• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1992년도 추계학술대회 논문집
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• pp.349-353
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• 1992

The purpose of this paper is to develop methods for the dynamic analysis of multibody system that consist of interconnected rigid and deformable component. The equations of motion are derived by using the Lagrange's equation and finite element theory for the elastic mechanism systems. The type of equation of motion is the differential algebraic equation included kinematic nonlinear algebraic equation. The generalized coordinate partitioning method is used for solving this equation. To show the validity of this analysis solver, couple of models were canalized and those results were compared with the commercial package(ADAMS).

• 정보처리학회논문지A
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• 제11A권7호
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• pp.571-576
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• 2004

비선형 클라인 고든 방정식의 수치해를 구하기 위해 라그란제 보간을 사용하는데 비선형 항을 계산하기위해 보간식의 차이가 거의 없는 변형된 식을 사용하여 해의 .안정성과 해의 수렴성을 밝히고 오차를 분석하였다. 즉 $I(x)^{3}$ 대신에 $f(x_i)^{3}I_i(x)$을 사용하였으며 오차는 $C(\frac{1}{N})^{N-1} hN(N-1)(\frac{N}{2})^{N-1} /(\frac{N}{2})!$ 이하임을 보였고 석기서 N은 다항식의 차수이다.

• Journal of Astronomy and Space Sciences
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• 제28권1호
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• pp.37-54
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• 2011

Two semi-analytic solutions for a perturbed two-body problem known as Lagrange planetary equations (LPE) were compared to a numerical integration of the equation of motion with same perturbation force. To avoid the critical conditions inherited from the configuration of LPE, non-singular orbital elements (EOE) had been introduced. In this study, two types of orbital elements, classical Keplerian orbital elements (COE) and EOE were used for the solution of the LPE. The effectiveness of EOE and the discrepancy between EOE and COE were investigated by using several near critical conditions. The near one revolution, one day, and seven days evolutions of each orbital element described in LPE with COE and EOE were analyzed by comparing it with the directly converted orbital elements from the numerically integrated state vector in Cartesian coordinate. As a result, LPE with EOE has an advantage in long term calculation over LPE with COE in case of relatively small eccentricity.

• 대한수학회논문집
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• 제28권2호
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• pp.319-333
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• 2013

Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces: $${\sum_{1{\leq}i_<j{\leq}n}}\;f(\frac{r_ix_i+r_jx_j}{k})=\frac{n-1}{k}{\sum_{i=1}^n}r_if(x_i)$$.

• 대한조선학회논문집
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• 제44권2호
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• pp.130-138
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• 2007

A coupled variational equation for fluid-structure interaction (FSI) problems is derived from a steady state Navier-Stokes equation for incompressible Newtonian fluid and an equilibrium equation for geometrically nonlinear structures. For a fully coupled FSI formulation, between fluid and structures, a traction continuity condition is considered at interfaces where a no-slip condition is imposed. Under total Lagrange formulation in the structural domain, finite rotations are well described by using the second Piola-Kirchhoff stress and Green-Lagrange strain tensors. An adjoint shape design sensitivity analysis (DSA) method based on material derivative approach is applied to the FSI problem to develop a shape design optimization method. Demonstrating some numerical examples, the accuracy and efficiency of the developed DSA method is verified in comparison with finite difference sensitivity. Also, for the FSI problems, a shape design optimization is performed to obtain a maximal stiffness structure satisfying an allowable volume constraint.

• Journal of Astronomy and Space Sciences
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• 제31권1호
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• pp.91-99
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• 2014

The atmospheric flow in the 3-Cell model of global atmosphere circulation is described by the Lagrange's equation of the non-inertial frame where pressure force, frictional force and fictitious force are mixed in complex form. The Coriolis force is an important factor which requires calculation of fictitious force effects on atmospheric flow viewed from the rotating Earth. We make new Mathematica platform to solve Lagrange's equation by numerical analysis in order to analyze dynamics of atmospheric general circulation in the non-inertial frame. It can simulate atmospheric circulation process anywhere on the earth. It is expected that this pedagogical platform can be utilized to help students studying the atmospheric flow understand the mechanisms of atmospheric global circulation.

• Structural Engineering and Mechanics
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• 제23권3호
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• pp.263-278
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• 2006

This work presents a time-truncation scheme, based on the Lagrange interpolation polynomial, for the solution of the two-dimensional scalar wave problem by the time-domain boundary element method. The aim is to reduce the number of stored matrices, due to the convolution integral performed from the initial time to the current time, and to keep a compromise between computational economy and efficiency and the numerical accuracy. In order to verify the accuracy of the proposed formulation, three examples are presented and discussed at the end of the article.

• 한국소음진동공학회논문집
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• 제22권7호
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• pp.659-666
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• 2012

A nonlinear dynamic model for the shaft-disk-blade unit is developed in this study. In this regard, the rotating flexible blade, with a pre-twist angle, attached to a rigid disk driven by a shaft which is flexible in torsion is developed. The rotor-blade coupled model is derived using Lagrange equation in conjunction with the assumed mode method to discretize the blade deformation. The equations of motion are analyzed based on the small deformation theory for the blade and shaft torsional deformation to obtain the system natural frequencies for various system parameters.

• 한국통신학회논문지
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• 제19권1호
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• pp.183-193
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• 1994

본 논문에서는 가정모드(assumed mode) 방법과 Lagrange 방식을 이용하여 유연성 로봇 매니퓰레이터의 동력학 방정식을 구하였으며, 조인트 구동기를 포함한 유연성 로봇 매니플레이터에 대한 제어기를 설계를 하였다. 제어기는 매개변수 추정부와 적응제어기로 구성하였으며, 매개변수 추정부는 RLS알고리즘을 이용하여 ARMA예측모델의 매개변수를 추정하도록 하였다. 적응제어기는 기준모델(reference)과 최소예측오차제어기(minimum prediction controller)로 구성하였다.

• 대한기계학회논문집
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• 제17권10호
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• pp.2457-2466
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• 1993

A simple method is presented for determining transient responses of locally nonlinear structures using substructure eigenproperties and Lagrange multiplier technique. Although the method is based upon the mode synthesis formulation procedure, the equations of the combined whole structure are not constructed compared with the conventional methods. Lagrange multi-pliers are used to enforce the conditions of geometric compatibility between the substructure interfaces and they are treated as external forces on each substructure itself. Substructure eigenvalue problem is defined with the substructure interface free of fixed. The transient analysis is based upon the recurrence discrete-time state equations and offers the simplicity of the Euler integration method without requiring small time increment and iterative solution procedure. Numerical examples reveal that the method is very accurated and efficient in calculating transient responses compared with the direct numerical integration method.