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Free vibrations of microstructured functionally graded plate band with clamped edges

Kaźmierczak-Sobińska Magda, Jędrysiak Jarosław

Vibrations in Physical Systems

2021

Vol. 32, nr 2

art. no. 2021216

In this paper there are presented free vibrations of thin functionally graded plate band. This kind of plates has tolerance-periodic microstructure on the microlevel in planes parallel to the plate midplane. Dynamic problems of plates of this kind are described by partial differential equations with highly oscillating, tolerance-periodic, non-continuous coefficients. Thus, there are proposed here two models describing these plates by equations with smooth, slowly-varying coefficients. As an example there are analyses of free vibration frequencies for thin functionally graded plate band clamped on both edges. Using the known Ritz method the frequencies are obtained in the framework of proposed two models - the tolerance model and the asymptotic model.

On free vibrations of thin functionally graded plate bands resting on an elastic foundation

Jędrysiak J., Kaźmierczak-Sobińska M.

Journal of Theoretical and Applied Mechanics

2015

Vol. 53 nr 3

629--642

In this note free vibrations of plate bands with functionally graded properties, resting on an elastic foundation, are investigated. On the micro-level, these plate bands have a tolerance- -periodic structure. It can be shown that in dynamic problems of those objects, the effect of the microstructure size plays a role. This effect can be described in the framework of the tolerance model, which is presented here for these bands. Obtained results are evaluated introducing the asymptotic model. Both fundamental and higher free vibration frequencies of these plate bands are calculated using the Ritz method. The effects of differences of material plate properties in the cell on the microlevel and of the foundation are shown.