Abstract
The characters of oscillations induced in a nonlinear vibratory system whose natural frequencies are not in the ratios of prime integers and yet satisfy the condition of internal resonance, are discussed via a typical example. The example taken up here is a three-degree-of-freedom system whose linearized natural frequencies pi (i=1, 2, 3; p1 < p2 < p3) satisfy the condition p1 + p2 = p3 of 2p1 + p2 = p3, and which is subjected to harmonic excitation. The characters of oscillations induced in the system near primary as well as secondary resonance points are examined. For analysis the harmonic balance method is employed. The analysis reveals that near some of the resonance points the internal resonance occurs accompanied with three harmonics with their frequencies satisfying a certain relation. With three harmonics with their frequencies satisfying a certain relation. Also it is shown that an almost periodic motion can occur. The validity of the obtained results is confirmed by direct numerical integration.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
