A note on the periodic and chaotic responses of an SDOF system with piecewise linear stiffness subjected to combined harmonic- and flow-induced excitations

In this note, the periodic and chaotic responses of two single-degree-of-freedom (SDOF) models are investigated and some interesting results obtained. The first model (original model) has been developed by Narayanan and Sekar [Periodic and chaotic responses of an SDOF system with piecewise linear stiffness subjected to combined harmonic and flow induced excitations, Journal of Sound and Vibration 184 (2) (1997) 281–298] and the second one corresponds to a modified system. The original model, involving a one-sided clearance (y0) between the mass and the linear spring, is subjected to combined harmonic (F cos ωt) and flow-induced excitations. Narayanan and Sekar (1997) has shown that periodic, quasi-periodic and chaotic motions of this original model may occur in a range of flow velocities for the case: y0=0 and F≠0. In the present work, numerical calculations are carried out for several other important cases of the original system, showing some interesting, and sometimes unexpected results. The modified model, in particular, involving both-sided clearances, is analyzed numerically subsequently. The effect of flow velocity, clearances on the global dynamics of this modified system is discussed finally.