• 한국정밀공학회지
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• 제19권11호
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• pp.65-74
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• 2002

This paper examines the usefulness of a Brake Steer System (BSS), which uses differential brake forces for steering intervention in the context of Intelligent Transportation Systems (ITS). In order to help the car to turn, a yaw moment can be achieved by altering the left/right and front/rear brake distribution. This resulting yaw moment on the vehicle affects lateral position thereby providing a limited steering function. The steering function achieved through BSS can then be used to control lateral position in an unintended road departure system. A 8-DOF nonlinear vehicle model including STI tire model will be validated using the equations of motion of the vehicle. Then a controller will be developed. This controller, which will be a PID controller tuned by Ziegler-Nichols, will be designed to explore BSS feasibility by modifying the brake distribution through the control of the yaw rate of the vehicle.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.561-577
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• 2002

In this paper, a two-dimensional finite volume unstructured mesh method (FVUM) based on a triangular background interpolation mesh is developed for analysing the evolution of the saltwater intrusion into single and multiple coastal aquifer systems. The model formulation consists of a ground-water flow equation and a salt transport equation. These coupled and non-linear partial differential equations are transformed by FVUM into a system of differential/algebraic equations, which is solved using backward differentiation formulas of order one through five. Simulation results are compared with previously published solutions where good agreement is observed.

• Structural Engineering and Mechanics
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• 제33권6호
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• pp.675-696
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• 2009

In this paper, a unified solution method is presented for the classical beam theory. In Strength of Materials approach, the geometry, material properties and load system are known and related with the unknowns of forces, moments, slopes and deformations by applying a classical differential analysis in addition to equilibrium, constitutive, and kinematic laws. All these relations are expressed in a unified formulation for the classical beam theory. In the special case of simple beams, a system of four linear ordinary differential equations of first order represents the general mechanical behaviour of a straight beam. These equations are solved using the numerical differential quadrature method (DQM). The application of DQM has the advantages of mathematical consistency and conceptual simplicity. The numerical procedure is simple and gives clear understanding. This systematic way of obtaining influence line, bending moment, shear force diagrams and deformed shape for the beams with geometric and load discontinuities has been discussed in this paper. Buckling loads and natural frequencies of any beam prismatic or non-prismatic with any type of support conditions can be evaluated with ease.

• Structural Engineering and Mechanics
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• 제23권6호
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• pp.599-613
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• 2006

A method for the dynamical analysis of FE discretized uncertain linear and nonlinear structures is presented. This method is based on the moment equation approach, for which the differential equations governing the response first and second-order statistical moments must be solved. It is shown that they require the cross-moments between the response and the random variables characterizing the structural uncertainties, whose governing equations determine an infinite hierarchy. As a consequence, a closure scheme must be applied even if the structure is linear. In this sense the proposed approach is approximated even for the linear system. For nonlinear systems the closure schemes are also necessary in order to treat the nonlinearities. The complete set of equations obtained by this procedure is shown to be linear if the structure is linear. The application of this procedure to some simple examples has shown its high level of accuracy, if compared with other classical approaches, such as the perturbation method, even for low levels of closures.

• Journal of Advanced Marine Engineering and Technology
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• 제15권4호
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• pp.46-53
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• 1991

In the present study, Navier-Stokes equation is numerically solved by use of a Finite analytic method to obtain the 2-dimensional flow field in the square cavity. The basic idea of F.A.M. is the incorporation of local analytic solutions in the numerical solution of linear or non-linear partial differential equations. In the F.A.M., the total problem is subdivided into a number of all elements. The local analytic solution is obtained for the small element in which the governing equation, if non-linear, to be linearized. The local analytic solutions are then expressed in algebraic form and are overlapped to cover the entire region of the problem. The assembly of these local analytic solutions, which still preserve the overall nonlinearity of the governing equations, results in a system of linear algebraic equations. The system of algebraic equations is then solved to provide the numerical solutions of the total problem. The computed flow field shows the same characteristics to physical concept of flow phenomena.

