Longitudinal-transversal vibrations of viscoelastic rods with consideration of physical and geometric nonlinearities. (English) Zbl 0365.73052
MSC:
74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
74B99 | Elastic materials |
74C99 | Plastic materials, materials of stress-rate and internal-variable type |
74D99 | Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) |
74K99 | Thin bodies, structures |
References:
[1] | A. R. Rzhanitsyn, The Theory of Creep [in Russian], Stroiizdat, Moscow (1968). |
[2] | H. Kauderer, Nonlinear Mechanics [Russian translation], IL, Moscow (1961). |
[3] | A. A. Il’yushin and B. E. Pobedrya, Foundations of the Mathematical Theory of Thermoviscoelasticity [in Russian], Nauka, Moscow (1970). |
[4] | N. N. Bogolyubov and Yu. A. Mitropol’skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], 4th Edition, Nauka, Moscow (1974). |
[5] | Yu. A. Mitropol’skii, The Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1971). |
[6] | A. N. Filatov, Asymptotic Methods in the Theory of Differential and Integrodifferential Equations [in Russian], Fan, Tashkent (1974). · Zbl 0364.45010 |
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