Nonlinear response and bifurcation analysis of a Duffing type rotor model under sine maneuver load

Abstract This paper focuses on the nonlinear dynamic and bifurcation characteristics of an aircraft rotor system affected by the maneuvering flight of the aircraft. The equations of motion of the system are formulated with the consideration of the nonlinear supports of Duffing type and the sine maneuver load of a proposed maneuvering flight model. By utilizing the multiple scales method to solve the motion equations analytically, the bifurcation equations are obtained. Accordingly, the response and the bifurcation characteristics of the system are analyzed respectively. Basically, the increase of the maneuver load may increase the formant frequency as well as the primary resonance frequencies. Through numerical simulations, four different types of response characteristics of the system during the maneuvering flight are found, which are compared with the theoretical results, and it shows good qualitative agreements between them. Furthermore, the maneuver load can make an apparent effect on the bifurcation. The results in this paper will provide a better understanding for the effect of aircraft maneuvering flight on the dynamics and bifurcations of the rotor system.

[1]  M. Golubitsky,et al.  Singularities and groups in bifurcation theory , 1985 .

[2]  Shin Murakami,et al.  Nonstationary vibration of a rotating shaft with nonlinear spring characteristics during acceleration through a critical speed (A critical speed of a summed-and-differential harmonic oscillation) , 1990 .

[3]  Yeong-Chun Kim,et al.  A finite element transient response analysis method of a rotor-bearing system to base shock excitations using the state-space Newmark scheme and comparisons with experiments , 2006 .

[4]  G. Ferraris,et al.  Dynamic Behavior and Stability of a Rotor Under Base Excitation , 2006 .

[5]  Lei Hou,et al.  Nonlinear vibration phenomenon of an aircraft rub-impact rotor system due to hovering flight , 2014, Commun. Nonlinear Sci. Numer. Simul..

[6]  Claude-Henri Lamarque,et al.  Theoretical and experimental analysis of a base-excited rotor , 2006 .

[7]  Lei Hou,et al.  Analysis of 1/2 sub-harmonic resonance in a maneuvering rotor system , 2014 .

[8]  Richard Markert,et al.  Acceleration of unbalanced flexible rotors through the critical speeds , 1979 .

[9]  Liao Ming-fu,et al.  The Vibration Performance of the Jeffcott Rotor System with SFD in Maneuver Flight , 2003 .

[10]  Asghar Najafi,et al.  Bifurcation and nonlinear analysis of nonconservative interaction between rotor and blade row , 2013 .

[11]  Samuel Doughty.  Response of single degree of freedom mechanisms to base excitation , 2001 .

[12]  Xingmin Ren,et al.  Analysis on the nonlinear response of cracked rotor in hover flight , 2010 .

[13]  Livija Cveticanin.  Analytic approach for the solution of the complex-valued strong non-linear differential equation of Duffing type , 2001 .

[14]  E. J. Gunter,et al.  Influence of Acceleration on the Critical Speed of a Jeffcott Rotor , 1981 .

[15]  G. Genta,et al.  Conditions for noncircular whirling of nonlinear isotropic rotors , 1993, Nonlinear Dynamics.

[16]  C. Pierre,et al.  Non-linear normal forced vibration modes in systems with internal resonance , 2013 .

[17]  Fawzi M.A. El-Saeidy,et al.  Dynamics of a Rigid Rotor Linear/Nonlinear Bearings System Subject to Rotating Unbalance and Base Excitations , 2010 .

[18]  Meng Guang,et al.  Nonlinear dynamics of a cracked rotor in a maneuvering aircraft , 2004 .

[19]  Guang Meng,et al.  Study on the dynamics of a rotor in a maneuvering aircraft , 2003 .

[20]  E. J. Gunter,et al.  Experimental study of the critical speed response, of a jeffcott rotor with acceleration , 1980 .

[21]  Fulei Chu,et al.  Dynamic response of cracked rotor-bearing system under time-dependent base movements , 2013 .