Undeservedly little attention is paid in the vast literature on the
theories of vibration and plasticity to the problem of steady-state
vibrations in elastoplastic bodies. This problem, however, is of
considerable interest and has many important applications. The problem
of low-cyclic fatigue of metals, which is now in a well de- veloped
state is one such application. The investigations within this area are
actually directed to collecting experimental facts about repeated cyclic
loadings, cf. [47J. Theoretical investigations within this area usually
con- sider the hysteretic loops and the construction of models of
plasticity theory which are applicable to the analysis of repeated
loadings and the study of the simplest dynamic problems. Another area of
application of the theory of the vibration of elastoplas- tic bodies is
the applied theory of amplitude-dependent internal damping. Another name
for this theory is the theory of energy dissipation in vibrat- ing
bodies. In accordance with the point of view of Davidenkov "internal
damping" in many metals, alloys and structural materials under consider-
able stress presents exactly the effect of micro plastic deformations.
There- fore, it may be described by the methods of plasticity theory.
This point of view is no doubt fruitful for the theory of energy
dissipation in vibrating bodies, as it allows one to write down the
constitutive equations appropri- ate both for vibrational analysis of
three-dimensional stress states and an investigation of nonharmonic
deformation. These problems are known to be important for the theory of
internal damping.
