Soil foundation effect on the vibration response of concrete foundations using mathematical model

In this paper, vibration analysis of concrete foundations resting on soil medium is studied. The soil medium is simulated by Winkler model considering spring element. The concrete foundation is modeled by thick plate elements based on classical plate theory (CPT). Utilizing energy method consists of potential energy, kinetic energy and external works in conjunction with Hamilton\'s principle, the motion equations are derived. Assuming the simply supported boundary condition for the concrete foundation, the Navier method is used for calculating the frequency of the structure. The effect of different parameters such as soil medium, mode numbers, length to width ratio and length to thickness ratio of the concrete foundation are shown on the frequency of the structure. At the first, the results are validated with other published works in order to show the accuracy of the obtained results. The results show that considering the soil medium, the frequency of the structure increases significantly.