Journal of Theoretical
and Applied Mechanics

41, 2, pp. 305-321, Warsaw 2003

On dynamic stability of an uniperiodic medium thickness plate band

Eugeniusz Baron
The aim of this contribution is to apply equations derived by Baron (2002) to the analysis of the dynamic stability of a periodically ribbed simply supported plate band. The general equation of motion for the plate band subjected to the time-dependent axial force was obtained. The considerations are related to the dynamic analysis for arbitrary boundary conditions. The obtained frequency equation can be treated as a certain generalization of the known Mathieu equation. By applying the procedure used for investigation of the Mathieu equation, two fundamental regions of the dynamic instability are determined. The obtained results are similar to those derived from known solutions, but also depend on the period l. We also deal with a new higher free vibration frequency.
Keywords: modelling; dynamic stability; medium thickness plate; periodic structure