• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.1 s.94
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• pp.46-52
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• 2005

This paper is concerned with the application of perturbation method to the dynamic analysis of free-free beam. In general, the rigid-body motions and elastic vibrations are analyzed separately. However, the rigid-body motions cause vibrations and elastic vibrations also affect rigid-body motions in turn, which indicates that the rigid-body motions and elastic vibrations are coupled in nature. The resulting equations of motion are hybrid and nonlinear. We can discretize the equations of motion by means of admissible functions but still we have to cope with nonlinear equations. In this paper, we propose the use of perturbation method to the coupled equations of motion. The resulting equations consist of zero-order equations of motion which depict the rigid-body motions and first-order equations of motion which depict the perturbed rigid-body motions and elastic vibrations. Numerical results show the efficacy of the proposed method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.300-306
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• 2004

This paper is concerned with the application of perturbation method to the dynamic analysis of free-free beam. In general, the rigid-body motions and elastic vibrations are analyzed separately. However, the rigid-body motions cause vibrations and elastic vibrations also affect rigid-body motions in turn, which indicates that the rigid-body motions and elastic vibrations are coupled in nature. The resulting equations of motion are hybrid and nonlinear. We can discretize the equations of motion by means of admissible functions but still we have to cope with nonlinear equations. In this paper, we propose the use of .perturbation method to the coupled equations of motion. The resulting equations consist of zero-order equations of motion which depict the rigid-body motions and first-order equations of motion which depict the perturbed rigid-body motions and elastic vibrations. Numerical results show the efficacy of the proposed method.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.12
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• pp.1354-1359
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• 2004

This paper is concerned with the application of perturbation method to the dynamic analysis of floating flexible body. In dealing with the dynamics of free-floating body, the rigid-body motions and elastic vibrations are analyzed separately. However, the rigid-body motions cause vibrations and elastic vibrations also affect rigid-body motions in turn, which indicates that the rigid-body motions and elastic vibrations are coupled in nature. The resulting equations of motion are hybrid and nonlinear. We can discretize the equations of motion by means of admissible functions but still we have to cope with nonlinear equations. In the previous paper, we proposed the use of perturbation method to the coupled equations of motion and derived zero-order and first-order equations of motion. The derivation process was lengthy and tedious. Hence, in this paper, we propose a new approach to the same problem by applying the perturbation method to the Lagrange's equations, thus providing a systematic approach to the addressed problem. Theoretical derivations show the efficacy of the proposed method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.2
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• pp.75-86
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• 2004

In this study, a recursive algorithm for generating the equations of motion of a chain of rigid rods is presented. The methods rests upon the idea of replacing the rigid body by a dynamically equivalent constrained system of particles. The concepts of linear and angular momentums are used to generate the rigid body equations of motion without either introducing any rotational coordinates or the corresponding transformation matrices. For open-chain, the equations of motion are generated recursively along the serial chains. For closed-chain, the system is transformed to open-chain by cutting suitable kinematic joints with the addition of cut-joints kinematic constraints. An example of a closed-chain of rigid rods is chosen to demonstrate the generality and simplicity of the proposed method.

• International Journal of Naval Architecture and Ocean Engineering
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• v.8 no.4
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• pp.320-329
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• 2016

An implicit method of solving the six degree-of-freedom rigid body motion equations based on the second order Adams-Bashforth-Moulten method was utilised as an improvement over the leapfrog scheme by making modifications to the rigid body motion solver libraries directly. The implementation will depend on predictor-corrector steps still residing within the hybrid Pressure Implicit with Splitting of Operators - Semi-Implicit Method for Pressure Linked Equations (PIMPLE) outer corrector loops to ensure strong coupling between fluid and motion. Aitken's under-relaxation is also introduced in this study to optimise the convergence rate and stability of the coupled solver. The resulting coupled solver ran on a free floating object tutorial test case when converged matches the original solver. It further allows a varying 70%-80% reduction in simulation times compared using a fixed under-relaxation to achieve the required stability.

