe is asssumed in the final motion equations. For the solution of motion equations, the differential quadrature method (DQM) and Newmark method are applied for deriving the dynamic deflection of the pipe. The effects of various parameters including boundary conditions, fluid and length to thickness ratio are presented on the seismic response of the concrete pipe. The outcomes show that the clamped pipe has lower dynamic deflection with respect to simply pipe. In addition, with the effect of fluid, the dynamic defelction is increased significantly.