Nonlinear vibrations of a solid body installed on viscous-elastic vibrating supports

In this paper, the nonlinear vibrations of a rigid body mounted on viscoelastic vibrating supports have been studied. The equations of motion of the system were expressed through the Lagrange equations of the second kind for a system with elastic supports by replacing the support stiffnesses with Boltzmann — Volterra integral operators; this way made it possible to obtain a system of nonlinear integro-differential ordinary differential equations. A periodic solution of the resulting system of integro-differential equations was sought in the form of infinite series. Numerical results for the Rzhanitsyn — Koltunov relaxation kernel were obtained. The amplitude-frequency characteristics of the center of mass of the rigid body with two degrees of freedom were constructed.