On the approximation of acceleration waves in rods |
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| Affiliation: | 1. Annai College of Naturopathy and Yoga Sciences, Anaikudi Road, Kovilachery, Kumbakonam, Tamil Nadu, India;2. Center for Integrative Medicine and Research, All India Institute of Medical Sciences, New Delhi, India;3. Division of Yoga and Life Sciences, Swami Vivekananda Yoga Anusandhana Samsthana, Bengaluru, India;1. Institute of Resource, Environment and Sustainable Development Research, College of Economics, Jinan University, Guangzhou, Guangdong 510632, China;2. College of New Energy and Environment, Jilin University, Changchun, Jilin 130012, China;3. Institute of Environmental and Ecological Engineering, Guangdong University of Technology, Guangzhou, Guangdong 510006, China;4. School of Management, Guangdong University of Technology, Guangzhou, Guangdong 510520, China;5. Energy and Sustainability Research Institute Groningen, University of Groningen, Groningen 9747 AG, Netherlands;6. China Science and Technology Exchange Center, Beijing 100045, China;1. Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering, School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China;2. School of Engineering and Computer Science, University of Hertfordshire, Hatfield AL10 9AB, UK;1. Medical Governance Research Institute, Minato-ku, Tokyo 1087505, Japan;2. Hamamatsu University School of Medicine, Hamamatsu, Shizuoka, Japan;3. Tohoku University School of Medicine, Sendai, Miyagi, Japan;4. Department of Internal Medicine, Navitas Clinic Shinjuku, Shinjuku, Tokyo, Japan;5. Department of Internal Medicine, Navitas Clinic Tachikawa, Tachikawa, Tokyo, Japan |
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| Abstract: | ![]()
This paper employs an approximate form of analysis based on the assumption of plane stress to find the transport equation and corresponding evolution law governing the intensity of acceleration wave propagation in an elastic rod of slowly varying area of cross-section. The result is then extended to include the case of slightly bent rods. In each of these cases it is shown that for a medium in which the strain energy function Σ(p) is such that d3Σ/dp3 ≠ 0, with p the displacement gradient, the acceleration wave intensity is governed by a Bernoulli equation. The work is concluded by showing that the analysis may also be applied to the case of a composite rod comprising an arbitrary number of homogeneous isotropic plane layers normal to the direction of acceleration wave propagation. |
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