The laws of variation of energy and momentum for one-dimensional systems with moving mountings and loads. (English. Russian original) Zbl 0562.73042
J. Appl. Math. Mech. 47, 692-695 (1985); translation from Prikl. Mat. Mekh. 47, 863-866 (1983).
Summary: The self-consistent dynamic behaviour of a one-dimensional system with a moving load is considered. The natural boundary conditions, previously obtained from the variational Hamiltonian principle [the authors, in Differential and integral equations. Gor’kii, Gork, Gosud. Univ. (1982)] for the self-consisistent problem of the dynamics of one-dimensional systems, when the boundary motions are not specified, are used to show that the motion of the load results in the appearance of additional forces that are proportional to the load velocity. Expressions are obtaind in terms of the density of the Lagrange function for the wave pressure, the wave energy flux, the wave momentum, the energy transport velocity, the work of the forces that vary the system parameters, and the distributed recoil forces that occur when waves propagate along a non- uniform system. The radiation conditions are discussed in the class of systems considered. The critical velocities of the load moving along a Timoshenko beam are determined.
MSC:
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 70H25 | Hamilton’s principle |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74J99 | Waves in solid mechanics |
Keywords:
self-consistent dynamic behaviour; one-dimensional system; moving load; natural boundary conditions; appearance of additional forces; proportional to the load velocity; density of the Lagrange function; wave pressure; wave energy flux; wave momentum; energy transport velocity; work of the forces; distributed recoil forces; non-uniform system; radiation conditions; critical velocities; Timoshenko beamReferences:
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