GLOBAL BEHAVIOR OF A BIASED NON-LINEAR OSCILLATOR UNDER EXTERNAL AND PARAMETRIC EXCITATIONS

✍ Scribed by N.E. Sanchez; A.H. Nayfeh

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 206 KB
• Volume: 207
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1997.0995

✦ Synopsis

In this work we expand our research on the global behavior of non-linear oscillators under external and parametric excitations. We consider a non-linear oscillator simultaneously excited by parametric and external functions. The oscillator has a bias parameter that breaks the symmetry of the motion. The example that we use to illustrate the problem is the rolling oscillation of a biased ship in longitudinal waves, but many mechanical systems display similar features. The global behavior of the system is characterized by bifurcation diagrams that identify the instabilities that appear when one of the excitations is slowly varied. The locus of these instabilities provides the stability boundaries of the system in a parameter space of physical significance. We found that the dynamics of the system significantly depends on the bias parameter, which confirms previous experimental observations. We also found a very interesting effect, which appears to result from the interaction between the parametric and external responses in a nonlinear manner and causes the primary response to lose stability. All results were obtained through analog simulation of the governing equation.