Investigation of Nonlinear Forced Vibrations of the “Rotor-Movable Foundation” System on Rolling Bearings by the Jacobi Elliptic Functions Method
Kydyrbekuly A. Zhauyt A. Ibrayev G.-G.A.
July 2022MDPI
Applied Sciences (Switzerland)
2022#12Issue 14
The paper considers a rotor system with a nonlinear characteristic. Its equations of motion are a kind of Duffing class equations with multiple degrees of freedom. The paper shows the advantage of using the method of elliptic functions for solving problems of this type. This method enables us to take into account not only vibrations of the rotor installed in elastic nonlinear supports, but also vibrations of the foundation. A comparative analysis of application of the method of elliptic functions proposed by the authors is carried out by comparing the derived equations of motion of the system, as well as by comparing the obtained amplitude-frequency characteristics with the results obtained by the numerical Runge–Kutta–Fehlberg’s 4-order method and the approximate analytical Van der Pol method. The regions of resonant frequencies for superharmonic oscillations and bifurcation regimes are determined. It is concluded that the method proposed by the authors is a more accurate and general case than the previously used approximate methods.
duffing equation , elliptic functions , nonlinear dynamics of rotor systems , steady-state forced oscillations
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Department of Mechanics, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Department of Electronics and Robotics, Almaty University of Power Engineering and Telecommunications, Almaty, 050013, Kazakhstan
Department of Mechanics
Department of Electronics and Robotics
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