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Tolerance modelling of nonstationary problems of microheterogeneous media and structures

Jędrysiak J., Domagalski Ł., Marczak J., Pazera E.

Vibrations in Physical Systems

2018

Vol. 29

art. no. 2018001

In this note a certain review of applications of a non-asymptotic modelling approach, called the tolerance modelling, is presented. Some objects and thermomechanical problems are shown, with a general outline of this method and an example of application for nonlinear vibrations of periodic beams.

Vibrations of periodic sandwich plates with inert core

Marczak J., Jędrysiak J.

Vibrations in Physical Systems

2016

Vol. 27

265--272

In this note a free vibration analysis of periodic three-layered sandwich structures is performed. The equations of motion of such structures, which are derived basing on Kirchhoff's thin plate theory, contain periodic, non-continuous and highly oscillating coefficients, which makes them difficult to solve. In this work, the tolerance averaging technique is applied in order to transform the mentioned system of equations into a form with constant coefficients, which takes into account the effect of the microstructure size. The differences between two modelling procedures are shown and discussed. Eventually, formulas for free vibration frequencies of an exemplary 2D structure are derived and an analysis of influence of certain varying material properties is performed.