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Content available Vibrations of microstructured beams with axial force
EN
In this contribution there are considered vibrations of microstructured periodic slender beams, with axial force. In order to analyse the effect of the microstructure size of the beams on their vibrations the tolerance modelling method is applied. Using this method there are derived governing equations of two tolerance models - general and standard, base on two various concepts - weakly-slowly-varying functions and slowly-varying functions. These models are applied to obtain formulas of lower order and higher order frequencies with influence of the axial force. To evaluate these results of the modelling the formula of lower order frequencies in the framework of the asymptotic model (neglecting the effect of the microstructure size) is also derived.
EN
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.
3
EN
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.
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