The multiple scattering of non-homogeneous shear waves from two cavities in functionally graded materials

Abstract

The propagation and multiple scattering of non-homogeneous shear waves resulting from two cavities embedded in exponential functional graded materials (FGMs) were investigated, and the dynamic stress around the two cavities derived. The non-homogeneous scattering fields of shear waves around the cavities are analytically expressed by using the wave function expansion method. The interaction of non-homogeneous scattering fields between the two cavities is described accurately. The dynamic stresses around the cavities under different geometrical and physical parameters are graphically illustrated and analyzed. Analysis shows that the non-homogeneous properties of FGMs exhibit a significant effect on the dynamic stress around the cavities. The effect of the non-homogeneous properties of FGMs on the dynamic stress is also dependent on the gradation direction, the distance between the two cavities, the relative position of the two cavities and the incident frequency of waves. A comparison with other existing studies in the literature is also presented.

Keywords:

• functionally graded material
• non-homogeneous shear wave
• multiple scattering
• two cavities

Acknowledgements

The paper is supported by the National Natural Science Foundation of China (Foundation No. 10972147), the Natural Science Foundation of Hebei Province, China (Foundation No. A2010001052), and the Program for Changjiang Scholars and Innovative Research Team in University. The authors are grateful to the anonymous reviewers for their constructive comments and suggestions.