An energy approach to the proof of the existence of Rayleigh waves in an anisotropic elastic half-space |
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| Authors: | IV Kamotskii AP Kiselev |
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| Institution: | 1. School of Highway, Chang’an University, Xi’an 710064, China;2. Department of Geotechnical Engineering, Tongji University, 1239 Siping Road, Shanghai, China;3. Department of Civil and Architectural Engineering and Mechanics, The University of Arizona, Tucson, A.Z. 85721, USA;4. Department of Civil Engineering, Shanghai University, Shanghai, China;1. State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China;2. School of Engineering, Nagasaki University, 1-14 Bunkyo-machi, 852-8521 Nagasaki, Japan;3. Shandong Provincial Key Laboratory of Civil Engineering Disaster Prevention and Mitigation, Shandong University of Science and Technology, Qingdao 266590, China;4. Fukumichi Limited Liability Company, Fukuoka 813-0041, Japan;5. Japan Railway Construction, Transport and Technology Agency (JRTT), Yokohama 231-8351, Japan;1. State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China;2. Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China;3. Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China |
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| Abstract: | An approach based on investigating the energy functional is applied for the first time to the classical problem of Rayleigh waves in an anisotropic half-space with a free boundary. The main object of the investigation is an ordinary differential operator in a variable characterizing the depth. An investigation of the spectrum by variational methods enables a new proof to be given of the existence of a Rayleigh wave in a linear elastic half-space with arbitrary anisotropy, which does not rest on the Stroh formalism. |
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