The tolerance averaging model of dynamic stability of thin plates with one-directional periodic structure

A dynamic stability of thin plates with one-directional periodic structure is investigated. An averaged non-asymptotic approach, called the tolerance averaging, is applied to derive governing equations of these plates. Obtained tolerance model equations of the Kirchhoff-type plate take into account the effect of the period lengths on the overall plate behaviour [Jędrysiak J. Dispersive models of thin periodic plates. Theory and applications. Sci. Bul. Łódź Tech. Univ., No. 872, series. Sci Trans 289, Łódź, 2001 [in Polish]]. It is shown that this effect plays a crucial role in some special cases of a dynamic stability of such plates.