A wavelet-based finite element method for in-plane vibration of curved pipes

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Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (17) : 256-260.

CAO Jianhua 1,2, LIU Yongshou 1, LIU Wei 1

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Abstract

In-plane vibrations of fluid-conveying curved pipes were investigated by using the wavelet-based finite element (FE) method as a new attempt of wavelet in numerical calculation. In order to solve the high order differential equation of fluid-conveying curved pipes’in-plane vibration,the interval spline wavelet function was taken as the interpolation one of the displacement field. The curved pipe element with interval spline wavelet of scale 4 and order 6 was established. The wavelet-based curved pipe element mass matrix,stiffness matrix and damping matrix were derived. Then,the dynamic equations for in-plane vibration of fluid-conveying curved pipes were derived. In numerical examples,natural frequencies of fluid-conveying straight pipe and curves one were computed with the proposed method under several typical boundary conditions. The numerical results agreed well with those obtained using Galerkin method and the traditional finite element one,and the former costed less time. The study showed that the new type wavelet-based curved pipe element has a certain advantage in solving in-plane linear vibration problems of curved pipes; after further studying,it can be extended to analyze nonlinear dynamic problems of fluid-conveying curved pipes.

Key words

fluid-conveying pipe / curved pipe / wavelet-based finite element (FE) / spline wavelet

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CAO Jianhua 1,2, LIU Yongshou 1, LIU Wei 1. A wavelet-based finite element method for in-plane vibration of curved pipes[J]. Journal of Vibration and Shock, 2018, 37(17): 256-260

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