Effect of the influence of rheological beam longitudinal strains on the disc motion state

The paper analyzes the effect that the material of a simple rheological beam has on the dynamics of a moving disc. The hybrid system of the differential equations describing the motion of the system disc–rheological beam consisting of the integro-differential equation of beam longitudinal vibrations and the Lagrange equations of the first kind, defining the motion of the disc, and the equations of nonholonomic constraints following from the difference between the Lagrange coordinates of the disc mass center and the beam point contacting with the disc is composed. The paper considers the mode of the disc steady motion, allowing to integrate the equation of beam vibrations regardless the system of equations describing the motion of the disc. It is identified that when the disc moves at a low speed, and in the mode corresponding to the limit value of the relaxation time it causes physically inadequate strain in the beam. When relaxation time is null there is a steady mode of forced beam vibrations at moderate amplitudes.