一种管道中的导波频散计算方法

为了求得管道中导波的频散特性,提出了一种基于有限元的模式分析法来求解频散关系。以导波理论为基础,构建了Navier-stokes方程,采用分离变量法得到Helmholtz方程及泛函形式,并利用COMSOL软件对Helmholtz方程进行特征值的求解,计算结果与半解析有限元法所求得的结果基本吻合,并且能够求解出环状模态,证明了该方法的有效性及求解的全面性。同时,运用导波理论及铁木辛柯梁理论对低频的频散关系进行理论求解,通过对比,验证了模式分析法的精度良好。最后通过位移分量分析了模态的特征,为管道导波无损检测提供了依据。

A method for calculating the dispersion of guided waves in pipe

A finite element based mode analysis method is proposed to solve the dispersion relations.Based on the guided wave theory,the Navier stokes equation is constructed.The Helmholtz equation and functional form are obtained by using the variable separation method and solved by the finite element method.The calculated results are basically consistent with the results obtained by the semi-analytical finite element method,and the ring modal can be gotten,which proves the effectiveness and comprehensiveness of this method.At the same time,the guided wave theory and the Timoshenko Beam theory are applied to theoretically solve the dispersion relations of low frequency,which shows the characteristics of the modal analysis method are superior.Finally,the modal characteristics are analyzed by the displacement component,which provides a basis for the mode selection of guided wave on nondestructive testing.