Abstract
The chaos and subharmonic bifurcation of a cantilever beam supported by oblique springs under bilateral asymmetric rigid constraints are investigated in this paper. It is difficult to investigate analytically the chaos and subharmonic bifurcation of the system because the stiffness term of the oblique spring support structure is a transcendental function. Firstly, the stiffness term of the system is fitted by the approximation method, and the homoclinic orbit and its internal orbits of the approximate system are compared with the orbits of the original system. Secondly, the threshold conditions for subharmonic bifurcation and homoclinic chaos are presented by applying the Melnikov method to the non-smooth impacting cantilever beam system. Moreover, the stability of impacting orbits is analyzed by combining characteristic multipliers of smooth manifolds with impact function, and the relationship between subharmonic bifurcation and chaos is investigated. Finally, the effects of damping, excitation frequency, excitation amplitude and impact coefficient of restitution on chaos and subharmonic bifurcation are investigated based on threshold conditions, which further verifies the theoretical analysis.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena
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.