Стационарные волны в нелинейно-упругой системе, взаимодействующей с движущейся нагрузкой

Stationary waves excited by a uniformly moving constant load in a string on a nonlinear visco-elastic foundation are investigated. An analysis is performed in a phase plane. It is shown that the case of the “stiff” nonlinearity is not qualitatively different from the linear case. The case of the “soft” nonlinearity has the following peculiarities: (1) if the velocity of the load does not exceed that of waves in the string, then stationary string deflection caused by the load is a discontinuous function of the load magnitude; (2) if the velocity of the load exceeds the velocity of waves, then there always exists a load magnitude starting from which the string deflection in the steady-state regime becomes unlimited.