Journal of Theoretical
and Applied Mechanics

54, 3, pp. 945-961, Warsaw 2016
DOI: 10.15632/jtam-pl.54.3.945

Geometrically nonlinear vibrations of thin visco-elastic periodic plates on a foundation with damping: non-asymptotic modelling

Jarosław Jędrysiak
The objects under consideration are thin visco-elastic periodic plates with moderately large deflections. Geometrically nonlinear vibrations of these plates are investigated. In order to take into account the effect of microstructure size on behaviour of these plates a non-asymptotic modelling method is proposed. Using this method, called the tolerance modelling, model equations with constant coefficients involving terms dependent on the microstructure size can be derived. In this paper, only theoretical considerations of the problem of nonlinear vibrations of thin visco-elastic periodic plates resting on a foundation with damping are presented.
Keywords: thin visco-elastic periodic plates, nonlinear vibrations, effect of microstructure size, analytical tolerance modelling