Axisymmetric dynamic response of the multi-layered transversely isotropic medium |
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| Institution: | 1. School of Hydraulic Engineering, Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China;2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China;3. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Najing Hydraulic Research Institute, Nanjing 210098, China;1. Academy of Scientific and Innovative Research, New Delhi 110 001, India;2. CSIR-Fourth Paradigm Institute, Bangalore 560037, India;1. School of Transportation & Logistics, Dalian University of Technology, China;2. Dept. of Civil Engineering and Dept. of Mathematics, University of Akron, USA;1. Department of Computational Science and Statistics, School of Science, Nantong University, Nantong, Jiangsu 226019, PR China;2. College of Civil Engineering and Architecture, East China Jiaotong University, Nanchang, Jiangxi 330013, PR China;3. School of Transportation and Civil Engineering, Nantong University, Nantong, Jiangsu 226019, PR China;1. Department of Disaster Mitigation for Structures, College of Civil Engineering, Tongji University, Shanghai 200092, China;2. School of Sciences and Technology, Hellenic Open University, Patras 26335, Greece |
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| Abstract: | By virtue of the precise integration method (PIM) and the technique of mixed variable formulations, solutions for the dynamic response of the multi-layered transversely isotropic medium subjected to the axisymmetric time-harmonic forces are presented. The planes of cross anisotropy are assumed to be parallel to the horizontal surface of the stratified media. Four kinds of vertically acting axisymmetric loads are prescribed either at the external surface or in the interior of the soil system. Thicknesses and number of the medium strata are not limited. Employing the Hankel integral transform in cylindrical coordinate, the axisymmetric governing equations in terms of displacements of the multi-layered media are uncoupled. Applying mixed variable formulations, more concise first-order ordinary differential matrix equations from the uncoupled motion equations can be obtained. Solutions of the ordinary differential matrix equations in the transformed domain are acquired by utilizing the approach of PIM. Since PIM is highly accurate to solve the sets of first-order ordinary differential equations, any desired accuracy of the solutions can be achieved. All calculations are based on the corresponding algebraic operations and computational efforts can be reduced to a great extent. Comparisons with the existing numerical solutions are made to confirm the accuracy of the present solutions proposed by this procedure. Several examples are illustrated to explore the influences of the type and degree of material anisotropy, the frequency of excitation and loading positions on the dynamic response of the stratified medium. |
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| Keywords: | Precise integration method Mixed variable formulation Multi-layered transverse isotropy Axisymmetric dynamic response Hankel integral transform |
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