Agglomerated SiO2 nanoparticles reinforced-concrete foundations based on higher order shear deformation theory: Vibration analysis

In this study, vibration analysis of a concrete foundation-reinforced by SiO2 nanoparticles resting on soil bed is investigated. The soil medium is simulated with spring constants. Furthermore, the Mori-Tanaka low is used for obtaining the material properties of nano-composite structure and considering agglomeration effects. Using third order shear deformation theory or Reddy theory, the total potential energy of system is calculated and by means of the Hamilton's principle, the coupled motion equations are obtained. Also, based an analytical method, the frequency of system is calculated. The effects of volume percent and agglomeration of SiO2 nanoparticles, soil medium and geometrical parameters of structure are shown on the frequency of system. Results show that with increasing the volume percent of SiO2 nanoparticles, the frequency of structure is increased.