Modelling of dynamic behaviour of microstructured thin functionally graded plates

• Vibrations of thin microstructured functionally graded plates are considered.
• The tolerance modelling method is applied.
• Model equations are differential equations with smooth, slowly-varying coefficients.
• Free vibration frequencies of functionally graded plate bands are analysed.
• The effect of various distribution functions of plate properties is shown.

Functionally graded plates with a special microstructure are considered. It is assumed that the size of the microstructure is of an order of the plate thickness. Moreover, these plates have functionally graded macrostructure along only one axis. To take into account the effect of the microstructure on dynamic behaviour of the plates under consideration the tolerance modelling method is applied, [cf. Kaźmierczak, Jędrysiak, Thin-Walled Structures 2011] Using this method there are obtained model equations with smooth functional coefficients involving terms dependent of the microstructure size. As an example free vibration frequencies of a plate band are investigated.