On the propagation of thermoelastic disturbances in thin plates and rods |
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| Affiliation: | 1. College of Science, Hunan City University, Yiyang 413000, China;2. Customer Service Center, State Grid Zhejiang Electric Power Research Institute, Hangzhou 310009, China;3. Department of Mathematics, Huzhou University, Hzhou 313000, China;4. Friedman Brain Institute, Icahn School of Medicine at Mount Sinai, New York, NY 10029, United States;1. Department of Chemistry, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran;2. Center of Climate Change and Global Warming, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran;3. Department of Chemistry, Dalhousie University, P.O. Box 15000, Halifax, Nova Scotia B3H 4R2, Canada;4. Research Center for Basic Sciences & Modern Technologies (RBST), Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran;5. Department of Biology, Faculty of Science, Tokyo University of Science, Kagurazaka 1-3, Shinjuku-ku, Tokyo 162-8601, Japan;6. Controlled Photobiosynthesis Laboratory, K.A. Timiryazev Institute of Plant Physiology, Russian Academy of Sciences, Botanicheskaya Street 35, Moscow 127276, Russia;7. Institute of Basic Biological Problems, Russian Academy of Sciences, Pushchino, Moscow Region 142290, Russia;8. Department of Plant Physiology, Faculty of Biology, M.V. Lomonosov Moscow State University, Leninskie Gory 1-12, Moscow 119991, Russia;9. Department of Molecular and Cell Biology, Moscow Institute of Physics and Technology, Institutsky lane 9, Dolgoprudny, Moscow Region 141700, Russia;10. Bionanotechnology Laboratory, Institute of Molecular Biology and Biotechnology, Azerbaijan National Academy of Sciences, Matbuat Avenue 2a, Baku 1073, Azerbaijan |
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| Abstract: | When restrictions are placed on the components of stress in an elastic body the linear thermoelastic equations which govern its internal motions differ from those which hold in general. The main purpose of this paper is to draw attention to these differences and to present a simple table by means of which results referring to the propagation of general, small amplitude, thermoelastic disturbances can be converted to results for longitudinal wave propagation in a thin plate and in a thin rod. Flexural vibrations are also briefly examined. By proceeding to the low frequency limit the classical equations of motion and of heat conduction appropriate to the thin plate and the thin rod are re-derived. |
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