Periodic and chaotic responses of an sdf system with piecewise linear stiffness subjected to combined harmonic and flow induced excitations

The response of a single-degree-of-freedom (sdf) vibrating system with unsymmetrical piecewise linear stiffness subjected to combined harmonic and flow induced excitations is investigated. Motion limiting stops, different tension and compression behavior, etc., may introduce an unsymmetrical piecewise linear stiffness characteristic. A multi-harmonic balance cum Newton-Raphson procedure in conjunction with an FFT algorithm is adopted to determine the stable and unstable periodic solutions. The stability of the periodic solutions is investigated by using Floquet theory. Digital simulation results reveal periodic, quasi-periodic and chaotic motions of the system in a range of flow velocities. Mode locked oscillations with period 5 motions are found to occur in certain range of flow velocities. Bifurcation diagrams and Lyapunov exponents are also presented. © 1995 by Academic Press, Inc.