Effect of resonant absorption in viscous and dry vibrating contact: Mathematical models and theory connected with slow dynamics and friction welding |
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| Affiliation: | 1. Laboratory “Group Analysis of Mathematical Models in Natural and Engineering Sciences”, Ufa State Aviation Technical University, Ufa, Russia;2. Research Centre ALGA: Advances in Lie Group Analysis, Department of Mathematics and Science, Blekinge Institute of Technology, Karlskrona, Sweden;3. Physical Faculty of M.V. Lomonosov Moscow State University, Russia;4. O.Yu. Schmidt Earth physics institute of Russian Academy of Sciences, Russia;5. N.I. Lobachevski Nizhni Novgorod State University, Russia;6. A.M. Prokhorov General physics institute of Russian Academy of Sciences, Russia;7. Department of Mechanical Engineering, Blekinge Institute of Technology, Karlskrona, Sweden;1. Blekinge Institute of Technology;1. Department of Mathematics and Mechanics, St Petersburg State University, St Petersburg 198504, Russia;2. Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Bolshoj 61, Vasilievskii Ostrov, St Petersburg 199178, Russia;3. St Petersburg State Polytechnical University, St Petersburg 195251, Russia;4. Ufa State Aviation Technical University, 12 K. Marx str., Ufa 450000, Russia;1. Laboratory “Group Analysis of Mathematical Models in Natural and Engineering Sciences”, Ufa State Aviation Technical University, 450 000 Ufa, Russia;2. Research Centre ALGA: Advances in Lie Group Analysis, Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona, Sweden;3. School of Mathematics, Suranaree University of Technology, Nakhon Ratchasima, 30000, Thailand;1. Keldysh Institute of Applied Mathematics, Russian Acad. Sci., Moscow, Russia;2. Laboratory “Group Analysis of Mathematical Models in Natural and Engineering Sciences”, Ufa State Aviation Technical University, Ufa, Russia;3. Research Centre ALGA: Advances in Lie Group Analysis, Department of Mathematics and Science, Blekinge Institute of Technology, Karlskrona, Sweden |
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| Abstract: | Process of heating of thin layer located between two vibrating surfaces is studied. Energy loss goes on due to viscous or dry friction. Optimal quantities of shear viscosity and friction corresponding to maximum energy loss are determined. Resonant behavior of loss must be taken into account in the description of “slow dynamics” of rocks and materials exposed to high-intensity seismic or acoustic irradiation as well as in various technologies. Bonding of materials by linear friction welding, widely used in propulsion engineering, can exemplify such a technology. |
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| Keywords: | Vibrating contact Resonant absorption Friction welding Mathematical model Conservation law |
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