Numerical study for vibration response of concrete beams reinforced by nanoparticles

Vibration of concrete beams reinforced by agglomerated silicon dioxide (SiO2) nanoparticles is studied based on numerical methods. The structure is simulated by Euler-Bernoulli beam model and the Mori-Tanaka model is used for obtaining the effective material properties of the structure. The concrete beam is located in soil medium which is modeled by spring elements. The motion equations are derived based on energy method and Hamilton's principle. Based on exact solution, the frequency of the structure is calculated. The effects of different parameters such as volume percent of SiO2 nanoparticles and agglomeration, soil medium and geometrical para parameters of beam are shown on the frequency of system. The results show that with increasing the volume percent of SiO2 nanoparticles, the frequency increases.