Extended Modal Reduction for On-Board Rotor With Multifrequency Parametric Excitation

Abstract

A new reduction method is proposed to investigate the behavior stability of rotor-bearing systems subject to a multifrequency rotational motion of their base. Combining the modal analysis and the construction of specific dynamic Ritz vectors, this method is able to deal with complex rotordynamics characteristics such as nonproportional damping, nonself-adjoint matrices, or time-varying parametric coefficients. This paper focuses first on assessing the accuracy and efficiency of the reduction method by computing time history and spectral responses of full and reduced models due to multifrequency base excitations. Its main potential is then highlighted in the parametric stability analysis through Floquet theory. The proposed numerical examples are composed with academic and industrial rotors, both modeled with one-dimensional Timoshenko beam finite element and supported by hydrodynamic journal bearings.

Theoretical Study on the Nonlinear Dynamic Response of Propulsion Shafting under Time-Varying Hull Motion

“…The effects of the coupling of base motion and rotor nonlinear variables on system dynamics have attracted the attention of academics. In addition to shaft breathing cracks and rotor/stator frictional shocks, the interaction between the base movement and nonlinear support forces, such as Duffing-type support forces [4,5], angular contact ball bearings [6], and hydrodynamic journal bearing forces [7,8], has been taken into account. Han et al [9] looked at how pendula motion affected the nonlinear dynamical behaviour of the rotor bearing system using the theory of short bearings in a non -inertial reference system.…”

Vibration Properties of Dual-Rotor Systems under Base Excitation, Mass Unbalance and Gravity

“…For the latter task, the application of the finite element method made the model more realistic [4,5] compared with the Jeffcott rotor [6][7][8][9][10][11], a rigid disk with only four degrees of freedom [12][13][14][15][16][17][18][19], and the rigid disk in the Rayleigh-Ritz method for the shaft [20][21][22][23]. Especially compared with the Euler-Bernoulli beam element [24][25][26][27][28][29], the Timoshenko beam element [4,5,12,13,[30][31][32][33][34][35][36][37] took the 2 of 19 shear deformation of the shaft into account. Therefore, it was used to improve the model established by the author in [1].…”

“…The periodic base motions are attracting more and more attention from scholars in recent years. The singular or combined effects of constant base rotation, harmonic base translation and harmonic base rotation are discussed in detail in [4,5,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. The specific stability problem induced by the nonlinearity from time-varying base rotations is a major topic of investigation [20][21][22]25,27,32,33].…”

“…The singular or combined effects of constant base rotation, harmonic base translation and harmonic base rotation are discussed in detail in [4,5,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. The specific stability problem induced by the nonlinearity from time-varying base rotations is a major topic of investigation [20][21][22]25,27,32,33]. In addition, some scholars [2,3,28,29] are devoted to minimizing the vibration induced by base motions by using an active control method or magnetic bearings.…”