Isolated sub-harmonic resonance branch in the frequency response of an oscillator with slight asymmetry in the clearance

A family of isolated sub-harmonic branches in nonlinear frequency response of piecewise linear system is examined in this paper. Given their peculiarity, they could be easily overlooked in frequency response studies in numerical integration or laboratory experiments when the quasi-static frequency sweeping technique is employed. An increase in the viscous damping ratio could shrink the isolated branches and ultimately the sub-harmonic resonance may vanish. Asymmetry does not appear to be the key factor that generates the isolated branches. Rather, the relationship between the linear mean operating and transition point seems to dictate their occurrence.