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Scattering by circular cavity in radially inhomogeneous medium with wave velocity variation

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Abstract

Based on the theory of complex function and the principle of homogenization, harmonic dynamics stress of a radially infinite inhomogeneous medium with a circular cavity is investigated. Due to the symmetry, wave velocity is assumed to have power-law variation in the radial direction only, and the shear modulus is constant. The Helmholtz equation with a variable coefficient is equivalently transformed into a standard Helmholtz equation with a general conformal transformation method (GCTM). The displacements and stress fields are proposed. Numerical results show that the wave number and the inhomogeneity parameter of the medium have significant effects on the dynamic stress concentration around the circular cavity. The dynamic stress concentration factor (DSCF) becomes singular when the inhomogeneity parameter of medium is close to zero.

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Authors and Affiliations

  1. College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, 150001, China

    Zailin Yang, Baoping Hei & Yao Wang

Authors
  1. Zailin Yang
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  2. Baoping Hei
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  3. Yao Wang
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Corresponding author

Correspondence to Zailin Yang.

Additional information

Project supported by the Earthquake Industry Special Science Research Foundation Project (No. 201508026-02) and the Natural Science Foundation of Heilongjiang Province of China (No.A201310)

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Yang, Z., Hei, B. & Wang, Y. Scattering by circular cavity in radially inhomogeneous medium with wave velocity variation. Appl. Math. Mech.-Engl. Ed. 36, 599–608 (2015). https://doi.org/10.1007/s10483-015-1937-7

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  • DOI: https://doi.org/10.1007/s10483-015-1937-7

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Chinese Library Classification

2010 Mathematics Subject Classification

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