• Journal of Astronomy and Space Sciences
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• v.15 no.1
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• pp.209-220
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• 1998

The stability problem of steady motion of a rigid body with multi-elastic appendages and multi-liquid-filled cavities, in the presence of no external forces or torque, is considered in this paper. The flexible appendages are modeled as the clamped -free-free-free rectangular plates, or/and as the discrete mass- spring sub-system. The motion of liquid in every single ellipsoidal cavity is modeled as the uniform vortex motion with a finite number of degrees of freedom. Assuming that stationary holonomic constraints imposed on the body allow its rotation about a spatially fixed axis, the equation of motion for such a systematic configuration can be very complex. It consists of a set of ordinary differential equations for the motion of the rigid body, the uniform rotation of the contained liquids, the motion of discrete elastic parts, and a set of partial differential equations for the elastic appendages supplemented by appropriate initial and boundary conditions. In addition, for such a hybrid system, under suitable assumptions, their equations of motion have four types of first integrals, i.e., energy and area, Helmholtz' constancy of liquid - vortexes, and the constant of the Poisson equation of motion. Chetaev's effective method for constructing Liapunov functions in the form of a set of first integrals of the equations of the perturbed motion is employed to investigate the sufficient stability conditions of steady motions of the complete system in the sense of Liapunov, i.e., with respect to the variables determining the motion of the solid body and to some quantities which define integrally the motion of flexible appendages. These sufficient conditions take into account the vortexes of the contained liquids, the vibration of the flexible components, and coupling among the liquid-elasticity solid.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.9 s.180
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• pp.2266-2273
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• 2000

Equations of motion of a multi-beam system undergoing overall rigid body motion are derived by employing finite element method. An orientation angle is employed to allow the arbitrary orientation o f the beam element. Modal coordinate reduction technique, which has been successfully utilized in the conventional linear modeling method, is employed for the present modeling method to reduce the computational effort. Different from the conventional linear modeling method, the present modeling method captures the motion-induced stiffness variations which are important for the dynamic analysis of structures undergoing overall rigid body motion. The numerical results are compared to those of a commercial program to verify the reliability of the present method.

• Journal of Mechanical Science and Technology
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• v.18 no.2
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• pp.193-202
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• 2004

This paper presents a computer method for the dynamic analysis of a system of rigid bodies in plane motion. The formulation rests upon the idea of replacing a rigid body by a dynamically equivalent constrained system of particles. Newton's second law is applied to study the motion of the resulting system of particles without introducing any rotational coordinates. A velocity transformation is used to transform the equations of motion to a reduced set. For an open-chain, this process automatically eliminates all of the non-working constraint forces and leads to an efficient integration of the equations of motion. For a closed-chain, suitable joints should be cut and few cut-joints constraint equations should be included. An example of a closed-chain is used to demonstrate the generality and efficiency of the proposed method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.6
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• pp.1014-1019
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• 2003

A dynamic modeling method for beams undergoing overall rigid body motion is presented in this paper. Two special deformation variables are introduced to represent the stretching and the curvature and are approximated by the assumed mode method. Geometric constraint equations that relate the two special deformation variables and the cartesian deformation variables are incorporated into the modeling method. By using the special deformation variables, all natural as well as geometric boundary conditions can be satisfied. It is shown that the geometric nonlinear effects of stretching and curvature play important roles to accurately predict the dynamic response when overall rigid body motion is involved.

• Journal of KSNVE
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• v.11 no.1
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• pp.111-117
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• 2001

Present work deals with a study on the deployment or retraction of cantilever beam that includes the rigid-body motion of large displacement of beam through the translational and rotational motions in 2-dimensional plane. The equations of motion are derived with respect to non-Cartesian coordinate system. In the formulation of equations of motion, shear deformations and geometrically non-linear effect are included. An assumed mode method is applied and numerical convergence characteristics are studied also. Types of motion of the moving beam are assumed to be classified as‘slow’or‘fast’motion, and the dynamic characteristics are investigated.