Dynamic Behavior of a Beam Resting on a Viscoelastic Two-Parameter Base and Carrying a Moving Load

We consider the dynamic behavior of a beam with a moving load resting on a deformable base and characterized by two bed coefficients with allowance for dissipative losses. A self-consistent boundary-value problem has been formulated which correctly takes into account the interaction forces in a moving contact. The features of the bending-wave generation by a zero-frequency oscillation source are studied. The critical velocities of the source motion are determined. In the case of low viscosity, the critical velocities do not depend on dissipative losses in the base and are determined by the physical and mechanical properties of the beam and the bed coefficients. An expression for the force due to the wave pressure (the force of resistance to motion) is obtained. The dependence of the constant component of this force on the object velocity and elastic and viscous parameters of the base is studied. The calculation of the energy consumption of the source, which ensures the object motion at a constant velocity, is carried out. When the load moves at a velocity not exceeding the minimum phase velocity of the bending-wave propagation in the beam, the motion-resistance force and the energy consumption are zero and differ from zero in the presence of dissipative losses in the deformable base. A comparison with the results obtained for the one-parameter elastic base of the Fuss-Winkler model is given.