A new combined asymptotic-tolerance model of vibrations of thin transversally graded plates

In this contribution a new model describing vibrations of thin plates with a functionally graded macrostructure and a tolerance-periodic microstructure in planes parallel to the plate midplane is proposed. This model is based on the Kirchhoff plate theory assumptions and additional hypothesis of the tolerance averaging technique [Woźniak Cz, Michalak, Jędrysiak, editors. Thermomechanics of heterogeneous solids and structures. Tolerance averaging approach. Łódź: University Press, Technical University of Łódź; 2008]. It takes into account the effect of the microstructure size on dynamic behavior of the plate and makes it possible to investigate macro- and micro-vibrations of the plate. Here, as an example free vibration frequencies of a functionally graded simply supported plate band are considered. These frequencies are obtained in the framework of three models – the tolerance model, the asymptotic model and the combined asymptotic-tolerance model, using the known Ritz method.