유체를 이송하는 직선관의 진동 해석을 위한 새로운 비선형 모델링

Abstract

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 Eulcr-Bemoulli 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-a 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 Pa'idoussis.