Abstract
The weakly non-linear resonance response of a two-degree-of-freedom shallow arch subjected to simple harmonic excitation is examined in detail for the case of 1:2 internal resonance. The method of averaging is used to yield a set of autonomous equations of the first-order approximations to the response of the system. The averaged equations are then examined to determine their bifurcation behavior. Our analysis indicates that by varying the detuning para- meters from the exact external and internal resonance conditions, the coupled mode response can undergo a Hopf bifurcation to limit cycle motion. It is also shown that the limit cycles quickly undergo period-doubling bifurcation, giving rise to chaos. In order to study the global bifurcation behavior, the Melnikov method is used to determine the analytical results for the critical parameter at which the dynamical system possesses a Smale horseshoe type of chaos.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.