Department of Mechanics, University Politehnica Bucharest, Splaiul Independentei 313, Bucharest 060042, Romania.
Ultrasonics. 2014 Sep;54(7):1825-31. doi: 10.1016/j.ultras.2014.01.019. Epub 2014 Feb 14.
The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method.
空心多层圆柱的频散曲线是此类结构上任何实际导波应用的前提条件。均质各向同性材料的方程早在 120 多年前就已建立。对于解析表达式的数值解的寻找仍然存在很大的困难，特别是如果材料是各向异性粘弹性的，如过去几十年中用于管道的复合材料。在其他数值技术中，半解析有限元法已证明其能够解决这个问题。存在两种可能性来模拟有限元特征值问题：管的二维横截面模型或与管的内半径和外半径之间的层相交的径向段模型。最后一种可能性在这里被采用，并且为纵向 L(0,n)、扭转 T(0,n)和弯曲 F(m,n)模式推导出不同的微分问题。为这三个模式类推导出特征值问题，为可用的通用有限元代码中使用的矩阵提供每个系数的显式形式。与填充非线性粘弹性流体或粘弹性涂层的管道以及完全各向异性空心圆柱的现有解决方案的比较都证明了该方法的可靠性和易用性。
