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정상 상태 내부 유동이 있는 양단 고정 곡선 파이프의 비선형 진동 특성
이수일,정진태,Lee, Su-Il,Jeong, Jin-Tae 대한기계학회 2002 大韓機械學會論文集A Vol.26 No.1
The nonlinear differential equations of motion of a fluid conveying curved pipe are derived by use of Hamiltonian approach. The extensible dynamics of curled pipe is based on the Euler-Bernoulli beam theory. Some significant differences between linear and nonlinear equations and the dynamic characteristics are discussed. Generally, it can be shown that the natural frequencies in curved pipes are changed with flow velocity. Linearized natural frequencies of nonlinear equations are slightly different from those of linear equations.
유체를 이송하는 직선관의 진동 해석을 위한 새로운 비선형 모델링
이수일,정진태,임형빈,Lee, Su-Il,Jeong, Jin-Tae,Im, Hyeong-Bin 대한기계학회 2002 大韓機械學會論文集A Vol.26 No.3
A new non-linear modelling of a straight pipe conveying fluid is presented for vibration analysis when the pipe is fixed at both ends. Using the Euler-Bernoulli beam theory and the non-linear Lagrange strain theory, from the extended Hamilton's principle are derived the coupled non-linear equations of motion for the longitudinal and transverse displacements. These equations of motion are discretized by using the Galerkin method. After the discretized equations are linearized in the neighbourhood of the equilibrium position, the natural frequencies are computed from the linearized equations. On the other hand, the time histories for the displacements are also obtained by applying the generalized-$\alpha$ time integration method to the non-linear discretized equations. The validity of the new modelling is provided by comparing results from the proposed non-linear equations with those from the equations proposed by Paidoussis.