In this paper mathematical modelling of vibrations and stability problems for slender visco-elastic periodic beams is considered. In order to take into account the effect of microstructure a certain non-asymptotic approach is applied, called the tolerance modelling method. This technique allows to replace the equation with non-continuous, highly oscillating, periodic coefficients by a system of differential equations with constant coefficients. Moreover, the derived equations describe the effect of microstructure on the overall behaviour of the beams under consideration. In the framework of the tolerance modelling governing equations of two different tolerance models can be obtained - the standard and the general, under weakened assumptions. To evaluate the proposed general tolerance model obtained results are compared with results calculated within the known asymptotic homogenization, i.e. by the asymptotic model. In this note mathematical models describing investigated beams are only presented and illustrated by a simple example.
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