Sub-harmonic resonant solutions of a harmonically excited dry friction oscillator

Abstract

Special sub-harmonic solutions of a harmonically forced dry-friction oscillator are analysed. Although the typical non-sticking solutions are stable and symmetric, a continuum of possible asymmetric, marginally stable solutions exist at excitation frequencies = 1/2n. We determine the explicit form of the one-parameter family of these solutions, and give the conditions under which our formulae are valid. The stability of the solutions is examined in the third-order approximation. Finally, our analytical results are checked by numerical simulations.

Two-stop-two-slip motions of a dry friction oscillator

“…In the borderline,    2 2 /(1 ) R for   1/ 2 , n which is the upper limit of pure slip motions with two phases. The conclusion agrees with the result of subharmonic asymmetric motion [11].…”

“…Guo [10] gave a condition of asymmetric pure slip motion. Csernak [11] analyzed the asymmetric motions in detail. However, the two-stop-two-slip (TSTS) motions have not been studied perfectly.…”

Sliding solutions of second‐order differential equations with discontinuous right‐hand side

“…Because , 0 is a regular value of h , and then, the switching set is a regular surface. In some applications, Σ corresponds to zero velocity for the dry‐friction oscillator (e.g., ).…”

“…The switching set is the line x =0 in ( t , x ) plane. In , the authors studied the dry friction oscillator (cf. Figure ) described by where the real parameters F , γ , and ω correspond, respectively, to the intensity of the friction, the amplitude, and frequency of the forcing.…”

Harmonic and subharmonic solutions of the SD oscillator

“…Equation (5) has at least one harmonic solution. Moreover, for any integer m > 1, there is at least one 2mπ -periodic solution(subharmonic solution) for (5).…”