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Scattering of Plane Sh-Wave From a Partially Debonded Shallow Cylindrical Elastic Inclusion

Published online by Cambridge University Press:  05 May 2011

J.X. Zhao  and
H. Qi
J.X. Zhao*
Affiliation:
College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, 150001, China
H. Qi*
Affiliation:
College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, 150001, China
*
*Ph.D., corresponding author
**Professor
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Abstract

The scattering of plane SH-wave from a partially debonded shallow cylindrical elastic inclusion in half space is investigated in this paper by complex function method and expansion method of wave function. The debonding regions are considered as multiple arc-shaped interface cracks with non-contacting faces. Firstly, in the inclusion district, the standing wave function in the elastic inclusion with unknown coefficients which satisfies the boundary condition is constructed and generated into the Fourier series; in the half space, the stress and displacement boundary condition around the elastic inclusion can be modeled as the same as the standing wave function in the elastic inclusion. Then, a set of infinite algebraic equations can be obtained around the same boundary and the solution of problem can be gained. In the end, numerical examples of the surface displacement are provided and discussed. It is found that the interface cracks can raise the surface displacement amplitudes to a certain degree.

Keywords

Scattering of plane SH-waveMultiple interface cracksComplex function methodThe surface displacementHalf space.
Type
Articles
Information
Journal of Mechanics , Volume 25 , Issue 4 , December 2009 , pp. 411 - 419
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2009

