The main characteristics of the building for dynamic calculation are the frequency and forms of natural oscillations. These values are related to the rigidity of the building, the rigidity of the elastic foundation and its mass. To study the effect of the stiffness of the elastic foundation, an equivalent idealized model of free oscillations of a cantilever rod is considered. The calculation takes into account the rigidity of the support. For the considered model, a transcendental equation and its numerical solution is obtained. Solutions for the limiting cases of elastic foundation stiffness are obtained. The obtained results allow us to analyze the effect of the stiffness of the elastic foundation on the frequencies of natural oscillations. It is calculated that with an increase in the stiffness of the elastic foundation, the frequencies of natural oscillations increase. The influence is limited and has an asymptotic character. The rigidity of the elastic foundation can have a significant effect on the natural frequencies of the first five bending forms of natural oscillations and may not be taken into account for higher-order forms.

Keywords: dynamics, natural oscillations, natural frequencies, building, structure, transcendental equation, elastic foundation, elastic support