Response and stability analysis of piecewise-linear oscillators under multi-forcing frequencies

✍ Scribed by Sang-Kyu Choi; Sherif T. Noah

• Book ID: 104628331
• Publisher: Springer Netherlands
• Year: 1992
• Tongue: English
• Weight: 772 KB
• Volume: 3
• Category: Article
• ISSN: 0924-090X
• DOI: 10.1007/bf00118988

✦ Synopsis

Steady-state solutions of a piecewise-linear oscillator under multi-forcing frequencies are obtained using the fixed point algorithm (FPA). Stability analysis is also performed using the same technique. For the periodic solutions of a piecewiseqinear oscillator with single forcing frequency, the harmonic balance method (HBM) is also used along with the FPA. Although both FPA and HBM generate accurate solutions, it is observed that the HBM failed to converge to solutions in the superharmonic range of the forcing frequency.

The fixed point algorithm was also applied to the oscillator under multifrequency excitation. The algorithm proved to be very effective in obtaining torus solutions and in ~ocating corresponding bifurcation thresholds. A piecewise-tinear oscillator model of an offshore articulated loading platform (ALP) subjected to two incommensurate wave frequencies is found to exhibit chaotic behavior. A second order Poincard mapping technique reveals the hidden fractal-like nature of the resulting chaotic response. A parametric stud)' is performed for the response of the ALP.