充水粘弹性管道的频散曲线计算分析*

针对谱方法分析计算充水粘弹性管道的广义特征值问题,根据Chebyshev多项式及微分矩阵、位移和应力连续条件,将波动方程离散为相应的线性方程。利用MATLAB数值编程计算充水弹性和粘弹性管道对应频率下的轴对称纵向导波频散曲线和衰减曲线。分析表明,波传播在粘弹性管道中不仅具有衰减特性,而且由于水和粘弹性壳体交叉耦合作用,在一定频率范围内产生两种截断模态。

Calculation and analysis of dispersion curve of water-filled viscoelastic tube

Based on the spectral method and calculation of the generalized eigenvalue problem of water-filled viscoelastic tube, the wave equation is discretized into the corresponding linear equation according to the Chebyshev polynomial and differential matrix, displacement and stress continuous conditions. By using MATLAB numerical solution, the dispersions and decay curves of axial symmetric longitudinal guided waves under water-filled elastic and viscoelastic tubes were calculated respectively. The analysis shows that the wave propagation in the viscoelastic tube not only has the attenuation characteristics, but also produces two discontinuous modes in a certain frequency range, due to the cross-coupling between the water and the viscoelastic shell.