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

Eliseev, V. V.

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.)

Keywords:

tension; transverse shear; eccentricity; rotational inertia; initial stresses; second-order theory; Timoshenko; classical-type models; linearized problem; stability; compressed column

References:

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