On calculating dispersion curves of waves in a functionally graded elastic plate
On calculating dispersion curves of waves in a functionally graded elastic plate
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功能梯度弹性板中波频散曲线的计算
DOI：
10.1016/j.compstruct.2006.08.009
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发表时间：
2007-11-01
影响因子：
6.3
通讯作者：
Bao, R. H.
中科院分区：
文献类型：
--
作者：
Chen, W. Q.;Wang, H. M.;Bao, R. H.
研究了材料性质沿厚度方向沿着变化的弹性板中波的频散特性。首先，非均匀板近似由足够大的层数，其中的每一个层，因此被视为均匀的层压板模型。然后，根据新发展的混响矩阵法，为任意一层建立两个局部坐标。相位关系的两个解决方案之间对应的两个坐标。通过考虑任意两个相邻层之间的界面处的连续性条件以及上下表面处的边界条件，也获得了散射关系。最后构造了混响矩阵，给出了控制波频散的特征方程。混响矩阵中没有一个元素包含正指数的指数函数，从而避免了由两个大数值之间的微小差异引起的数值不稳定性。给出了数值算例，并与传统位移法和状态空间法进行了比较（为了完整起见，附录A中给出了两种公式）。结果表明，混响矩阵法表现良好的所有值的波数，除了当频率很低，而状态空间法是非常有效的，以及在小波数的数值稳定。建议将这两种方法结合起来，以便计算宽波数范围内的频散曲线。(c)2006爱思唯尔有限公司保留所有权利。
The dispersion behavior of waves in an elastic plate with material properties varying along the thickness direction is studied. First, the inhomogeneous plate is approximated by a laminate plate model consisting of a sufficiently large number of layers, each of which is therefore regarded as homogeneous. Then, two local coordinates are set up for any layer according to the newly developed reverberation matrix method. Phase relations are derived between two solutions corresponding to the two coordinates. Scattering relations are also obtained by considering the continuity conditions at the interfaces between any two adjacent layers as well as the boundary conditions at the upper and lower surfaces. A reverberation matrix is finally constructed and the characteristic equation governing the dispersion of waves is presented. It is noted that no element of the reverberation matrix contains exponential function with positive index, hence avoiding the numerical instability induced by the small difference between two large numbers. Numerical examples are presented and comparison is made with the traditional displacement method and the state-space method (both formulations are presented in Appendix A for completeness). It is shown that the reverberation matrix method behaves well for all values of wave numbers except when the frequency is very low, while the state-space method is very efficient as well as numerically stable at small wave numbers. It is recommended that tile two methods be combined together for the purpose of calculating dispersion curves over a wide range of wave numbers. (c) 2006 Elsevier Ltd. All rights reserved.