• 한국추진공학회지
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• 제22권3호
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• pp.46-52
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• 2018

액체산소 및 탄화수소를 사용하는 연소기의 고주파 연소불안정을 해석하기 위해 단순모델로서 Crocco의 $n-{\tau}$ 시간지연 연소모델을 적용하고, 음향과 커플된 연소기 내 유동에 대해 선형해석을 수행하였다. 변수분리를 통해 편미분 포텐셜함수 식을 원통좌표계 미분방정식으로 만들고, 연소기의 접선방향 공진모드에 대한 고유 값을 계산하였다. 분사면 및 노즐입구를 경계조건으로 적용하여 미분식의 해를 구했다. 시스템의 안정성 판정을 위해 전달함수를 주파수 해석 하였으며, 관심 영역 주파수인 1T 모드 주변 주파수에서 시스템 게인 및 위상각으로 안정성 여유를 평가하였다. 또한 1T 모드 안정성 향상을 위해 배플 길이 및 형상에 대한 영향을 평가하였다.

• Earthquakes and Structures
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• 제8권5호
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• pp.1255-1276
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• 2015

The importance of considering soil-structure interaction effect in the analysis and design of RC frame buildings is increasingly recognized but still not penetrated to the grass root level owing to various complexities involved. It is well established fact that the soil-structure interaction effect considerably influence the design of multi-storey buildings subjected to lateral seismic loads. The shear walls are often provided in such buildings to increase the lateral stability to resist seismic lateral loads. In the present work, the linear soil-structure analysis of a G+5 storey RC shear wall building frame resting on isolated column footings and supported by deformable soil is presented. The finite element modelling and analysis is carried out using ANSYS software under normal loads as well as under seismic loads. Various load combinations are considered as per IS-1893 (Part-1):2002. The interaction analysis is carried out with and without shear wall to investigate the effect of inclusion of shear wall on the total and differential settlements in the footings due to deformations in the soil mass. The frame and soil mass both are considered to behave in linear elastic manner. It is observed that the soil-structure interaction effect causes significant total and differential settlements in the footings. Maximum total settlement in footings occurs under vertical loads and inner footings settle more than outer footings creating a saucer shaped settlement profile of the footings. Each combination of seismic loads causes maximum differential settlement in one or more footings. Presence of shear wall decreases pulling/pushing effect of seismic forces on footings resulting in more stability to the structures.

• 대한수학회보
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• 제51권1호
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• pp.221-227
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• 2014

Our goal is to relax a sufficient condition for the exponential almost sure stability of a certain class of stochastic differential equations. Compared to the existing theory, we prove the almost sure stability, replacing Lipschitz continuity and linear growth conditions by the existence of a strong solution of the underlying stochastic differential equation. This result is extendable for the regime-switching system. An explicit example is provided for the illustration purpose.

• 제어로봇시스템학회논문지
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• 제9권7호
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• pp.556-562
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• 2003

This paper presents new attitude error differential equations to define attitude errors as the rotation vector for inertial navigation systems. Attitude errors are defined with the rotation vector between the reference coordinate frame and the platform coordinate frame, and Platform dynamics to the reference coordinate frame due to platform torque command errors are defined. Using these concepts for attitude error definition and platform dynamics, we have derived attitude error differential equations expressed in original nonlinear form for GINS and SDINS and showed that these are equivalent to attitude error differential equations expressed in known linear form. The relation between attitude errors defined by the rotation vector and attitude errors defined by quaternion is clearly presented as well.

• 제어로봇시스템학회논문지
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• 제5권6호
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• pp.647-655
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• 1999

For linear time-varying systems described by the triple (A(t),B(t),C(t)) where A(t),B(t),C(t) are the system, the input, and the output matrices, respectively, we propose concepts for measures of modal and gross controllability /observability. We introduce a differential algebraic eigenbvalue theory for linear time-varying systems to calculate the PD-eigenvalues and left and right PD-eigenvectors of the system matrix A(t) which will be used to derive the concepts for the measures. The time-dependent angle between the left PD-eigenvectors of the system matrix A(t) and the columns of the input matrix B(t), and the magnitude of the each element of the input matrix B(t) are used to propose the modal controllability measure. Similarly, the time-dependent angle between the right PD-eigenvectors of the system matrix A(t) and the rows of the output matrix C(t) are used to propose the madal observability measure. Gross measure of controllability of a mode from all inputs and its gross measure of observability in all outputs for the linear time-varying systems are also proposed. Numerical examples are presented to illustrate the proposed concepts.