On the modelling of dynamic problems for micro-periodic beams

In the paper a new approach to the dynamics of beams with periodically and functionally graded structure is presented.The beam is assumed to be resting on an elastic foundation characterized by the Winkler coefficient. Assumptions to the Bernoulli - Euler beam theory as well as the influence of the axial forces on deflection of the beam are taking into account. The solution is based on concepts of the tolerace averaging approach (TAA) by Wierzbicki and Woźniak (2000).The obtained averaged model make it possible to describe the response of micro-inhomogeneous beams better than the known homogenization theory.

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W pracy zaproponowano nowe podejście do dynamiki belek o periodycznej i funkcyjnie zmiennej strukturze. Uważa się, że belka spoczywa na podłożu Winklera, zaś do modelowania belek użyto teorii Bernoulilego–Eulea. Podejście jest oparte na metodzie uśredniania tolerancyjnego zaproponowanego przez Wierzbickego i Woźniaka (2000). Otrzymany uśredniony model pozwala dokładniej opisać zachowanie belki.