Investigation of the possibility of existence the asymmetrical steady-state nonlinear vibrations of the oscillator with dry friction

Forced vibrations of the oscillator with dry (Coulomb) friction are studied. Earlier the class of asymmetrical decisions describing the steady-state nonlinear vibrations of the oscillator was found. Asymmetry of vibrations is exhibit in distinction of amplitudes in opposite directions. The specified class of decisions is received on the following assumptions: duration of one cycle of vibrations is equal to the period of force exciting vibrations, duration of half-cycles (time of movement in opposite directions) are equal, there are no stops of nonzero duration and change of the movement direction on each of the half-cycles. In this work the question of the possibility of the specified class decisions expansion due to refusal of a condition of equality of half-cycles is investigated. It is shown that there can be only two types of decisions. The first decision is received in an explicit form, however numerical modeling for rather representative set of parameters showed that it doesn't meet a condition of the absence of the movement direction change on each of the half-cycles. For the second type of decisions the transcendental equation determining duration of half-cycles is established.