Mathematical modeling of smart nanoparticles-reinforced concrete foundations: Vibration analysis

In this research, vibration and smart control analysis of a concrete foundation reinforced by SiO₂ nanoparticles and covered by piezoelectric layer on soil medium is investigated. The soil medium is simulated with spring constants and the Mori-Tanaka low is used for obtaining the material properties of nano-composite structure and considering agglomeration effects. With considering first order shear deformation theory, the total potential energy of system is calculated and by means of Hamilton.s principle in three displacement directions and electric potential, the six coupled equilibrium equations are obtained. Also, based an analytical method, the frequency of system is calculated. The effects of applied voltage, 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 applying negative voltage, the frequency of structure is increased.