输流曲管面内振动的小波有限元方法研究

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

将小波有限元应用于求解输流曲管面内流致振动问题,是小波在数值计算上一个新的尝试。针对输流曲管面内振动高阶微分方程,采用区间样条小波函数作为位移场的插值函数,建立了尺度为4、阶数为6的区间样条小波输流曲管单元,推导了小波单元质量矩阵、小波单元刚度矩阵和小波单元阻尼矩阵,从而获得了输流曲管面内振动的动力学方程组。在数值算例中,计算了输流直管和曲管在几种典型边界条件下的频率,这些数值结果与伽辽金方法、传统有限元方法所得结果吻合较好,并且计算时间短。研究表明,新型小波曲管单元在求解输流曲管面内线性振动问题有一定的优势,进一步的研究可望推广到输流曲管的非线性动力学分析中。

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.