Tolerance modelling of free vibration frequencies of thin functionally graded plates with one-directional microstructure

A tolerance modelling approach for problems of periodic media and structures is adopted here to investigate free vibrations of thin functionally graded plates with a microstructure along one direction in the planes parallel to the plate midplane. The size of the microstructure is assumed to be of an order of the plate thickness. To show the effect of the microstructure on dynamic behaviour of these plates the tolerance modelling method is used, cf. Jędrysiak (2013). This method leads to model equations with smooth functional coefficients, which describe the effect of the microstructure size of these plates not only in dynamic but also in stationary problems. In order to take into account this effect two models - the asymptotic-tolerance model and the tolerance model are used. As an example of applications of these models free vibration frequencies for simply supported rectangular plate are calculated. A certain verification for some cases is also shown by using the finite element method.