NONLINEAR ANALYSIS OF RESONANCE BETWEEN THE BLADE AND ROTOR BY THE BIFURCATION EQUATION AND NUMERICAL METHOD

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NAJAFI ASGHAR; GHAZAVI MOHAMMAD REZA; JAFARI ALI ASGHAR

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Journal: Modares Mechanical Engineering Year:2015 | Volume:14 | Issue:12 Page(s): 43-51

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Title

NONLINEAR ANALYSIS OF RESONANCE BETWEEN THE BLADE AND ROTOR BY THE BIFURCATION EQUATION AND NUMERICAL METHOD

Author(s)

NAJAFI ASGHAR | GHAZAVI MOHAMMAD REZA | JAFARI ALI ASGHAR | Issue Writer Certificate

Keywords

HAMILTONIAN HOPF BIFURCATIONQ2

CONICAL WHIRLINGQ2

CYLINDRICAL WHIRLINGQ2

BLADED ROTORQ3

BIFURCATION EQUATIONQ2

Abstract

Asshown inthe previous studies, blades can cause resonance in BLADED ROTORs under some specific conditions. In this paper, the nonlinear behavior of a rotor, which faces with this kind of resonance, is investigated. In order to reach this goal, a model of BLADED ROTOR, in which the disk and shaft are rigid, is considered. The blades are modeled by flexible beams. It is assumed that both ends of the shaftare supported by elastic and nonlinear bearings. The nonlinear term of the bearing stiffness functionis cubic. The rotor vibrations include both cylindrical and CONICAL WHIRLING. The BIFURCATION EQUATION on the stability boundary is obtained by the method of multiple time scales. The nonlinear effects are studied by this equation. It is revealed that the system behavior, when it encounters HAMILTONIAN HOPF BIFURCATION, is dependent on the bearing stiffness nonlinearity type. Accordingly, both subcritical and supercritical Hopf bifurcationsare possible. Eventually, a numerical simulation is performed in order to study the effects of damping coefficients on the trajectory of rotating disk center. The results and methods, which are used in this paper, can be used for studying HAMILTONIAN HOPF BIFURCATION in other fields.

Cites

FREE VIBRATION OF MICRO ROTATING EULER-BERNOULLI BEAMS BASED ON THE STRAIN GRADIENT THEORY

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APA: Copy

NAJAFI, ASGHAR, GHAZAVI, MOHAMMAD REZA, & JAFARI, ALI ASGHAR. (2015). NONLINEAR ANALYSIS OF RESONANCE BETWEEN THE BLADE AND ROTOR BY THE BIFURCATION EQUATION AND NUMERICAL METHOD. MODARES MECHANICAL ENGINEERING, 14(12), 43-51. SID. https://sid.ir/paper/177679/en

Vancouver: Copy

NAJAFI ASGHAR, GHAZAVI MOHAMMAD REZA, JAFARI ALI ASGHAR. NONLINEAR ANALYSIS OF RESONANCE BETWEEN THE BLADE AND ROTOR BY THE BIFURCATION EQUATION AND NUMERICAL METHOD. MODARES MECHANICAL ENGINEERING[Internet]. 2015;14(12):43-51. Available from: https://sid.ir/paper/177679/en

IEEE: Copy

ASGHAR NAJAFI, MOHAMMAD REZA GHAZAVI, and ALI ASGHAR JAFARI, “NONLINEAR ANALYSIS OF RESONANCE BETWEEN THE BLADE AND ROTOR BY THE BIFURCATION EQUATION AND NUMERICAL METHOD,” MODARES MECHANICAL ENGINEERING, vol. 14, no. 12, pp. 43–51, 2015, [Online]. Available: https://sid.ir/paper/177679/en

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