EXTERNAL PRIMARY RESONANCE OF SELF-EXCITED OSCILLATORS WITH 1:3 INTERNAL RESONANCE

✍ Scribed by S. Natsiavas; P. Metallidis

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 299 KB
• Volume: 208
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1997.1145

✦ Synopsis

The forced response of a class of weakly non-linear oscillators with self-excited characteristics is investigated. The non-linearity is symmetric, the external forcing is harmonic and the essential dynamics are described by a two-degree-of-freedom oscillator, whose linear natural frequencies satisfy conditions of 1:3 internal resonance. Firstly, sets of equations governing the slow time variation of the amplitudes and phases of approximate solutions of the equations of motion are obtained by applying an asymptotic analytical method. For primary resonance of the first mode, only mixed-mode response is possible, since the second mode is always activated through the non-linearities. On the other hand, when conditions of primary resonance of the second mode are met, single-mode response is also possible. In both cases, a methodology is developed which reduces the determination of constant solutions of the slow-flow equations to the solution of two coupled polynomial equations. The stability analysis of these solutions is also provided. Next, numerical results are presented for an example practical system, in the form of response diagrams. These results show the effect of some system parameters on the existence and interaction of various branches of constant solutions. Then, more numerical results are presented, obtained by direct integration of the slow-flow equations in forcing frequency ranges where these equations possess no stable constant solution. The results demonstrate the existence of periodic and chaotic solutions of these equations.