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The nonlinear dynamics of elastic rods. (English. Russian original) Zbl 0708.73039

J. Appl. Math. Mech. 52, No. 4, 493-498 (1988); translation from Prikl. Mat. Mekh. 52, No. 4, 635-641 (1988).
Summary: The general equations of nonlinear dynamics of elastic rods are examined taking tension, transverse shear, eccentricity, rotational inertia, and also initial stresses into account. A second-order theory is constructed for Timoshenko and classical-type models. A variational formulation is given for the linearized problem. Tension and shear effects are examined in the problem of the stability of a compressed column.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74B20 Nonlinear elasticity
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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References:

[1] Antman, S.S., ()
[2] Lur’ye, A.I., Theory of elasticity, (1970), Nauka Moscow
[3] Saetlitskii, V.A., Mechanics of flexible rods and strings, (1978), Mashinostroyeniye Moscow
[4] Berdichevskii, V.L., Variational principles of the mechanics of a continuous medium, (1983), Nauka Moscow · Zbl 0158.46505
[5] Berdichevskii, V.L.; Starosel’skii, L.A., On the theory of curvilinear rods of Timoshenko-type, Pmm, 47, 6, (1983)
[6] Eliseyev, V.V., On the construction of a refined model of an elastic beam, Trudy, leningrad, politekhn. inst., 386, (1982)
[7] Panovko, Ya.G., Mechanics of a deformable solid, (1985), Nauka Moscow · Zbl 0025.11204
[8] Ostrovskii, L.A.; Sutin, A.M., Non-linear elastic waves in rods, Pmm, 41, 3, (1977) · Zbl 0392.73030
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