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Riemann surface of dispersion diagram of a multilayer acoustical waveguide |
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| Institution: | 1. Institute of General Mechanics, RWTH Aachen University, Templergraben 64, 52062 Aachen, Germany;2. School of Computing and Mathematics, Keele University, Staffordshire, ST5 5BG, UK;3. Carnegie Mellon University in Qatar, P.O. Box 24866, Doha, Qatar;4. Center for Advanced Materials, Qatar University, P.O. Box 2713, Doha, Qatar;1. Department of Civil Engineering, Hormozgan University, P.O. Box 3995, Bandar Abbas, Iran;2. Department of Civil Engineering, Sharif University of Technology, 11155-9313 Tehran, Iran;3. Institute for Nanoscience and Nanotechnology, Sharif University of Technology, 11155-9161 Tehran, Iran;4. Department of Civil Engineering, School of Science and Engineering, Sharif University of Technology, International Campus, Kish Island, P.O. Box 79417-76655, Kish, Iran;1. Department of Mechanical Engineering, Wayne State University, Detroit, MI 48202, USA;2. Institut für Allgemeine Mechanik, RWTH Aachen University, 52056 Aachen, Germany |
| Abstract: | A Riemann surface of a dispersion diagram of a multilayer planar waveguide is studied. Structure of this surface is linked with the transient wave phenomena in the waveguide. A method is proposed to study the dispersion diagram. The method is constituted in introducing of an artificial parameter controlling the links between the layers of the waveguide. The strength of the links varies from the full isolation to the realistic physical contact. The dependence of the solution on the artificial parameter is analytical. Using this approach it is proven that the branch points of the Riemann surface can be listed as the crossing points of the branches of non-interacting layers. A numerical procedure of finding the branch points positions is described. An explanation of the types of waves corresponding to different parts of the Riemann surface of the dispersion diagram is given. |
| Keywords: | Waveguide Dispersion diagram Precursor Forerunner First-arriving signal Orthogonality relations |
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