• Structural Engineering and Mechanics
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• 제12권1호
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• pp.85-100
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• 2001

In this paper, an analytical procedure for solving several static and dynamic problems of non-uniform beams is proposed. It is shown that the governing differential equations for several stability, free vibration and static problems of non-uniform beams can be written in the from of a unified self-conjugate differential equation of the second-order. There are two functions in the unified equation, unlike most previous researches dealing with this problem, one of the functions is selected as an arbitrary expression in this paper, while the other one is expressed as a functional relation with the arbitrary function. Using appropriate functional transformation, the self-conjugate equation is reduced to Bessel's equation or to other solvable ordinary differential equations for several cases that are important in engineering practice. Thus, classes of exact solutions of the self-conjugate equation for several static and dynamic problems are derived. Numerical examples demonstrate that the results calculated by the proposed method and solutions are in good agreement with the corresponding experimental data, and the proposed procedure is a simple, efficient and exact method.

• Computers and Concrete
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• 제23권5호
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• pp.303-309
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• 2019

This study investigates axisymmetric fractional vibration of an isotropic hyperelastic semi-linear thin disc with a view to examine effects of finite deformation associated with the material of the disc and effects of fractional vibration associated with the motion of the disc. The generalized three-dimensional equation of motion is reduced to an equivalent time fraction one-dimensional vibration equation. Using the method of variable separable, the resulting equation is further decomposed into second-order ordinary differential equation in spatial variable and fractional differential equation in temporal variable. The obtained solution of the fractional vibration problem under consideration is described by product of one-parameter Mittag-Leffler and Bessel functions in temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem in literature. Finally, and amongst other things, the Cauchy's stress distribution in thin disc under finite deformation exhibits nonlinearity with respect to the displacement fields whereas in infinitesimal deformation hypothesis, these stresses exhibit linear relation with the displacement field.

• Korean Journal of Mathematics
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• 제9권1호
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• pp.9-20
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• 2001

We are concerned with an activator-inhibitor system proposed by Ohta [8]. The purpose of this paper is to study the dynamics of interfaces in an interfacial problem which is reduced from the system in order to examine how this problem is different from an activator-inhibitor system [3, 7].

• 한국전산구조공학회논문집
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• 제13권4호
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• pp.427-436
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• 2000

이 논문은 불규칙 가진력을 받는 회전-고정보의 비선형 응답특성을 나타낸다. 불규칙 가진력은 두 번째 고유모드의 절점과 최대변위점에 가했다. 비선형 편미분 방정식과 경계조건으로 표현되는 이 문제를 Galerkin의 방법을 이용하여 연립 비선형 상미분방정식으로 변환하였다. 이 상미분방정식으로부터 Fokker-Planck방정식과 모멘트 방정식을 얻은 후 Gaussian closure 방법 및 non-Gaussian closure 방법을 이용하여 3 모드 근사시 각각 27개 및 209개의 자율 상미분방정식을 구하였다. Gaussian closure 방법과 non-Gaussian closure 방법으로 2 모드 및 3 모드 근사해석을 수행하였고 해석적 결과들은 Monte Carlo 시뮬레이션 결과와 비교되었다. 해석결과 2 모드 근사해와 3 모드 근사해가 거의 일치하였고 2 모드 내부공진만 고려하여도 해석결과에 별 영향을 주지 않는다는 것을 알 수 있다.

• KIEE International Transaction on Systems and Control
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• 제12D권1호
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• pp.33-38
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• 2002

In this paper, the infinite time optimal regulation problem for weakly coupled bilinear systems with quadratic performance criteria is obtained by a sequence of algebraic Lyapunov equations. This is the new approach is based on the successive approximation. In particular, the order reduction is achieved by using suitable state transformation so that the original Lyapunov equations are decomposed into the reduced-order local Lyapunov equations. The proposed algorithms not only solve optimal control problems in the weakly coupled bilinear system but also reduce the computation time. This paper also includes an example to demonstrate the procedures.

