The tolerance modelling of vibrations of periodic sandwich structures – Comparison of simple modelling approaches

•The vibration analysis of sandwich microheterogeneous plates is performed.•A set of assumptions of a versatile and sufficiently precise model is determined.•The analysed models must be convenient for use for engineers.•The tolerance averaging technique is used within the modelling procedure. In literature one can find many different modelling approaches towards sandwich structures, such as: double-plate system with an elastic core, multi-layered plate, models based on advanced deformation hypothesis, etc. Those models are significantly varying from each other with a set of assumptions made at the beginning of the modelling process. In order to determine the set of assumptions of the simple and sufficiently precise model of the sandwich plate, which would be convenient for engineers, the assumptions made in four basic models of sandwich plates are presented and discussed. Consequently, the initial systems of governing equations for vibration analysis of sandwich structures made of isotropic materials are derived. Additionally, those equations are transformed with the use of the tolerance averaging technique, so as the structures with a periodic microstructure can be also analysed. Eventually, the application of the derived models in the free vibration analysis is presented and used to assess the correctness of the modelling assumptions of every each model.