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References

REFERENCES

1.Lee, V. W. and Trifunac, M. D., “Response of Tunnels to Incident SH-Waves,” ASCE, Engrg. Mechanics Div., 105, pp. 643–659 (1979).CrossRefGoogle Scholar
2.Pao, Y. H. and Mow, C. C., “Diffraction of Elastic Waves and Dynamic Stress Concentrations,” New Work: Crane and Russak (1973).CrossRefGoogle Scholar
3.Lee, V. W., “On Deformations Near a Circular Underground Cavity Subjected to Incident Plane SH-Waves,” Proc. Application ofComp. Methods in Engry. Conf., Vol. II,Univ. of Southern California, Los Angeles, Calif. pp. 951–961 (1977).Google Scholar
4.Gregory, R. D., “An Expansion Theorem Applicable to Problems of Wave Propagation in an Elastic Half-Space,” Proc. Camb. Philos. Soc., 63, pp. 1341–1367 (1967).CrossRefGoogle Scholar
5.Gregory, R. D., “The Propagation of Waves in an Elastic Half-Space Containing a Circular Cylindrical Cavity,” Proc. Camb. Philos. Soc., 67, pp. 689–710 (1967).CrossRefGoogle Scholar
6.Datta, S. K., “Scattering of Elastic Waves,” Mechanics Today., 4, pp. 149–208 (1978).CrossRefGoogle Scholar
7.Dravinski, M., “Ground Motion Amplification Due to Elastic Inclusions in a Half-Space,” International Journal Earthquake Engrg. and Struct. Dynamics., 11, pp. 313–335 (1983).CrossRefGoogle Scholar
8.Manoogian, M. E. and Lee, V. W., “Diffraction of SHWave by Subsurface Inclusions of Arbitrary Shape,” ASCE, Eng. Mechanics Div., 122, pp. 123–129 (1996).CrossRefGoogle Scholar
9.Lee, V. W., “Three-Dimensional Diffraction of Elastic Waves by a Spherical Cavity in an Elastic Half-Space. I: Closed-Form Solutions,” International Journal of Soil Dynamics and Earthquake Engrg., 7, pp. 149–161 (1988).CrossRefGoogle Scholar
10.Chen, J. T., Chen, P. Y. and Chen, C. T., “Surface Motion of Multiple Alluvial Valleys for Incident Plane SH Waves by Using a Semi-Analytical Approach,” Soil. Dyn. andEarthq. Eng., 28, pp. 58–72 (2008).CrossRefGoogle Scholar
11.Chen, J. T., Chen, C. T., Chen, P. Y. and Chen, I. L., “A Semi-Analytical Approach for Radiation and Scattering Problems with Circular Boundaries,” Comput. Method. Appl. Mechanics and Eng., 196, pp. 2751–2764 (2007).CrossRefGoogle Scholar
12.Belyaev, K. P., “Interaction of a Shear with an Elastic Cylindrical Inclusion Having a Crack Along its Contour,” Prikl. Mekh., 21, pp. 112–116 (1985).Google Scholar
13.Coussy, O., “Scattering of SH-Waves by a Cylindrical Inclusion Presenting an Interface Crack,” CR. Acad. Sci. Paris., 295, pp. 1043–1046 (1982).Google Scholar
14.Coussy, O., “Scattering of Elastic Waves by an Inclusion with an Interface Crack,” Wave Motion, 6, pp. 223–236 (1983).CrossRefGoogle Scholar
15.Yang, Y. and Norris, A. N., “Shear Wave Scattering from a Debonded Fiber,” Journal of Mechanics and Physics of Solids, 39, pp. 273–294 (1991).CrossRefGoogle Scholar
16.Norris, A. and Yang, Y., “Dynamic Stress on a Partially Bonded Fiber,” Journal of Applied Mechanics, 58, pp. 404–409 (1991).CrossRefGoogle Scholar
17.Yang, Y. and Norris, A., “Longitudinal Wave Scattering from a Partially Bonded Fiber,” Wave Motion, 15, pp. 43–50 (1992).CrossRefGoogle Scholar
18.Wang, Y. S. and Wang, D., “Scattering of Elastic Waves by a Rigid Cylindrical Inclusion Partially Debonded from its Surrounding Matrix, Part I. SH Case,” International Journal of Solids and Structures, 33, pp. 2789–2815 (1996).CrossRefGoogle Scholar
19.Wang, Y. S. and Wang, D., “Scattering of Elastic Waves by a Rigid Cylindrical Inclusion Partially Debonded from its Surrounding Matrix, Part II. P and SV Cases,” International Journal of Solids and Structures, 33, pp. 2817–2840 (1996).CrossRefGoogle Scholar
20.Wang, Y. S. and Wang, D., “Elastic Wave Scattering from a Partially Debonded Elastic Cylindrical Inclusion,” J Harbin Institute of Technology, E–1, pp. 71–79 (1994).Google Scholar
21.Wang, Y. S. and Wang, D., “Diffraction of SH-Waves by a Circular Cavity with a Partially Debonded Liner,” Acta. Mechanics Sinica., 26, pp. 462–469 (1994).Google Scholar
22.Wang, Y. S., Yu, G. L. and Wang, D., “Dynamic Analysis of an Embedded Semicylindrical Foundation Partially Debonded from Soil,” Proc. of ICMSGE'94, China Translation and Printing Services Ltd., pp. 318–323(1994).Google Scholar
23.Coussy, O., “Scattering of SH-Waves by a Rigid Elliptic Fiber Partially Debonded from its Surrounding Matrix,” Mechanics Res. Commu., 13, pp. 39–45 (1986).CrossRefGoogle Scholar
24.Wang, Y. S., “Elliptic Arc Crack Subjected to AntiPlane Shear Wave,” Eng. Fract. Mechanics, 48, pp. 289–297 (1994).CrossRefGoogle Scholar
25.Wang, Y. S. and Wang, D., “Shear Wave Scattering from a Partially Debonded Elastic Elliptic Inclusion,” Mechanics, Res. Commu., 22, pp. 79–86 (1995).CrossRefGoogle Scholar
26.Liu, D. K. and Wang, G. Q., “Antplane SH-Deformation of a Semi-Cylindrical Hill Above a Subsurface Cavity,” Acta. Mechanics Sinica., 3, pp. 209–218 (2006).Google Scholar
27.Liu, D. K. and Lin, H., “Scattering of SH-Waves by a Shallow Buried Cylindrical Cavity and the Ground Motion,” Explosion and Shock Waves, 1, pp. 6–12 (2003).Google Scholar