3D Scattering and Dynamic Stress Concentration of SH Waves in Spherical Shells With Spherical Inclusions

QIAO Song; SHANG Xin-chun

doi:10.3879/j.issn.1000-0887.2016.05.008

Volume 37 Issue 5

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Article Navigation > Applied Mathematics and Mechanics > 2016 > 37(5): 522-533

QIAO Song, SHANG Xin-chun. 3D Scattering and Dynamic Stress Concentration of SH Waves in Spherical Shells With Spherical Inclusions[J]. Applied Mathematics and Mechanics, 2016, 37(5): 522-533. doi: 10.3879/j.issn.1000-0887.2016.05.008

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3D Scattering and Dynamic Stress Concentration of SH Waves in Spherical Shells With Spherical Inclusions

doi: 10.3879/j.issn.1000-0887.2016.05.008

QIAO Song¹,
SHANG Xin-chun^1,2

¹National Center for Materials Service Safety(University of Science and Technology Beijing), Beijing 100083, P.R.China;²Department of Applied Mechanics, School of Mathematics and Physics,University of Science and Technology Beijing, Beijing 100083, P.R.China

Funds: The National Natural Science Foundation of China（10772024）

Received Date: 2015-10-10
Rev Recd Date: 2016-01-12
Publish Date: 2016-05-15

Abstract

Abstract

Spherical shells are widely applied in many engineering fields, and dynamic stress concentration generated by the inclusions (including cavities) will affect the bearing strengths and service lives of the structures directly. The 3D scattering and dynamic stress concentration of SH waves around spherical inclusions in thick spherical shells were investigated theoretically and numerically. 2 spherical coordinate systems, located at the spherical shell center and the inclusion center, were established to express the incidence and scattered waves in the expansion form of spherical wave functions. The addition formulas were employed to perform the coordinate transformation and the analytical solutions of the displacements and stresses were derived. Finally, computation and comparison of wave scattering and dynamic stress concentration by the inclusions of different materials and a cavity were conducted, and the results revealed the influences of the incidence frequency and the inclusion center position on the distributions of the dynamic stress concentration factors. This research provides a theoretical support for the dynamic analysis and nondestructive examination of spherical shells.
- dynamic stress concentration,
- wave scattering,
- spherical wave function,
- addition formula,
- spherical inclusion,
- spherical thick shell

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References

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