基于层状模型的功能梯度板中兰姆波传播研究

Propagation of Lamb wave in a functionally graded plate with a layered model

功能梯度板中的兰姆波的传播在实际工程中有着非常广泛的应用。采用层状模型研究了兰姆波在材料特性沿厚度方向连续变化的功能梯度板中的传播特性。通过数值计算获得了层状板中兰姆波的色散关系,并与已有结果进行了比较,获得了材料属性沿厚度方向呈指数变化和多项式变化时功能梯度板中兰姆波的波速和位移解。当材料属性连续变化时,兰姆波各阶模态的波速与位移都将发生变化。相比于兰姆波的高阶模态,低阶模态的波速变化更加明显。本文的研究可为功能梯度板的设计提供参考。

The propagation of Lamb waves in functionally graded plates has been widely used in engineering. The Lamb wave propagation in a functionally graded plate with material property continuously varying along the thickness direction has been analyzed by a layered model. The dispersion relationship of Lamb wave of layered plate has been obtained by using the numerical calculation and compared with the known results. The wave velocity and displacements of Lamb wave also have been obtained with exponential and polynomial property grading schemes. With continuous variation of material property, the wave velocity and displacements of Lamb wave changed. Compared with the high order mode of Lamb wave, the change of wave velocity of the low order is more significant. This study can be used for designing of the functionally graded plate.