To study frictional vibration problems in areo-engine

piecewise expression of frictional force in symmetric stick-slip motion was presented.Analytical series solution of symmetric stick-slip motion with even stops was derived by using harmonic balance method.Stick-slip boundary function in parameter plane was derived based on the series solution.Stick-slip response contained only odd harmonic components and super-harmonic resonances existed at odd fractional frequency ratios.When frequency ratio was less than 0.4

the stick-slip boundary curve had the feature of concave-convex alternation and its local minimums located at the super-harmonic resonant frequencies.Increase in viscous damping reduced the non-sticking parameter range at most frequency ratio ranges except near super-harmonic resonant frequencies

where larger viscous damping led to larger non-sticking parameter range.