• 대한조선학회논문집
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• 제29권1호
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• pp.61-70
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• 1992

본 연구에서는 파에 의한 선체의 횡요 운동에 대한 예측의 문제를 다루었다. 설계시 필요한 횡요 운동의 확률 밀도 함수를 구하기 위하여 FRK방정식을 이용하겠다. FRK방정식의 해는 평균화 과정을 통하여 근사적으로 구하였다. 이 근사해를 Dalzell[4]의 Simulation과 Roberts[14]의 계산 결과와 비교하여 그 정확도를 검토하여 보았다.

• International Journal of Aeronautical and Space Sciences
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• 제18권4호
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• pp.816-826
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• 2017

In this paper, a generalized discretization scheme is proposed that can derive general-order finite difference equations representing the joint probability density function of dynamic response of stochastic systems. The various order of finite difference equations are applied to solutions of the Fokker-Planck-Kolmogorov (FPK) equation. The finite difference equations derived by the proposed method can greatly increase accuracy even at the tail parts of the probability density function, giving accurate reliability estimations. Compared with exact solutions and finite element solutions, the generalized finite difference method showed increasing accuracy as the order increases. With the proposed method, it is allowed to use different orders and types (i.e. forward, central or backward) of discretization in the finite difference method to solve FPK and other partial differential equations in various engineering fields having requirements of accuracy or specific boundary conditions.

• Wind and Structures
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• 제36권2호
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• pp.133-147
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• 2023

The random vibration of saddle membrane structures under wind load is studied theoretically and experimentally. First, the nonlinear random vibration differential equations of saddle membrane structures under wind loads are established based on von Karman's large deflection theory, thin shell theory and potential flow theory. The probabilistic density function (PDF) and its corresponding statistical parameters of the displacement response of membrane structure are obtained by using the diffusion process theory and the Fokker Planck Kolmogorov equation method (FPK) to solve the equation. Furthermore, a wind tunnel test is carried out to obtain the displacement time history data of the test model under wind load, and the statistical characteristics of the displacement time history of the prototype model are obtained by similarity theory and probability statistics method. Finally, the rationality of the theoretical model is verified by comparing the experimental model with the theoretical model. The results show that the theoretical model agrees with the experimental model, and the random vibration response can be effectively reduced by increasing the initial pretension force and the rise-span ratio within a certain range. The research methods can provide a theoretical reference for the random vibration of the membrane structure, and also be the foundation of structural reliability of membrane structure based on wind-induced response.