• 제어로봇시스템학회논문지
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• 제20권5호
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• pp.584-591
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• 2014

This paper presents a novel aided navigation method for AUV (Autonomous Underwater Vehicles). The navigation system for AUV includes several sensors such as IMU (Inertial Measurement Unit), DVL (Doppler Velocity Log) and depth sensor. In general, the $13^{th}$ order INS error model, which includes depth error, velocity error, attitude error, and the accelerometer and gyroscope biases as state variables is used with measurements from DVL and depth sensors. However, the model may degrade the estimation performance of the heading state. Therefore, the $11^{th}$ INS error model is proposed. Its validity is verified by using a degree of observability and analyzing steady state error. The performance of the proposed model is shown by the computer simulation. The results show that the performance of the reduced $11^{th}$ order error model is better than that of the conventional $13^{th}$ order error model.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2007년도 춘계학술대회A
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• pp.921-926
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• 2007

A dynamic system under random disturbance is considered in the study. In order to control the system efficiently, proper reduction of system dimension is indispensible in design stage. The reduction method using component cost analysis in conjunction with stochastic analysis is proposed for the control of a system. System response is obtained in terms of dynamic moment equation via Fokker-Plank-Kolmogorov(F-P-K) equation. The dynamic moment response of the system under random disturbance are reduced by using of deterministic version of component cost analysis. The reduced system via proposed "stochastic component cost analysis" is successfully implemented for dynamic response and shows remarkable control performance effectively utilizing "stochastic controller" in physical time domain.

• Structural Engineering and Mechanics
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• 제81권2호
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• pp.179-194
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• 2022

The bending, buckling and free vibration responses of functionally graded material (FGM) beams are investigated semi-analytically by the scaled boundary finite element method (SBFEM) in this paper. In the concepts of the SBFEM, the dimension of computational domain can be reduced by one, therefore only the axial dimension of the beam is discretized using the higher order spectral element, which reduces the amount of calculation and greatly improves the calculation efficiency. The governing equation of FGM beams is derived in detail by the means of the principle of virtual work. Compared with the higher-order beam theory, fewer parameters and simpler control equations are used. And the governing equation is transformed into a first-order ordinary differential equation by introducing intermediate variables. Analytical solutions of the governing equation can be obtained by pade series expansion in the direction of thickness. Numerical example are compared with the numerical solutions provided by the previous researchers to verify the accuracy and applicability of the proposed method. The results show that the proposed formulations can quickly converge to the reference solutions by increasing the order of higher order spectral elements, and high accuracy can be achieved by using a small number of the elements. In addition, the influence of the structural sizes, material properties and boundary conditions on the mechanical behaviors of FG beams subjected to different load types is discussed.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1998년도 춘계학술대회논문집; 용평리조트 타워콘도, 21-22 May 1998
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• pp.392-398
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• 1998

In order to check the validity of nonlinear normal modes of continuous, systems by means of the energy-based formulation, we consider a beam with a nonlinear boundary condition. The initial and boundary e c6nsl of a linear partial differential equation and a nonlinear boundary condition is reduced to a linear boundary value problem consisting of an 8th order ordinary differential equations and linear boundary conditions. After obtaining the asymptotic solution corresponding to each normal mode, we compare this with numerical results by the finite element method.

• 조명전기설비학회논문지
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• 제19권1호
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• pp.70-79
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• 2005

본 논문은 축소차원 상태방정식을 사용한 전차원 관측기를 이용하여 저속도 영역에서의 운전 성능 개선방법을 제안하였다. 축소차원 상태방정식을 사용한 전차원 관측기는 간단한 모터속도 및 외란토크 관측기이다. 제안한 알고리즘은 약 1.9[rpm]의 저속도에서 매우 안정적인 결과를 보였다. 모터구동 시스템에서 외란토크는 저속도 영역에서 속도제어 성능을 저하시킨다. 제안한 알고리즘은 모터속도와 외란토크를 모두 추정한다. 추정된 외란 토크는 속도제어기의 출력에 전향보상 값으로 사용되며, 그 결과 저속도 영역(1.9rpm)에서 부하토크 응답특성이 향상된 것을 확인하였다.