On the periodic response of a harmonically excited dry friction oscillator

A harmonically excited dry friction oscillator is examined analytically and numerically. We search for 2 π / Ω -periodic non-sticking solutions, where Ω is the excitation frequency. Using the assumption that there are only two turnarounds during each cycle, we prove that the motion is symmetric in space and time at almost all the values of Ω . We also show that the parameter domain of non-sticking symmetric solutions is smaller than it was published in earlier contributions. The analytical results are confirmed by numerical simulation. We point out that a strange beating phenomenon may cause quite large numerical errors close to resonance.