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C. Adam, F. Ziegler:
"Flexural vibrations of viscoplastic composite beams";
in: "Computational Mechanics '95 - Proc. of International Conference on Computing Engineering Science 1995 (ICES'95)", S.N. Atluri, G. Yagawa, T.A. Cruse (ed.); Springer, Berlin, 1995, ISBN: 3-540-59114-1, 1235 - 1240.

A flexural theory of symmetrically designed layered beams is presented. Rate-dependent plastic materials are considered. The assumptions of the Timoshenko theory of shear-deformable beams are applied to each individual layer. Core and faces are perfectly bonded. The continuity of the transverse shear stresses across the interfaces is preserved by defining the interlaminar shear stress through the generalized Hooke's law. By definition of an effective cross-sectional rotation the complex problem reduces to the simpler case of an equivalent homogeneous beam with effective stiffness and mass density and with properly assigned boundary conditions. The dynamic response analysis based on sources of selfstress is used. The plastic strains generate selfstress in the linear elastic beam of virgin stiffness, which serves as the ideal background structure. In such a manner the solution methods of the linear theory of flexural vibrations, like the mode superposition, Duhamel's integral and Green's functions, can be used. 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. Analysis is based on an integral equation formulation with a truncated modal solution. However, the modal expansion is performed only on the complementary dynamic part of the solution, whereas the quasistatic portion is determined separately in a closed form. Splitting the deflection in such a way is crucial for getting precise results at low computing costs.