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C. Adam, F. Ziegler:
"Moderately large forced oblique vibrations of elastic-plastic deteriorating beams";
Talk: 2nd European Conference on Structural Dynamics (Eurodyn'93), Trondheim, Norway; 1993-06-21 - 1993-06-23.

An integral equation formulation for the dynamic biaxial response of elastic-plastic beams is presented, including the influence of moderately large deflections. Materials are considered which are described by rate-dependent plasticity and which are subjected to ductile damage in alternating plasticity. In that case ductile damage is given by means of void-growth in porous materials. Inelastic defects of the material and geometric nonlinearities both are treated as additional sources of selfstresses in the associated linear elastic (background) beam with time-independent virgin stiffness. Thus, superposition applies in an incremental formulation and linear methods like those based on Green's functions and Duhamel's integral are used to account for the given as well as for the internal loads. The intensity and the distribution of the internal sources are calculated incrementally in a time-stepping procedure and they are determined by the constitutive law and by means of the nonlinear geometric relations. As an illustrative problem, the oblique vibrations of a preloaded viscoplastic beam with respect to one of the principal axis and under the action of a harmonic lateral force are considered.