Abstract
Self-oscillatory solutions of dynamic equations of transverse vibrations of a distributed rotating ideally balanced rotor (shaft) on an isotropic support made of a material with nonlinear hereditary properties are studied. The derivation of dynamic equations (mathematical model), which are a system of two nonlinear partial differential equations with an infinite (integral) delay of the time argument, is given. A mathematical formulation of the initial–boundary value problem is formulated, its solvability and correctness are proven. The stability of the zero solution (stable rotation), the mechanisms of loss of stability, and the self-oscillatory solutions bifurcating in this case are studied. The possibility of bifurcation of periodic solutions (direct asynchronous precessions) and invariant two-dimensional tori (beat modes) is shown. The stability of self-oscillating solutions is determined by the parameters of the problem under consideration. The method of central manifolds of distributed systems and the theory of bifurcations were used as a research method. Asymptotic formulas are constructed for self-oscillating solutions.
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: Partial Differential Equations in Applied Mathematics
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.