Tolerance modelling of vibrations of periodic three-layered plates with inert core

In this note a free vibration analysis of periodic three-layered sandwich structures is performed. Basing on the Kirchhoff’s thin plate theory simplified equations of motion are derived, which are characterised by highly-oscillating, periodic and non-continuous coefficients. In order to obtain a system of equations with constant coefficients, the tolerance averaging technique is used. An application of the proposed tolerance model to analyse free vibration frequencies of a three-layered plate strip is shown – for both lower order frequencies related to its macrostructure and higher order frequencies related to its microstructure. Some comparisons of results of lower frequencies, obtained in the tolerance, the asymptotic and the known homogenised models are presented. Moreover, a certain verification of the proposed model is performed using the Ritz method. It can be observed that the tolerance model can be successfully applied to analyse vibration problems of vast variety of periodic three-layered plates and can significantly improve the optimisation process of such structures.