Complex variable function method for the scattering of plane waves by an arbitrary hole in a porous medium |
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| Authors: | Jian-Hua Wang Jian-Fei Lu Xiang-Lian Zhou |
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| Affiliation: | 1. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai, 200030, PR China;2. Civil Engineering Department of Jiangsu University, Jiangsu, Zhenjiang, 212013, PR China;1. CICECO - Aveiro Institute of Materials and Departamento de Física, Universidade de Aveiro, 3810-193 Aveiro, Portugal;2. IFIMUP and IN-Institute of Nanoscience and Nanotechnology, Rua do Campo Alegre, 678, 4169-007 Porto, Portugal;1. State Key Laboratory Cultivation Base for Nonmetal Composites and Functional Materials of Sichuan Province, Southwest University of Science and Technology, Mianyang 621010, China;2. Physical School of Nanjing University, Hankou Road, Nanjing 210093, China;3. Analytical and Testing Center, Southwest University of Science and Technology, Mianyang 621010, China;1. Laboratoire Mécanique des Sols, Structures et Matériaux, CNRS UMR 8579, Ecole Centrale Supelec, Université Paris Saclay, Grande Voie des Vignes, 92290, Chatenay-Malabry, France;2. State Key Lab Incubation Base of Photoelectric Technology and Functional Materials, International Collaborative Center on Photoelectric Technology and Nano Functional Materials, Northwest University, Xi’an 710069, PR China;3. School of Materials Engineering, Shanghai University of Engineering Science, 333 Longteng Road, 201620, PR China;1. Department of Electronic Engineering, Semyung University, Jecheon 390-711, Republic of Korea;2. School of Electrical and Electronic Engineering, Chung-Ang University, Seoul 156-756, Republic of Korea;3. Department of Transportation System Engineering, Graduate School of Transportation, Korea National University of Transportation, Uiwang-si, Gyeonggi-do 437-763, Republic of Korea |
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| Abstract: | Based on the complex variable function method, a new approach for solving the scattering of plane elastic waves by a hole with an arbitrary configuration embedded in an infinite poroelastic medium is developed in the paper. The poroelastic medium is described by Biot's theory. By introducing three potentials, the governing equations for Biot's theory are reduced to three Helmholtz equations for the three potentials. The series solutions of the Helmholtz equations are obtained by the wave function expansion method. Through the conformal mapping method, the arbitrary hole in the physical plane is mapped into a unit circle in the image plane. Integration of the boundary conditions along the unit circle in the image plane yields the algebraic equations for the coefficients of the series solutions. Numerical solution of the resulting algebraic equations yields the displacements, the stresses and the pore pressure for the porous medium. In order to demonstrate the proposed approach, some numerical results are given in the paper. |
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