• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.167-178
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• 2007

This paper deals with the solutions of linear inhomogeneous time-fractional partial differential equations in applied mathematics and fluid mechanics. The fractional derivatives are described in the Caputo sense. The fractional Green function method is used to obtain solutions for time-fractional wave equation, linearized time-fractional Burgers equation, and linear time-fractional KdV equation. The new approach introduces a promising tool for solving fractional partial differential equations.

• 한국추진공학회지
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• 제23권6호
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• pp.1-10
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• 2019

노즐 내 파동은 노즐목을 빠져나가는 유동의 공력음향학적인 효과로 인해 연소불안정을 감쇠시키는 주요 요소 중 하나로 알려져 있다. 이와 같은 효과는 노즐 어드미턴스라는 지표를 통해 정량적으로 평가가 가능하다. 본 연구에서는 현재까지 로켓 연소불안정 억제에 가장 효과적인 노즐감쇠(nozzle damping)와 연계된 노즐 어드미턴스를 구하는 여러 기법을 소개한다. 이중, 가장 널리 알려진 1차원 선형 오일러 방정식을 도입하여 노즐의 주 설계 변수에 따른 노즐 어드미턴스의 경향을 분석하였다. 분석 결과, 노즐 수축부 길이가 짧아질수록 축방향 노즐 어드미턴스의 값이 낮게 나타나는 주파수 영역대가 확장되므로 짧은 노즐일수록 주파수 의존성을 줄인다는 기존 이론을 검증하였다. 또한, 짧은 노즐 이론을 통한 어드미턴스 예측은 1차 접선방향 압력 섭동에는 적합하지 않음을 알 수 있었다.

• 대한토목학회논문집
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• 제13권3호
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• pp.129-138
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• 1993

본 연구는 Navier-Stokes 식의 모형방정식으로 이류 및 확산거동을 갖는 선형화된 Burgers 방정식과 비선형 형태의 Burgers 방정식을 선택하여, 이에 대한 유한차분법과 유한해석법의 수치해를 해석해와 비교하여 봄으로써, 유한해석법의 응용성에 대해 고찰한 것이다. 본 연구를 통하여 얻어진 성과를 요약하면 다음과 같다. Burgers 방정식 및 선형화된 Burgers 방정식의 정상상태의 해석해를 사용하여 두 수치기법에 따른 수치해를 비교해 본 결과, 해석해와의 근사정도를 동일 기준 하에서 살펴볼 때, 유한해석법이 유한차분법보다 우수한 것으로 나타났다. Burgers 방정식의 비정상상태의 해석해에 대한 정확성 또한 유한해석법이 보다 잘 일치하는 것으로 나타났다. 특히 유한해석법은 유한차분법의 사용시 격자 크기의 선택에 따라 해의 수렴과정에서 발생할 수 있는 위상오차에 기인한 진동현상이 전혀 발생하지 않는다는 것을 확인할 수 있었으며, 따라서 유한해석법은 수치기법상 위상오차로부터 자유로운 안정된 해석기법이라고 판단된다.

• International Journal of Precision Engineering and Manufacturing
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• 제1권2호
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• pp.24-34
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• 2000

In this paper we propose a controller design method, called Quasi-LQG/$H_{\infty}$/LTR for nonlinear servo systems with hard nonlinearities such as Coulomb friction, dead-zone. Introducing the RIDF method to model Coulomb friction and dead-zone, the statistically linearized system is built. Then, we consider $H_{\infty}$ performance constraint for the optimization of statistically linearized systems, by replacing a covariance Lyapunov equation into a modified Riccati equation of which solution leads to an upper bound of the LQG performance. As a result, the nonlinear correction term is included in coupled Riccati equation, which is generally very difficult to thave a numerical solution. To solve this problem, we use the modified loop shaping technique and show some analytic proofs on LTR condition. Finally, the Quasi-LQG/$H_{\infty}$/LTR controller for a nonlinear system is synthesized by inverse random input describing function techniques (ITIDF). It is shown that the proposed design method has a better performance robustness to the hard nonlinearity than LQG/$H_{\infty}$/LTR method via simulations and experiments for the timing-belt driving servo system that contains the Coulomb friction and dead-zone.

• 한국경영과학회지
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• 제19권3호
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• pp.203-217
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• 1994

In this paper we develop an exponentialization procedure for the modelling of open FMS networks with general processing time at each station and limited buffer size. By imposing a reasonable assumption on the solution set, the nonlinear equation system for the exponentialization procedure is formulated as a variational inequality problem and the solution existence is examined. The efficient algorithm for the nonlinear equation system is developed using linearized Jacobi approximation method.

• 한국가스학회:학술대회논문집
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• 한국가스학회 1998년도 추계학술발표회 논문집
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• pp.241-246
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• 1998

This paper considers the applicability of a pseudosteady-state approach to the long-time behavior of real gas flow in a closed reservoir. The method involves a combination of a linearized gas diffusivity equation using a normalized pseudotime and a material balance equation. Comparison with a commercial reservoir simulator showed that highly accurate values of pseudopressure drawdown and well pressure are obtained by the pseudosteady-state approach with much less computational effort.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1993년도 봄 학술발표회논문집
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• pp.53-60
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• 1993

Nonlinear equation of motion due to material nonlinearity of structure is transformed to linear equation of motion by treating the nonlinear elastic force term as an applied force. The solution in a time step is carried out by iterative linear dynamic analysis. The present simple algorithm is varidated by several examples .The results show that this algorithm is and efficient.

• 대한전기학회논문지
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• 제34권7호
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• pp.283-288
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• 1985

This paper is concerned with the analysis of microprocessor-based PID control for the current source inverter-induction motor derive system. A linearized dynamic model of the motor is derived and is converted into the discrete-time model. With the equation, the overall system including the feedback loops is formulated into a single discrete-time state equation. The stability regions are determined at various values of controller gains. The transient responses of the motor speed are simulated by digital computer and are verified by laboratory experiments.

• 대한수학회보
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• 제40권2호
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• pp.289-300
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• 2003

We prove a simplified version of the Nash-Moser implicit function theorem in weighted Banach spaces. We relax the conditions so that the linearized equation has an approximate inverse in different weighted Banach spaces in each recurrence step.

• 대한기계학회논문집A
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• 제24권6호
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• pp.1520-1528
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• 2000

This study presents a method for determining bearing stiffness and damping coefficients of air-lubricated slider bearing, and shows influences of air-bearing surface geometry(recess depth, crown an d pivot location) on flying attitude and dynamic characteristics. To derive the dynamic lubrication equation, the perturbation method is applied to the generalized lubrication equation which based on linearized Boltzmann equation. The generalized lubrication equation and the dynamic lubrication equation are converted to a control volume formulation, and then, the static and dynamic pressure distributions are calculated by finite difference method. The recess depth and crown of the slider show significantly influence on flying attitude and dynamic characteristics comparing with those of pivot location.