Scattering of plane SH waves by an isosceles trapezoidal hill |
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| Institution: | 1. Department of Leisure and Recreation Management/Ph.D. Program in Engineering Science, Chung Hua University, Hsin-Chu 30012, Taiwan;2. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan;3. Department of Computer Science and Engineering, National Sun Yat-sen University, Kaohsiung 80424, Taiwan;4. Department of Applied Mathematics, I-Shou University, Kaohsiung 84001, Taiwan;5. Department of Healthcare Administration and Medical Informatics, Kaohsiung Medical University 80708, Taiwan;1. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland;2. Department of Vehicles, Warsaw University of Technology, 84 Narbutt Str., 02-524 Warsaw, Poland;3. Department of Mathematics and Modeling, Saratov State Technical University, Politehnicheskaya 77, 410054 Saratov, Russian Federation;4. Department Applied Mathematics and Systems Analysis, Saratov State Technical University, Politehnicheskaya 77, 410054 Saratov, Russian Federation;1. College of Civil Engineering, Nanjing Tech University, Nanjing 211816, China;2. Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA;1. Department of Civil Engineering, Faculty of Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran;2. Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089, USA |
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| Abstract: | This paper presents a theoretical approach to study the surface motion of an isosceles trapezoidal hill impacted by incident SH waves. A rigorous solution has been derived by applying an accurate region-matching technique. The solution region is divided into three parts by an appropriate partitioning method. Based on complex function method and multipolar coordinates, a fractional factor is introduced to construct suitable wave functions which satisfy the governing equation and zero-stress condition on the free surface in each sub-region. According to the continuity condition at the auxiliary boundary, surface displacements are expressed in series of infinite algebraic equations, and the unknown coefficients of the series can be determined by Fourier series expansion technique in complex domain. Numerical results demonstrate the analytical results depend on the following parameters: The slope, the height and the width of the trapezoidal hill, the frequency content of the excitation and the incidence angle. |
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| Keywords: | SH waves scattering Isosceles trapezoidal hill Complex function method Region-matching technique Multipolar coordinates Complex topography |
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