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Vibrations of thin functionally graded plates with tolerance-periodic microstructure

Kaźmierczak-Sobińska M., Jędrysiak J.

Vibrations in Physical Systems

2014

Vol. 26

99--104

This paper presents a problem of vibrations of thin functionally graded plates. To describe this kind of plates three averaged models are proposed: a tolerance model, an asymptotic model and a combined asymptotictolerance model, cf. [10]. Calculational results obtained for a functionally graded plate band using the proposed models are compared to each other.

Free vibrations of thin microstructured plates

Jędrysiak J., Pazera E.

Vibrations in Physical Systems

2014

Vol. 26

93--98

In this paper it is presented a problem of free vibrations of thin microstructured plates, which can be treated as made of functionally graded material on the macrolevel. The size of the microstructure of the plates is of an order of the plate thickness. In order to obtain averaged governing equations of these plates the tolerance modelling technique is applied, cf. [14, 15, 7]. The derived tolerance model equations have the terms dependent of the microstructure size. Hence, the tolerance model describes the effect of the microstructure size. In order to evaluate results, the asymptotic model is introduced. Obtained results can be compared to those calculated by using the finite element method.

Asymptotic-tolerance modelling on vibrations of functionally graded thin plates

Kaźmierczak M., Jędrysiak J.

Vibrations in Physical Systems

2012

Vol. 25

217--222

In this note there are considered functionally graded plates. To describe vibrations of these plates and take into account the effect of the microstructure, the tolerance averaging method is applied, cf. [7, 8]. There are formulated governing equations of the asymptotic-tolerance model, cf. [8]. Calculational results obtained for a functionally graded plate band using the proposed model, are compared to results by the known – tolerance and asymptotic models.