The article is devoted to the study of the oscillatory motion of an elastic structure with variable sections on rolling bearings with straightened surfaces, which simulates a number of technical solutions, which has received its practical embodiment in the problem of ensuring the seismic resistance of building structures and vibration isolation of massive bodies. Equations of motion of an elastic structure with variable sections on rolling bearings bounded by high-order surfaces of revolution are obtained. The resonant modes of parametric vibrational motion of an elastic structure with variable sections are investigated using the Ritz variational method.

      In the resonant zone of the oscillatory movements of the base, the movement of the elastic structure will be small, and when the natural frequencies of the elastic structure coincide with the frequency of the disturbance, the phenomenon of resonance will appear.

    The amplitude of the parametric disturbance of the resonant zones of bending vibrations of elastic structures expands with increasing

    The amplitude-frequency characteristics of parametric oscillations depend on the parameters of the structure. An increase in the parameters of the base of wedge-shaped elastic structures leads to a shift of the resonance curves towards an increase in the disturbance frequencies