Explicit formulas for the reflection and transmission coefficients of one-component waves through a stack of an arbitrary number of layers |
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| Affiliation: | 1. Faculty of Mathematics, Mechanics and Informatics, Hanoi University of Science, 334, Nguyen Trai Str., Thanh Xuan, Hanoi, Viet Nam;2. CIMAT, Guanajuato Gto, Mexico 36000, Mexico;1. School of Civil Engineering, The University of Queensland, Brisbane, QLD, 4072, Australia;2. Geotechnical Engineering Group, CSIR-Central Building Research Institute, Roorkee, 247667, India;3. AcSIR-Academy of Scientific and Innovative Research, Ghaziabad, 201002, India;1. Department of Continuum Mechanics and Structures, E.T.S. Ing. Caminos, Canales y Puertos, Universidad Politecnica de Madrid, 28040 Madrid, Spain;2. Faculty of Mathematics, Mechanics and Informatics, Hanoi University of Science, 334, Nguyen Trai Str., Thanh Xuan, Hanoi, Vietnam;1. Department of Physics, Sciences Faculty, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran;2. Department of Physics, Sciences Faculty, Golestan University, P.O. Box 49138-15759, Gorgan, Iran;1. Faculty of Mathematics, Mechanics and Informatics, Hanoi University of Science, 334, Nguyen Trai Str., Thanh Xuan, Hanoi, Viet Nam;2. Faculty of Civil and Industrial Construction, National University of Civil Engineering, 55 Giai Phong Str., Hanoi, Viet Nam;1. School of Electronic Information, Wuhan University, 430072 Wuhan, PR China;2. Institute of Space Science and Technology, Nanchang University, 330031 Nanchang, PR China;3. Space Science Institute, School of Astronautics, Beihang University, 100191 Beijing, PR China;4. School of Physics and Optoelectronic Engineering, Xidian University, 710126 Xi’an, PR China |
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| Abstract: | ![]()
The transmission and reflection of one-component elastic, acoustic, optical waves on a stack of arbitrary number of different homogeneous layers have been intensively studied in the literature. However, all obtained formulas for the reflection and transmission coefficients are in implicit form. In this paper, we provide the explicit formulas for them. From these formulas we immediately arrive at the explicit formulas for the reflection and transmission coefficients of one-component waves through an FGM layer. Based on the obtained exact formulas, approximate formulas for the reflection and transmission coefficients are established for a stack of thin layers and for a thin FGM layer. It is numerically shown that they are good approximations. Since the obtained formulas are totally explicit, they are useful in evaluating, not only numerically but also analytically, the transmission and reflection coefficients of one-component waves. |
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| Keywords: | One-component waves Reflection coefficient Transmission coefficient A stack of arbitrary number of layers A composite layer An FGM layer |
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