The interplay between multiscale homogenization and dimension reduction for nonlinear elastic thin plates is analyzed in the case in which the scaling of the energy corresponds to Kirchhoff’s nonlinear bending theory for plates. Different limit models are deduced depending on the relative ratio between the thickness parameter h and the two homogenization scales ε and ε.

The aim of this document is to summarise the information on elastic material properties, and wave propagation which I have found in my recent reading. The books and papers read are listed at the end of this document, and cited throughout. First, the basic consititutive equations governing elastic solids are presented. Once the concept of elastic properties has been established, our attention tu...

In this paper, free vibration analysis of a polymer-based nano-composite beam reinforced by boron-nitride nanotubes and subjected on elastic foundation, is studied. Smooth and defect-free nanotubes with uniform and directly- orientated in matrix are intended. Also, nanotubes’ distribution in the thickness direction of beam is regarded as a uniform distribution of the three different targeted on...